hol88 →
2.02.19940316dfsg-5 →
armhf → 2023-01-19 18:34:40
sbuild (Debian sbuild) 0.71.0 (24 Aug 2016) on bm-wb-02
+==============================================================================+
| hol88 2.02.19940316dfsg-5 (armhf) Thu, 19 Jan 2023 17:08:50 +0000 |
+==============================================================================+
Package: hol88
Version: 2.02.19940316dfsg-5
Source Version: 2.02.19940316dfsg-5
Distribution: bookworm-staging
Machine Architecture: armhf
Host Architecture: armhf
Build Architecture: armhf
I: NOTICE: Log filtering will replace 'var/lib/schroot/mount/bookworm-staging-armhf-sbuild-2b0bf318-a64c-4702-90d8-a4ecf95f17e4' with '<<CHROOT>>'
+------------------------------------------------------------------------------+
| Update chroot |
+------------------------------------------------------------------------------+
Get:1 http://172.17.4.1/private bookworm-staging InRelease [11.3 kB]
Get:2 http://172.17.4.1/private bookworm-staging/main Sources [13.6 MB]
Get:3 http://172.17.4.1/private bookworm-staging/main armhf Packages [14.4 MB]
Fetched 28.0 MB in 34s (832 kB/s)
Reading package lists...
W: No sandbox user '_apt' on the system, can not drop privileges
W: http://172.17.4.1/private/dists/bookworm-staging/InRelease: Key is stored in legacy trusted.gpg keyring (/etc/apt/trusted.gpg), see the DEPRECATION section in apt-key(8) for details.
+------------------------------------------------------------------------------+
| Fetch source files |
+------------------------------------------------------------------------------+
Check APT
---------
Checking available source versions...
Download source files with APT
------------------------------
Reading package lists...
Need to get 10.5 MB of source archives.
Get:1 http://172.17.4.1/private bookworm-staging/main hol88 2.02.19940316dfsg-5 (dsc) [2257 B]
Get:2 http://172.17.4.1/private bookworm-staging/main hol88 2.02.19940316dfsg-5 (tar) [10.4 MB]
Get:3 http://172.17.4.1/private bookworm-staging/main hol88 2.02.19940316dfsg-5 (diff) [132 kB]
Fetched 10.5 MB in 1s (9978 kB/s)
Download complete and in download only mode
I: NOTICE: Log filtering will replace 'build/hol88-herlqK/hol88-2.02.19940316dfsg' with '<<PKGBUILDDIR>>'
I: NOTICE: Log filtering will replace 'build/hol88-herlqK' with '<<BUILDDIR>>'
+------------------------------------------------------------------------------+
| Install build-essential |
+------------------------------------------------------------------------------+
Setup apt archive
-----------------
Merged Build-Depends: build-essential, fakeroot
Filtered Build-Depends: build-essential, fakeroot
dpkg-deb: building package 'sbuild-build-depends-core-dummy' in '/<<BUILDDIR>>/resolver-sBjFzP/apt_archive/sbuild-build-depends-core-dummy.deb'.
dpkg-scanpackages: warning: Packages in archive but missing from override file:
dpkg-scanpackages: warning: sbuild-build-depends-core-dummy
dpkg-scanpackages: info: Wrote 1 entries to output Packages file.
gpg: keybox '/<<BUILDDIR>>/resolver-sBjFzP/gpg/pubring.kbx' created
gpg: /<<BUILDDIR>>/resolver-sBjFzP/gpg/trustdb.gpg: trustdb created
gpg: key 35506D9A48F77B2E: public key "Sbuild Signer (Sbuild Build Dependency Archive Key) <buildd-tools-devel@lists.alioth.debian.org>" imported
gpg: Total number processed: 1
gpg: imported: 1
gpg: key 35506D9A48F77B2E: "Sbuild Signer (Sbuild Build Dependency Archive Key) <buildd-tools-devel@lists.alioth.debian.org>" not changed
gpg: key 35506D9A48F77B2E: secret key imported
gpg: Total number processed: 1
gpg: unchanged: 1
gpg: secret keys read: 1
gpg: secret keys imported: 1
gpg: using "Sbuild Signer" as default secret key for signing
Ign:1 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ InRelease
Get:2 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Release [957 B]
Get:3 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Release.gpg [370 B]
Get:4 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Sources [349 B]
Get:5 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Packages [432 B]
Fetched 2108 B in 1s (2600 B/s)
Reading package lists...
W: No sandbox user '_apt' on the system, can not drop privileges
Reading package lists...
Install core build dependencies (apt-based resolver)
----------------------------------------------------
Installing build dependencies
Reading package lists...
Building dependency tree...
Reading state information...
The following packages were automatically installed and are no longer required:
krb5-locales libldap-common libpam-cap netbase
Use 'apt autoremove' to remove them.
The following NEW packages will be installed:
sbuild-build-depends-core-dummy
0 upgraded, 1 newly installed, 0 to remove and 68 not upgraded.
Need to get 852 B of archives.
After this operation, 0 B of additional disk space will be used.
Get:1 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ sbuild-build-depends-core-dummy 0.invalid.0 [852 B]
debconf: delaying package configuration, since apt-utils is not installed
Fetched 852 B in 0s (18.8 kB/s)
Selecting previously unselected package sbuild-build-depends-core-dummy.
(Reading database ... 13212 files and directories currently installed.)
Preparing to unpack .../sbuild-build-depends-core-dummy_0.invalid.0_armhf.deb ...
Unpacking sbuild-build-depends-core-dummy (0.invalid.0) ...
Setting up sbuild-build-depends-core-dummy (0.invalid.0) ...
W: No sandbox user '_apt' on the system, can not drop privileges
+------------------------------------------------------------------------------+
| Check architectures |
+------------------------------------------------------------------------------+
Arch check ok (armhf included in any all)
+------------------------------------------------------------------------------+
| Install package build dependencies |
+------------------------------------------------------------------------------+
Setup apt archive
-----------------
Merged Build-Depends: debhelper (>= 9), gcl (>= 2.6.14-1), texlive-latex-base
Filtered Build-Depends: debhelper (>= 9), gcl (>= 2.6.14-1), texlive-latex-base
dpkg-deb: building package 'sbuild-build-depends-hol88-dummy' in '/<<BUILDDIR>>/resolver-sBjFzP/apt_archive/sbuild-build-depends-hol88-dummy.deb'.
dpkg-scanpackages: warning: Packages in archive but missing from override file:
dpkg-scanpackages: warning: sbuild-build-depends-core-dummy sbuild-build-depends-hol88-dummy
dpkg-scanpackages: info: Wrote 2 entries to output Packages file.
gpg: using "Sbuild Signer" as default secret key for signing
Ign:1 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ InRelease
Get:2 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Release [963 B]
Get:3 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Release.gpg [370 B]
Get:4 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Sources [508 B]
Get:5 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ Packages [589 B]
Fetched 2430 B in 1s (2709 B/s)
Reading package lists...
W: No sandbox user '_apt' on the system, can not drop privileges
Reading package lists...
Install hol88 build dependencies (apt-based resolver)
-----------------------------------------------------
Installing build dependencies
Reading package lists...
Building dependency tree...
Reading state information...
The following packages were automatically installed and are no longer required:
krb5-locales libldap-common libpam-cap netbase
Use 'apt autoremove' to remove them.
The following additional packages will be installed:
adwaita-icon-theme at-spi2-common autoconf automake autopoint autotools-dev
bsdextrautils dbus dbus-bin dbus-daemon dbus-session-bus-common
dbus-system-bus-common dbus-user-session dconf-gsettings-backend
dconf-service debhelper dh-autoreconf dh-strip-nondeterminism dmsetup dwz
emacs emacs-bin-common emacs-common emacs-el emacs-gtk emacsen-common file
fontconfig fontconfig-config fonts-dejavu-core fonts-lmodern gcl gettext
gettext-base groff-base gtk-update-icon-cache hicolor-icon-theme
install-info intltool-debian libabsl20220623 libaom3 libapparmor1
libarchive-zip-perl libargon2-1 libasound2 libasound2-data
libatk-bridge2.0-0 libatk1.0-0 libatspi2.0-0 libavahi-client3
libavahi-common-data libavahi-common3 libavif15 libbrotli1 libbsd0
libcairo-gobject2 libcairo2 libcolord2 libcryptsetup12 libcups2 libdatrie1
libdav1d6 libdbus-1-3 libdconf1 libde265-0 libdebhelper-perl libdeflate0
libdevmapper1.02.1 libedit2 libelf1 libepoxy0 libexpat1 libfdisk1
libfile-stripnondeterminism-perl libfontconfig1 libfreetype6 libfribidi0
libgav1-1 libgccjit0 libgd3 libgdk-pixbuf-2.0-0 libgdk-pixbuf2.0-common
libgif7 libglib2.0-0 libgpm2 libgraphite2-3 libgtk-3-0 libgtk-3-common
libharfbuzz0b libheif1 libice6 libicu72 libip4tc2 libjbig0 libjpeg62-turbo
libjson-c5 libkmod2 libkpathsea6 liblcms2-2 liblerc4 libm17n-0 libmagic-mgc
libmagic1 libmd0 libotf1 libpam-systemd libpango-1.0-0 libpangocairo-1.0-0
libpangoft2-1.0-0 libpaper-utils libpaper1 libpipeline1 libpixman-1-0
libpng16-16 libproc2-0 libptexenc1 librav1e0 librsvg2-2 libsm6
libsub-override-perl libsvtav1enc1 libsynctex2 libsystemd-shared libsystemd0
libtcl8.6 libteckit0 libtexlua53-5 libtexluajit2 libthai-data libthai0
libtiff5 libtiff6 libtk8.6 libtool libuchardet0 libudev1 libwayland-client0
libwayland-cursor0 libwayland-egl1 libwebp7 libx11-6 libx11-data libx265-199
libxau6 libxaw7 libxcb-render0 libxcb-shm0 libxcb1 libxcomposite1
libxcursor1 libxdamage1 libxdmcp6 libxext6 libxfixes3 libxft2 libxi6
libxinerama1 libxkbcommon0 libxml2 libxmu6 libxpm4 libxrandr2 libxrender1
libxss1 libxt6 libyuv0 libzzip-0-13 m17n-db m4 man-db po-debconf procps
shared-mime-info systemd systemd-sysv t1utils tex-common texlive-base
texlive-binaries texlive-latex-base ucf x11-common xdg-utils xkb-data
Suggested packages:
autoconf-archive gnu-standards autoconf-doc dh-make emacs-common-non-dfsg
ncurses-term gcl-doc gettext-doc libasprintf-dev libgettextpo-dev groff
libasound2-plugins alsa-utils colord cups-common libgd-tools
low-memory-monitor gpm gvfs liblcms2-utils m17n-docs librsvg2-bin tcl8.6
tk8.6 libtool-doc gfortran | fortran95-compiler gcj-jdk gawk m4-doc apparmor
less www-browser libmail-box-perl systemd-container systemd-homed
systemd-userdbd systemd-boot systemd-resolved libfido2-1 libqrencode4
libtss2-esys-3.0.2-0 libtss2-mu0 libtss2-rc0 polkitd | policykit-1
ghostscript gv | postscript-viewer perl-tk xpdf | pdf-viewer xzdec
texlive-latex-base-doc wp2latex
Recommended packages:
librsvg2-common mailutils fonts-noto-color-emoji curl | wget | lynx
alsa-ucm-conf alsa-topology-conf at-spi2-core libarchive-cpio-perl
libgdk-pixbuf2.0-bin libglib2.0-data xdg-user-dirs libgtk-3-bin libltdl-dev
libmail-sendmail-perl psmisc systemd-timesyncd | time-daemon libnss-systemd
lmodern dvisvgm libfile-mimeinfo-perl libnet-dbus-perl libx11-protocol-perl
x11-utils x11-xserver-utils
The following NEW packages will be installed:
adwaita-icon-theme at-spi2-common autoconf automake autopoint autotools-dev
bsdextrautils dbus dbus-bin dbus-daemon dbus-session-bus-common
dbus-system-bus-common dbus-user-session dconf-gsettings-backend
dconf-service debhelper dh-autoreconf dh-strip-nondeterminism dmsetup dwz
emacs emacs-bin-common emacs-common emacs-el emacs-gtk emacsen-common file
fontconfig fontconfig-config fonts-dejavu-core fonts-lmodern gcl gettext
gettext-base groff-base gtk-update-icon-cache hicolor-icon-theme
install-info intltool-debian libabsl20220623 libaom3 libapparmor1
libarchive-zip-perl libargon2-1 libasound2 libasound2-data
libatk-bridge2.0-0 libatk1.0-0 libatspi2.0-0 libavahi-client3
libavahi-common-data libavahi-common3 libavif15 libbrotli1 libbsd0
libcairo-gobject2 libcairo2 libcolord2 libcryptsetup12 libcups2 libdatrie1
libdav1d6 libdbus-1-3 libdconf1 libde265-0 libdebhelper-perl libdeflate0
libdevmapper1.02.1 libedit2 libelf1 libepoxy0 libexpat1 libfdisk1
libfile-stripnondeterminism-perl libfontconfig1 libfreetype6 libfribidi0
libgav1-1 libgccjit0 libgd3 libgdk-pixbuf-2.0-0 libgdk-pixbuf2.0-common
libgif7 libglib2.0-0 libgpm2 libgraphite2-3 libgtk-3-0 libgtk-3-common
libharfbuzz0b libheif1 libice6 libicu72 libip4tc2 libjbig0 libjpeg62-turbo
libjson-c5 libkmod2 libkpathsea6 liblcms2-2 liblerc4 libm17n-0 libmagic-mgc
libmagic1 libmd0 libotf1 libpam-systemd libpango-1.0-0 libpangocairo-1.0-0
libpangoft2-1.0-0 libpaper-utils libpaper1 libpipeline1 libpixman-1-0
libpng16-16 libproc2-0 libptexenc1 librav1e0 librsvg2-2 libsm6
libsub-override-perl libsvtav1enc1 libsynctex2 libsystemd-shared libtcl8.6
libteckit0 libtexlua53-5 libtexluajit2 libthai-data libthai0 libtiff5
libtiff6 libtk8.6 libtool libuchardet0 libwayland-client0 libwayland-cursor0
libwayland-egl1 libwebp7 libx11-6 libx11-data libx265-199 libxau6 libxaw7
libxcb-render0 libxcb-shm0 libxcb1 libxcomposite1 libxcursor1 libxdamage1
libxdmcp6 libxext6 libxfixes3 libxft2 libxi6 libxinerama1 libxkbcommon0
libxml2 libxmu6 libxpm4 libxrandr2 libxrender1 libxss1 libxt6 libyuv0
libzzip-0-13 m17n-db m4 man-db po-debconf procps
sbuild-build-depends-hol88-dummy shared-mime-info systemd systemd-sysv
t1utils tex-common texlive-base texlive-binaries texlive-latex-base ucf
x11-common xdg-utils xkb-data
The following packages will be upgraded:
libsystemd0 libudev1
2 upgraded, 183 newly installed, 0 to remove and 66 not upgraded.
Need to get 169 MB of archives.
After this operation, 661 MB of additional disk space will be used.
Get:1 copy:/<<BUILDDIR>>/resolver-sBjFzP/apt_archive ./ sbuild-build-depends-hol88-dummy 0.invalid.0 [876 B]
Get:2 http://172.17.4.1/private bookworm-staging/main armhf libargon2-1 armhf 0~20171227-0.3 [19.6 kB]
Get:3 http://172.17.4.1/private bookworm-staging/main armhf libudev1 armhf 252.4-1+rpi1 [98.2 kB]
Get:4 http://172.17.4.1/private bookworm-staging/main armhf dmsetup armhf 2:1.02.185-2 [81.8 kB]
Get:5 http://172.17.4.1/private bookworm-staging/main armhf libdevmapper1.02.1 armhf 2:1.02.185-2 [123 kB]
Get:6 http://172.17.4.1/private bookworm-staging/main armhf libjson-c5 armhf 0.16-2 [40.0 kB]
Get:7 http://172.17.4.1/private bookworm-staging/main armhf libcryptsetup12 armhf 2:2.6.0-2 [190 kB]
Get:8 http://172.17.4.1/private bookworm-staging/main armhf libfdisk1 armhf 2.38.1-4 [179 kB]
Get:9 http://172.17.4.1/private bookworm-staging/main armhf libkmod2 armhf 30+20221128-1 [49.9 kB]
Get:10 http://172.17.4.1/private bookworm-staging/main armhf libapparmor1 armhf 3.0.8-1 [37.0 kB]
Get:11 http://172.17.4.1/private bookworm-staging/main armhf libip4tc2 armhf 1.8.8-1 [32.9 kB]
Get:12 http://172.17.4.1/private bookworm-staging/main armhf libsystemd-shared armhf 252.4-1+rpi1 [1505 kB]
Get:13 http://172.17.4.1/private bookworm-staging/main armhf libsystemd0 armhf 252.4-1+rpi1 [295 kB]
Get:14 http://172.17.4.1/private bookworm-staging/main armhf systemd armhf 252.4-1+rpi1 [2874 kB]
Get:15 http://172.17.4.1/private bookworm-staging/main armhf systemd-sysv armhf 252.4-1+rpi1 [41.0 kB]
Get:16 http://172.17.4.1/private bookworm-staging/main armhf libdbus-1-3 armhf 1.14.4-1 [211 kB]
Get:17 http://172.17.4.1/private bookworm-staging/main armhf dbus-bin armhf 1.14.4-1 [137 kB]
Get:18 http://172.17.4.1/private bookworm-staging/main armhf dbus-session-bus-common all 1.14.4-1 [112 kB]
Get:19 http://172.17.4.1/private bookworm-staging/main armhf libexpat1 armhf 2.5.0-1 [77.2 kB]
Get:20 http://172.17.4.1/private bookworm-staging/main armhf dbus-daemon armhf 1.14.4-1 [204 kB]
Get:21 http://172.17.4.1/private bookworm-staging/main armhf dbus-system-bus-common all 1.14.4-1 [113 kB]
Get:22 http://172.17.4.1/private bookworm-staging/main armhf dbus armhf 1.14.4-1 [129 kB]
Get:23 http://172.17.4.1/private bookworm-staging/main armhf install-info armhf 6.8-6+b1 [161 kB]
Get:24 http://172.17.4.1/private bookworm-staging/main armhf libuchardet0 armhf 0.0.7-1 [65.0 kB]
Get:25 http://172.17.4.1/private bookworm-staging/main armhf groff-base armhf 1.22.4-9 [774 kB]
Get:26 http://172.17.4.1/private bookworm-staging/main armhf bsdextrautils armhf 2.38.1-4 [78.8 kB]
Get:27 http://172.17.4.1/private bookworm-staging/main armhf libpipeline1 armhf 1.5.7-1 [33.4 kB]
Get:28 http://172.17.4.1/private bookworm-staging/main armhf man-db armhf 2.11.2-1 [1342 kB]
Get:29 http://172.17.4.1/private bookworm-staging/main armhf libproc2-0 armhf 2:4.0.2-3 [53.6 kB]
Get:30 http://172.17.4.1/private bookworm-staging/main armhf procps armhf 2:4.0.2-3 [679 kB]
Get:31 http://172.17.4.1/private bookworm-staging/main armhf libmagic-mgc armhf 1:5.41-4 [295 kB]
Get:32 http://172.17.4.1/private bookworm-staging/main armhf libmagic1 armhf 1:5.41-4 [120 kB]
Get:33 http://172.17.4.1/private bookworm-staging/main armhf file armhf 1:5.41-4 [65.8 kB]
Get:34 http://172.17.4.1/private bookworm-staging/main armhf gettext-base armhf 0.21-10 [156 kB]
Get:35 http://172.17.4.1/private bookworm-staging/main armhf libpam-systemd armhf 252.4-1+rpi1 [196 kB]
Get:36 http://172.17.4.1/private bookworm-staging/main armhf ucf all 3.0043 [74.0 kB]
Get:37 http://172.17.4.1/private bookworm-staging/main armhf hicolor-icon-theme all 0.17-2 [11.4 kB]
Get:38 http://172.17.4.1/private bookworm-staging/main armhf libgdk-pixbuf2.0-common all 2.42.10+dfsg-1 [306 kB]
Get:39 http://172.17.4.1/private bookworm-staging/main armhf libglib2.0-0 armhf 2.74.4-1 [1204 kB]
Get:40 http://172.17.4.1/private bookworm-staging/main armhf libicu72 armhf 72.1-3 [9009 kB]
Get:41 http://172.17.4.1/private bookworm-staging/main armhf libxml2 armhf 2.9.14+dfsg-1.1 [570 kB]
Get:42 http://172.17.4.1/private bookworm-staging/main armhf shared-mime-info armhf 2.2-1 [726 kB]
Get:43 http://172.17.4.1/private bookworm-staging/main armhf libjpeg62-turbo armhf 1:2.1.2-1 [144 kB]
Get:44 http://172.17.4.1/private bookworm-staging/main armhf libpng16-16 armhf 1.6.39-2 [258 kB]
Get:45 http://172.17.4.1/private bookworm-staging/main armhf libdeflate0 armhf 1.14-1 [50.9 kB]
Get:46 http://172.17.4.1/private bookworm-staging/main armhf libjbig0 armhf 2.1-6.1 [27.0 kB]
Get:47 http://172.17.4.1/private bookworm-staging/main armhf liblerc4 armhf 4.0.0+ds-2 [133 kB]
Get:48 http://172.17.4.1/private bookworm-staging/main armhf libwebp7 armhf 1.2.2-2+b2 [237 kB]
Get:49 http://172.17.4.1/private bookworm-staging/main armhf libtiff6 armhf 4.5.0-3 [292 kB]
Get:50 http://172.17.4.1/private bookworm-staging/main armhf libgdk-pixbuf-2.0-0 armhf 2.42.10+dfsg-1+b1 [123 kB]
Get:51 http://172.17.4.1/private bookworm-staging/main armhf gtk-update-icon-cache armhf 3.24.36-1 [41.0 kB]
Get:52 http://172.17.4.1/private bookworm-staging/main armhf adwaita-icon-theme all 43-1 [5124 kB]
Get:53 http://172.17.4.1/private bookworm-staging/main armhf at-spi2-common all 2.46.0-4 [161 kB]
Get:54 http://172.17.4.1/private bookworm-staging/main armhf m4 armhf 1.4.19-2 [256 kB]
Get:55 http://172.17.4.1/private bookworm-staging/main armhf autoconf all 2.71-2 [343 kB]
Get:56 http://172.17.4.1/private bookworm-staging/main armhf autotools-dev all 20220109.1 [51.6 kB]
Get:57 http://172.17.4.1/private bookworm-staging/main armhf automake all 1:1.16.5-1.3 [823 kB]
Get:58 http://172.17.4.1/private bookworm-staging/main armhf autopoint all 0.21-10 [495 kB]
Get:59 http://172.17.4.1/private bookworm-staging/main armhf dbus-user-session armhf 1.14.4-1 [112 kB]
Get:60 http://172.17.4.1/private bookworm-staging/main armhf libdconf1 armhf 0.40.0-4 [36.0 kB]
Get:61 http://172.17.4.1/private bookworm-staging/main armhf dconf-service armhf 0.40.0-4 [28.9 kB]
Get:62 http://172.17.4.1/private bookworm-staging/main armhf dconf-gsettings-backend armhf 0.40.0-4 [23.1 kB]
Get:63 http://172.17.4.1/private bookworm-staging/main armhf libdebhelper-perl all 13.11.4 [81.2 kB]
Get:64 http://172.17.4.1/private bookworm-staging/main armhf libtool all 2.4.7-5 [517 kB]
Get:65 http://172.17.4.1/private bookworm-staging/main armhf dh-autoreconf all 20 [17.1 kB]
Get:66 http://172.17.4.1/private bookworm-staging/main armhf libarchive-zip-perl all 1.68-1 [104 kB]
Get:67 http://172.17.4.1/private bookworm-staging/main armhf libsub-override-perl all 0.09-4 [9304 B]
Get:68 http://172.17.4.1/private bookworm-staging/main armhf libfile-stripnondeterminism-perl all 1.13.1-1 [19.4 kB]
Get:69 http://172.17.4.1/private bookworm-staging/main armhf dh-strip-nondeterminism all 1.13.1-1 [8620 B]
Get:70 http://172.17.4.1/private bookworm-staging/main armhf libelf1 armhf 0.187-2+rpi2 [177 kB]
Get:71 http://172.17.4.1/private bookworm-staging/main armhf dwz armhf 0.15-1 [92.4 kB]
Get:72 http://172.17.4.1/private bookworm-staging/main armhf gettext armhf 0.21-10 [1203 kB]
Get:73 http://172.17.4.1/private bookworm-staging/main armhf intltool-debian all 0.35.0+20060710.6 [22.9 kB]
Get:74 http://172.17.4.1/private bookworm-staging/main armhf po-debconf all 1.0.21+nmu1 [248 kB]
Get:75 http://172.17.4.1/private bookworm-staging/main armhf debhelper all 13.11.4 [942 kB]
Get:76 http://172.17.4.1/private bookworm-staging/main armhf emacs-el all 1:28.2+1-9 [16.9 MB]
Get:77 http://172.17.4.1/private bookworm-staging/main armhf emacsen-common all 3.0.5 [12.3 kB]
Get:78 http://172.17.4.1/private bookworm-staging/main armhf emacs-common all 1:28.2+1-9 [14.0 MB]
Get:79 http://172.17.4.1/private bookworm-staging/main armhf emacs-bin-common armhf 1:28.2+1-9 [84.2 kB]
Get:80 http://172.17.4.1/private bookworm-staging/main armhf libasound2-data all 1.2.8-1 [20.5 kB]
Get:81 http://172.17.4.1/private bookworm-staging/main armhf libasound2 armhf 1.2.8-1 [304 kB]
Get:82 http://172.17.4.1/private bookworm-staging/main armhf libbrotli1 armhf 1.0.9-2+b2 [260 kB]
Get:83 http://172.17.4.1/private bookworm-staging/main armhf libfreetype6 armhf 2.12.1+dfsg-4 [329 kB]
Get:84 http://172.17.4.1/private bookworm-staging/main armhf fonts-dejavu-core all 2.37-2 [1069 kB]
Get:85 http://172.17.4.1/private bookworm-staging/main armhf fontconfig-config armhf 2.14.1-3 [315 kB]
Get:86 http://172.17.4.1/private bookworm-staging/main armhf libfontconfig1 armhf 2.14.1-3 [366 kB]
Get:87 http://172.17.4.1/private bookworm-staging/main armhf libpixman-1-0 armhf 0.42.2-1 [461 kB]
Get:88 http://172.17.4.1/private bookworm-staging/main armhf libxau6 armhf 1:1.0.9-1 [19.1 kB]
Get:89 http://172.17.4.1/private bookworm-staging/main armhf libmd0 armhf 1.0.4-2 [28.6 kB]
Get:90 http://172.17.4.1/private bookworm-staging/main armhf libbsd0 armhf 0.11.7-1 [112 kB]
Get:91 http://172.17.4.1/private bookworm-staging/main armhf libxdmcp6 armhf 1:1.1.2-3 [25.0 kB]
Get:92 http://172.17.4.1/private bookworm-staging/main armhf libxcb1 armhf 1.15-1 [139 kB]
Get:93 http://172.17.4.1/private bookworm-staging/main armhf libx11-data all 2:1.8.3-3 [292 kB]
Get:94 http://172.17.4.1/private bookworm-staging/main armhf libx11-6 armhf 2:1.8.3-3 [687 kB]
Get:95 http://172.17.4.1/private bookworm-staging/main armhf libxcb-render0 armhf 1.15-1 [114 kB]
Get:96 http://172.17.4.1/private bookworm-staging/main armhf libxcb-shm0 armhf 1.15-1 [106 kB]
Get:97 http://172.17.4.1/private bookworm-staging/main armhf libxext6 armhf 2:1.3.4-1 [48.0 kB]
Get:98 http://172.17.4.1/private bookworm-staging/main armhf libxrender1 armhf 1:0.9.10-1.1 [30.0 kB]
Get:99 http://172.17.4.1/private bookworm-staging/main armhf libcairo2 armhf 1.16.0-7 [482 kB]
Get:100 http://172.17.4.1/private bookworm-staging/main armhf libgccjit0 armhf 12.2.0-10+rpi1 [6398 kB]
Get:101 http://172.17.4.1/private bookworm-staging/main armhf libgif7 armhf 5.2.1-2.5 [44.7 kB]
Get:102 http://172.17.4.1/private bookworm-staging/main armhf libgpm2 armhf 1.20.7-10+b2 [35.5 kB]
Get:103 http://172.17.4.1/private bookworm-staging/main armhf libatk1.0-0 armhf 2.46.0-4 [41.4 kB]
Get:104 http://172.17.4.1/private bookworm-staging/main armhf libxi6 armhf 2:1.8-1 [78.1 kB]
Get:105 http://172.17.4.1/private bookworm-staging/main armhf libatspi2.0-0 armhf 2.46.0-4 [63.8 kB]
Get:106 http://172.17.4.1/private bookworm-staging/main armhf libatk-bridge2.0-0 armhf 2.46.0-4 [55.4 kB]
Get:107 http://172.17.4.1/private bookworm-staging/main armhf libcairo-gobject2 armhf 1.16.0-7 [111 kB]
Get:108 http://172.17.4.1/private bookworm-staging/main armhf liblcms2-2 armhf 2.14-1+b1 [124 kB]
Get:109 http://172.17.4.1/private bookworm-staging/main armhf libcolord2 armhf 1.4.6-2.1 [117 kB]
Get:110 http://172.17.4.1/private bookworm-staging/main armhf libavahi-common-data armhf 0.8-7 [106 kB]
Get:111 http://172.17.4.1/private bookworm-staging/main armhf libavahi-common3 armhf 0.8-7 [38.2 kB]
Get:112 http://172.17.4.1/private bookworm-staging/main armhf libavahi-client3 armhf 0.8-7 [40.8 kB]
Get:113 http://172.17.4.1/private bookworm-staging/main armhf libcups2 armhf 2.4.2-1+b1 [311 kB]
Get:114 http://172.17.4.1/private bookworm-staging/main armhf libepoxy0 armhf 1.5.10-1 [172 kB]
Get:115 http://172.17.4.1/private bookworm-staging/main armhf libfribidi0 armhf 1.0.8-2.1 [63.7 kB]
Get:116 http://172.17.4.1/private bookworm-staging/main armhf libgraphite2-3 armhf 1.3.14-1 [70.3 kB]
Get:117 http://172.17.4.1/private bookworm-staging/main armhf libharfbuzz0b armhf 6.0.0-1 [1886 kB]
Get:118 http://172.17.4.1/private bookworm-staging/main armhf fontconfig armhf 2.14.1-3 [449 kB]
Get:119 http://172.17.4.1/private bookworm-staging/main armhf libthai-data all 0.1.29-1 [176 kB]
Get:120 http://172.17.4.1/private bookworm-staging/main armhf libdatrie1 armhf 0.2.13-2+b2 [39.9 kB]
Get:121 http://172.17.4.1/private bookworm-staging/main armhf libthai0 armhf 0.1.29-1 [54.5 kB]
Get:122 http://172.17.4.1/private bookworm-staging/main armhf libpango-1.0-0 armhf 1.50.12+ds-1 [186 kB]
Get:123 http://172.17.4.1/private bookworm-staging/main armhf libpangoft2-1.0-0 armhf 1.50.12+ds-1 [40.5 kB]
Get:124 http://172.17.4.1/private bookworm-staging/main armhf libpangocairo-1.0-0 armhf 1.50.12+ds-1 [30.1 kB]
Get:125 http://172.17.4.1/private bookworm-staging/main armhf libwayland-client0 armhf 1.21.0-1 [23.3 kB]
Get:126 http://172.17.4.1/private bookworm-staging/main armhf libwayland-cursor0 armhf 1.21.0-1 [13.2 kB]
Get:127 http://172.17.4.1/private bookworm-staging/main armhf libwayland-egl1 armhf 1.21.0-1 [8448 B]
Get:128 http://172.17.4.1/private bookworm-staging/main armhf libxcomposite1 armhf 1:0.4.5-1 [16.2 kB]
Get:129 http://172.17.4.1/private bookworm-staging/main armhf libxfixes3 armhf 1:6.0.0-2 [21.2 kB]
Get:130 http://172.17.4.1/private bookworm-staging/main armhf libxcursor1 armhf 1:1.2.1-1 [38.0 kB]
Get:131 http://172.17.4.1/private bookworm-staging/main armhf libxdamage1 armhf 1:1.1.6-1 [14.7 kB]
Get:132 http://172.17.4.1/private bookworm-staging/main armhf libxinerama1 armhf 2:1.1.4-3 [17.4 kB]
Get:133 http://172.17.4.1/private bookworm-staging/main armhf xkb-data all 2.35.1-1 [764 kB]
Get:134 http://172.17.4.1/private bookworm-staging/main armhf libxkbcommon0 armhf 1.5.0-1 [93.1 kB]
Get:135 http://172.17.4.1/private bookworm-staging/main armhf libxrandr2 armhf 2:1.5.2-2 [35.5 kB]
Get:136 http://172.17.4.1/private bookworm-staging/main armhf libgtk-3-common all 3.24.36-1 [3877 kB]
Get:137 http://172.17.4.1/private bookworm-staging/main armhf libgtk-3-0 armhf 3.24.36-1 [2352 kB]
Get:138 http://172.17.4.1/private bookworm-staging/main armhf x11-common all 1:7.7+23 [252 kB]
Get:139 http://172.17.4.1/private bookworm-staging/main armhf libice6 armhf 2:1.0.10-1 [51.7 kB]
Get:140 http://172.17.4.1/private bookworm-staging/main armhf m17n-db all 1.8.0-3 [1289 kB]
Get:141 http://172.17.4.1/private bookworm-staging/main armhf libaom3 armhf 3.5.0-1 [1302 kB]
Get:142 http://172.17.4.1/private bookworm-staging/main armhf libdav1d6 armhf 1.0.0-2+rpi1 [205 kB]
Get:143 http://172.17.4.1/private bookworm-staging/main armhf libabsl20220623 armhf 20220623.1-1+rpi1 [361 kB]
Get:144 http://172.17.4.1/private bookworm-staging/main armhf libgav1-1 armhf 0.18.0-1+rpi1+b1 [285 kB]
Get:145 http://172.17.4.1/private bookworm-staging/main armhf librav1e0 armhf 0.5.1-6 [521 kB]
Get:146 http://172.17.4.1/private bookworm-staging/main armhf libsvtav1enc1 armhf 1.4.1+dfsg-1 [880 kB]
Get:147 http://172.17.4.1/private bookworm-staging/main armhf libyuv0 armhf 0.0~git20230104.6e4b0ac-1 [82.2 kB]
Get:148 http://172.17.4.1/private bookworm-staging/main armhf libavif15 armhf 0.11.1-1 [84.1 kB]
Get:149 http://172.17.4.1/private bookworm-staging/main armhf libde265-0 armhf 1.0.9-1+rpi1 [186 kB]
Get:150 http://172.17.4.1/private bookworm-staging/main armhf libx265-199 armhf 3.5-2 [548 kB]
Get:151 http://172.17.4.1/private bookworm-staging/main armhf libheif1 armhf 1.13.0-1 [169 kB]
Get:152 http://172.17.4.1/private bookworm-staging/main armhf libxpm4 armhf 1:3.5.12-1 [43.6 kB]
Get:153 http://172.17.4.1/private bookworm-staging/main armhf libgd3 armhf 2.3.3-7+b1 [102 kB]
Get:154 http://172.17.4.1/private bookworm-staging/main armhf libotf1 armhf 0.9.16-3 [50.4 kB]
Get:155 http://172.17.4.1/private bookworm-staging/main armhf libxft2 armhf 2.3.6-1 [53.7 kB]
Get:156 http://172.17.4.1/private bookworm-staging/main armhf libsm6 armhf 2:1.2.3-1 [32.9 kB]
Get:157 http://172.17.4.1/private bookworm-staging/main armhf libxt6 armhf 1:1.2.1-1 [159 kB]
Get:158 http://172.17.4.1/private bookworm-staging/main armhf libm17n-0 armhf 1.8.0-5 [209 kB]
Get:159 http://172.17.4.1/private bookworm-staging/main armhf librsvg2-2 armhf 2.54.5+dfsg-1 [2217 kB]
Get:160 http://172.17.4.1/private bookworm-staging/main armhf libtiff5 armhf 4.4.0-6 [278 kB]
Get:161 http://172.17.4.1/private bookworm-staging/main armhf emacs-gtk armhf 1:28.2+1-9 [5445 kB]
Get:162 http://172.17.4.1/private bookworm-staging/main armhf emacs all 1:28.2+1-9 [15.7 kB]
Get:163 http://172.17.4.1/private bookworm-staging/main armhf fonts-lmodern all 2.005-1 [4540 kB]
Get:164 http://172.17.4.1/private bookworm-staging/main armhf libedit2 armhf 3.1-20221030-2 [76.2 kB]
Get:165 http://172.17.4.1/private bookworm-staging/main armhf libtcl8.6 armhf 8.6.13+dfsg-1 [906 kB]
Get:166 http://172.17.4.1/private bookworm-staging/main armhf libxss1 armhf 1:1.2.3-1 [17.3 kB]
Get:167 http://172.17.4.1/private bookworm-staging/main armhf libtk8.6 armhf 8.6.13-1 [680 kB]
Get:168 http://172.17.4.1/private bookworm-staging/main armhf gcl armhf 2.6.14-1+rpi1 [27.2 MB]
Get:169 http://172.17.4.1/private bookworm-staging/main armhf libkpathsea6 armhf 2022.20220321.62855-5 [142 kB]
Get:170 http://172.17.4.1/private bookworm-staging/main armhf libpaper1 armhf 1.1.28 [20.5 kB]
Get:171 http://172.17.4.1/private bookworm-staging/main armhf libpaper-utils armhf 1.1.28 [17.7 kB]
Get:172 http://172.17.4.1/private bookworm-staging/main armhf libptexenc1 armhf 2022.20220321.62855-5 [40.1 kB]
Get:173 http://172.17.4.1/private bookworm-staging/main armhf libsynctex2 armhf 2022.20220321.62855-5 [46.3 kB]
Get:174 http://172.17.4.1/private bookworm-staging/main armhf libteckit0 armhf 2.5.11+ds1-1 [256 kB]
Get:175 http://172.17.4.1/private bookworm-staging/main armhf libtexlua53-5 armhf 2022.20220321.62855-5 [81.3 kB]
Get:176 http://172.17.4.1/private bookworm-staging/main armhf libtexluajit2 armhf 2022.20220321.62855-5 [187 kB]
Get:177 http://172.17.4.1/private bookworm-staging/main armhf libxmu6 armhf 2:1.1.3-3 [52.0 kB]
Get:178 http://172.17.4.1/private bookworm-staging/main armhf libxaw7 armhf 2:1.0.14-1 [165 kB]
Get:179 http://172.17.4.1/private bookworm-staging/main armhf libzzip-0-13 armhf 0.13.72+dfsg.1-1.1 [54.3 kB]
Get:180 http://172.17.4.1/private bookworm-staging/main armhf t1utils armhf 1.41-4 [52.3 kB]
Get:181 http://172.17.4.1/private bookworm-staging/main armhf tex-common all 6.18 [32.5 kB]
Get:182 http://172.17.4.1/private bookworm-staging/main armhf texlive-binaries armhf 2022.20220321.62855-5 [7474 kB]
Get:183 http://172.17.4.1/private bookworm-staging/main armhf xdg-utils all 1.1.3-4.1 [75.5 kB]
Get:184 http://172.17.4.1/private bookworm-staging/main armhf texlive-base all 2022.20221123-1 [21.9 MB]
Get:185 http://172.17.4.1/private bookworm-staging/main armhf texlive-latex-base all 2022.20221123-1 [1175 kB]
debconf: delaying package configuration, since apt-utils is not installed
Fetched 169 MB in 15s (11.6 MB/s)
Selecting previously unselected package libargon2-1:armhf.
(Reading database ... 13212 files and directories currently installed.)
Preparing to unpack .../libargon2-1_0~20171227-0.3_armhf.deb ...
Unpacking libargon2-1:armhf (0~20171227-0.3) ...
Preparing to unpack .../libudev1_252.4-1+rpi1_armhf.deb ...
Unpacking libudev1:armhf (252.4-1+rpi1) over (252.2-1+rpi1) ...
Setting up libudev1:armhf (252.4-1+rpi1) ...
Selecting previously unselected package dmsetup.
(Reading database ... 13217 files and directories currently installed.)
Preparing to unpack .../0-dmsetup_2%3a1.02.185-2_armhf.deb ...
Unpacking dmsetup (2:1.02.185-2) ...
Selecting previously unselected package libdevmapper1.02.1:armhf.
Preparing to unpack .../1-libdevmapper1.02.1_2%3a1.02.185-2_armhf.deb ...
Unpacking libdevmapper1.02.1:armhf (2:1.02.185-2) ...
Selecting previously unselected package libjson-c5:armhf.
Preparing to unpack .../2-libjson-c5_0.16-2_armhf.deb ...
Unpacking libjson-c5:armhf (0.16-2) ...
Selecting previously unselected package libcryptsetup12:armhf.
Preparing to unpack .../3-libcryptsetup12_2%3a2.6.0-2_armhf.deb ...
Unpacking libcryptsetup12:armhf (2:2.6.0-2) ...
Selecting previously unselected package libfdisk1:armhf.
Preparing to unpack .../4-libfdisk1_2.38.1-4_armhf.deb ...
Unpacking libfdisk1:armhf (2.38.1-4) ...
Selecting previously unselected package libkmod2:armhf.
Preparing to unpack .../5-libkmod2_30+20221128-1_armhf.deb ...
Unpacking libkmod2:armhf (30+20221128-1) ...
Selecting previously unselected package libapparmor1:armhf.
Preparing to unpack .../6-libapparmor1_3.0.8-1_armhf.deb ...
Unpacking libapparmor1:armhf (3.0.8-1) ...
Selecting previously unselected package libip4tc2:armhf.
Preparing to unpack .../7-libip4tc2_1.8.8-1_armhf.deb ...
Unpacking libip4tc2:armhf (1.8.8-1) ...
Selecting previously unselected package libsystemd-shared:armhf.
Preparing to unpack .../8-libsystemd-shared_252.4-1+rpi1_armhf.deb ...
Unpacking libsystemd-shared:armhf (252.4-1+rpi1) ...
Preparing to unpack .../9-libsystemd0_252.4-1+rpi1_armhf.deb ...
Unpacking libsystemd0:armhf (252.4-1+rpi1) over (252.2-1+rpi1) ...
Setting up libsystemd0:armhf (252.4-1+rpi1) ...
Selecting previously unselected package systemd.
(Reading database ... 13286 files and directories currently installed.)
Preparing to unpack .../systemd_252.4-1+rpi1_armhf.deb ...
Unpacking systemd (252.4-1+rpi1) ...
Setting up libargon2-1:armhf (0~20171227-0.3) ...
Setting up libjson-c5:armhf (0.16-2) ...
Setting up libfdisk1:armhf (2.38.1-4) ...
Setting up libkmod2:armhf (30+20221128-1) ...
Setting up libapparmor1:armhf (3.0.8-1) ...
Setting up libip4tc2:armhf (1.8.8-1) ...
Setting up libsystemd-shared:armhf (252.4-1+rpi1) ...
Setting up libdevmapper1.02.1:armhf (2:1.02.185-2) ...
Setting up libcryptsetup12:armhf (2:2.6.0-2) ...
Setting up systemd (252.4-1+rpi1) ...
Created symlink /etc/systemd/system/getty.target.wants/getty@tty1.service -> /lib/systemd/system/getty@.service.
Created symlink /etc/systemd/system/multi-user.target.wants/remote-fs.target -> /lib/systemd/system/remote-fs.target.
Created symlink /etc/systemd/system/sysinit.target.wants/systemd-pstore.service -> /lib/systemd/system/systemd-pstore.service.
Initializing machine ID from random generator.
Creating group 'systemd-journal' with GID 999.
Creating user '_apt' (n/a) with UID 42 and GID 65534.
Creating group 'systemd-network' with GID 998.
Creating user 'systemd-network' (systemd Network Management) with UID 998 and GID 998.
Setting up dmsetup (2:1.02.185-2) ...
Selecting previously unselected package systemd-sysv.
(Reading database ... 14118 files and directories currently installed.)
Preparing to unpack .../0-systemd-sysv_252.4-1+rpi1_armhf.deb ...
Unpacking systemd-sysv (252.4-1+rpi1) ...
Selecting previously unselected package libdbus-1-3:armhf.
Preparing to unpack .../1-libdbus-1-3_1.14.4-1_armhf.deb ...
Unpacking libdbus-1-3:armhf (1.14.4-1) ...
Selecting previously unselected package dbus-bin.
Preparing to unpack .../2-dbus-bin_1.14.4-1_armhf.deb ...
Unpacking dbus-bin (1.14.4-1) ...
Selecting previously unselected package dbus-session-bus-common.
Preparing to unpack .../3-dbus-session-bus-common_1.14.4-1_all.deb ...
Unpacking dbus-session-bus-common (1.14.4-1) ...
Selecting previously unselected package libexpat1:armhf.
Preparing to unpack .../4-libexpat1_2.5.0-1_armhf.deb ...
Unpacking libexpat1:armhf (2.5.0-1) ...
Selecting previously unselected package dbus-daemon.
Preparing to unpack .../5-dbus-daemon_1.14.4-1_armhf.deb ...
Unpacking dbus-daemon (1.14.4-1) ...
Selecting previously unselected package dbus-system-bus-common.
Preparing to unpack .../6-dbus-system-bus-common_1.14.4-1_all.deb ...
Unpacking dbus-system-bus-common (1.14.4-1) ...
Selecting previously unselected package dbus.
Preparing to unpack .../7-dbus_1.14.4-1_armhf.deb ...
Unpacking dbus (1.14.4-1) ...
Selecting previously unselected package install-info.
Preparing to unpack .../8-install-info_6.8-6+b1_armhf.deb ...
Unpacking install-info (6.8-6+b1) ...
Setting up install-info (6.8-6+b1) ...
Selecting previously unselected package libuchardet0:armhf.
(Reading database ... 14234 files and directories currently installed.)
Preparing to unpack .../000-libuchardet0_0.0.7-1_armhf.deb ...
Unpacking libuchardet0:armhf (0.0.7-1) ...
Selecting previously unselected package groff-base.
Preparing to unpack .../001-groff-base_1.22.4-9_armhf.deb ...
Unpacking groff-base (1.22.4-9) ...
Selecting previously unselected package bsdextrautils.
Preparing to unpack .../002-bsdextrautils_2.38.1-4_armhf.deb ...
Unpacking bsdextrautils (2.38.1-4) ...
Selecting previously unselected package libpipeline1:armhf.
Preparing to unpack .../003-libpipeline1_1.5.7-1_armhf.deb ...
Unpacking libpipeline1:armhf (1.5.7-1) ...
Selecting previously unselected package man-db.
Preparing to unpack .../004-man-db_2.11.2-1_armhf.deb ...
Unpacking man-db (2.11.2-1) ...
Selecting previously unselected package libproc2-0:armhf.
Preparing to unpack .../005-libproc2-0_2%3a4.0.2-3_armhf.deb ...
Unpacking libproc2-0:armhf (2:4.0.2-3) ...
Selecting previously unselected package procps.
Preparing to unpack .../006-procps_2%3a4.0.2-3_armhf.deb ...
Unpacking procps (2:4.0.2-3) ...
Selecting previously unselected package libmagic-mgc.
Preparing to unpack .../007-libmagic-mgc_1%3a5.41-4_armhf.deb ...
Unpacking libmagic-mgc (1:5.41-4) ...
Selecting previously unselected package libmagic1:armhf.
Preparing to unpack .../008-libmagic1_1%3a5.41-4_armhf.deb ...
Unpacking libmagic1:armhf (1:5.41-4) ...
Selecting previously unselected package file.
Preparing to unpack .../009-file_1%3a5.41-4_armhf.deb ...
Unpacking file (1:5.41-4) ...
Selecting previously unselected package gettext-base.
Preparing to unpack .../010-gettext-base_0.21-10_armhf.deb ...
Unpacking gettext-base (0.21-10) ...
Selecting previously unselected package libpam-systemd:armhf.
Preparing to unpack .../011-libpam-systemd_252.4-1+rpi1_armhf.deb ...
Unpacking libpam-systemd:armhf (252.4-1+rpi1) ...
Selecting previously unselected package ucf.
Preparing to unpack .../012-ucf_3.0043_all.deb ...
Moving old data out of the way
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Setting up libexpat1:armhf (2.5.0-1) ...
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Setting up libgraphite2-3:armhf (1.3.14-1) ...
Setting up liblcms2-2:armhf (2.14-1+b1) ...
Setting up libpixman-1-0:armhf (0.42.2-1) ...
Setting up libaom3:armhf (3.5.0-1) ...
Setting up libabsl20220623:armhf (20220623.1-1+rpi1) ...
Setting up systemd-sysv (252.4-1+rpi1) ...
Setting up libxau6:armhf (1:1.0.9-1) ...
Setting up libgpm2:armhf (1.20.7-10+b2) ...
Setting up libicu72:armhf (72.1-3) ...
Setting up liblerc4:armhf (4.0.0+ds-2) ...
Setting up bsdextrautils (2.38.1-4) ...
Setting up hicolor-icon-theme (0.17-2) ...
Setting up libdatrie1:armhf (0.2.13-2+b2) ...
Setting up libmagic-mgc (1:5.41-4) ...
Setting up libarchive-zip-perl (1.68-1) ...
Setting up libglib2.0-0:armhf (2.74.4-1) ...
Setting up libtexluajit2:armhf (2022.20220321.62855-5) ...
Setting up libdebhelper-perl (13.11.4) ...
Setting up libbrotli1:armhf (1.0.9-2+b2) ...
Setting up libgdk-pixbuf2.0-common (2.42.10+dfsg-1) ...
Setting up x11-common (1:7.7+23) ...
Running in chroot, ignoring request.
Setting up libmagic1:armhf (1:5.41-4) ...
Setting up libdeflate0:armhf (1.14-1) ...
Setting up m17n-db (1.8.0-3) ...
Setting up gettext-base (0.21-10) ...
Setting up m4 (1.4.19-2) ...
Setting up xkb-data (2.35.1-1) ...
Setting up libzzip-0-13:armhf (0.13.72+dfsg.1-1.1) ...
Setting up file (1:5.41-4) ...
Setting up libsvtav1enc1:armhf (1.4.1+dfsg-1) ...
Setting up libjbig0:armhf (2.1-6.1) ...
Setting up librav1e0:armhf (0.5.1-6) ...
Setting up libcolord2:armhf (1.4.6-2.1) ...
Setting up libdconf1:armhf (0.40.0-4) ...
Setting up libasound2-data (1.2.8-1) ...
Setting up autotools-dev (20220109.1) ...
Setting up libjpeg62-turbo:armhf (1:2.1.2-1) ...
Setting up emacsen-common (3.0.5) ...
Setting up libx11-data (2:1.8.3-3) ...
Setting up libepoxy0:armhf (1.5.10-1) ...
Setting up libteckit0:armhf (2.5.11+ds1-1) ...
Setting up libavahi-common-data:armhf (0.8-7) ...
Setting up libdbus-1-3:armhf (1.14.4-1) ...
Setting up libfribidi0:armhf (1.0.8-2.1) ...
Setting up t1utils (1.41-4) ...
Setting up libtexlua53-5:armhf (2022.20220321.62855-5) ...
Setting up libproc2-0:armhf (2:4.0.2-3) ...
Setting up libpng16-16:armhf (1.6.39-2) ...
Setting up libtcl8.6:armhf (8.6.13+dfsg-1) ...
Setting up autopoint (0.21-10) ...
Setting up fonts-dejavu-core (2.37-2) ...
Setting up libgav1-1:armhf (0.18.0-1+rpi1+b1) ...
Setting up ucf (3.0043) ...
Setting up libdav1d6:armhf (1.0.0-2+rpi1) ...
Setting up libkpathsea6:armhf (2022.20220321.62855-5) ...
Setting up autoconf (2.71-2) ...
Setting up libx265-199:armhf (3.5-2) ...
Setting up libwebp7:armhf (1.2.2-2+b2) ...
Setting up libgif7:armhf (5.2.1-2.5) ...
Setting up libmd0:armhf (1.0.4-2) ...
Setting up at-spi2-common (2.46.0-4) ...
Setting up libtiff6:armhf (4.5.0-3) ...
Setting up dbus-session-bus-common (1.14.4-1) ...
Setting up libuchardet0:armhf (0.0.7-1) ...
Setting up procps (2:4.0.2-3) ...
Setting up libasound2:armhf (1.2.8-1) ...
Setting up fonts-lmodern (2.005-1) ...
Setting up libsub-override-perl (0.09-4) ...
Setting up libthai-data (0.1.29-1) ...
Setting up libatk1.0-0:armhf (2.46.0-4) ...
Setting up libtiff5:armhf (4.4.0-6) ...
Setting up libwayland-egl1:armhf (1.21.0-1) ...
Setting up dbus-system-bus-common (1.14.4-1) ...
Setting up libde265-0:armhf (1.0.9-1+rpi1) ...
Setting up libgccjit0:armhf (12.2.0-10+rpi1) ...
Setting up libbsd0:armhf (0.11.7-1) ...
Setting up libyuv0:armhf (0.0~git20230104.6e4b0ac-1) ...
Setting up libelf1:armhf (0.187-2+rpi2) ...
Setting up libxml2:armhf (2.9.14+dfsg-1.1) ...
Setting up xdg-utils (1.1.3-4.1) ...
update-alternatives: using /usr/bin/xdg-open to provide /usr/bin/open (open) in auto mode
Setting up dbus-bin (1.14.4-1) ...
Setting up libsynctex2:armhf (2022.20220321.62855-5) ...
Setting up libxkbcommon0:armhf (1.5.0-1) ...
Setting up libwayland-client0:armhf (1.21.0-1) ...
Setting up automake (1:1.16.5-1.3) ...
update-alternatives: using /usr/bin/automake-1.16 to provide /usr/bin/automake (automake) in auto mode
Setting up libfile-stripnondeterminism-perl (1.13.1-1) ...
Setting up libpaper1:armhf (1.1.28) ...
Creating config file /etc/papersize with new version
Setting up libice6:armhf (2:1.0.10-1) ...
Setting up libxdmcp6:armhf (1:1.1.2-3) ...
Setting up libxcb1:armhf (1.15-1) ...
Setting up gettext (0.21-10) ...
Setting up libavif15:armhf (0.11.1-1) ...
Setting up libtool (2.4.7-5) ...
Setting up libxcb-render0:armhf (1.15-1) ...
Setting up fontconfig-config (2.14.1-3) ...
Setting up libedit2:armhf (3.1-20221030-2) ...
Setting up libheif1:armhf (1.13.0-1) ...
Setting up libavahi-common3:armhf (0.8-7) ...
Setting up libxcb-shm0:armhf (1.15-1) ...
Setting up dbus-daemon (1.14.4-1) ...
Setting up libpaper-utils (1.1.28) ...
Setting up intltool-debian (0.35.0+20060710.6) ...
Setting up dh-autoreconf (20) ...
Setting up tex-common (6.18) ...
update-language: texlive-base not installed and configured, doing nothing!
Setting up libthai0:armhf (0.1.29-1) ...
Setting up libptexenc1:armhf (2022.20220321.62855-5) ...
Setting up libfreetype6:armhf (2.12.1+dfsg-4) ...
Setting up dbus (1.14.4-1) ...
Running in chroot, ignoring request.
Setting up shared-mime-info (2.2-1) ...
Setting up dh-strip-nondeterminism (1.13.1-1) ...
Setting up dwz (0.15-1) ...
Setting up groff-base (1.22.4-9) ...
Setting up libwayland-cursor0:armhf (1.21.0-1) ...
Setting up libpam-systemd:armhf (252.4-1+rpi1) ...
Setting up libx11-6:armhf (2:1.8.3-3) ...
Setting up libharfbuzz0b:armhf (6.0.0-1) ...
Setting up libgdk-pixbuf-2.0-0:armhf (2.42.10+dfsg-1+b1) ...
Setting up libxcomposite1:armhf (1:0.4.5-1) ...
Setting up libsm6:armhf (2:1.2.3-1) ...
Setting up libavahi-client3:armhf (0.8-7) ...
Setting up libotf1:armhf (0.9.16-3) ...
Setting up gtk-update-icon-cache (3.24.36-1) ...
Setting up libxdamage1:armhf (1:1.1.6-1) ...
Setting up libxpm4:armhf (1:3.5.12-1) ...
Setting up libxrender1:armhf (1:0.9.10-1.1) ...
Setting up po-debconf (1.0.21+nmu1) ...
Setting up libxext6:armhf (2:1.3.4-1) ...
Setting up man-db (2.11.2-1) ...
Not building database; man-db/auto-update is not 'true'.
Created symlink /etc/systemd/system/timers.target.wants/man-db.timer -> /lib/systemd/system/man-db.timer.
Setting up dbus-user-session (1.14.4-1) ...
Setting up adwaita-icon-theme (43-1) ...
update-alternatives: using /usr/share/icons/Adwaita/cursor.theme to provide /usr/share/icons/default/index.theme (x-cursor-theme) in auto mode
Setting up libxfixes3:armhf (1:6.0.0-2) ...
Setting up libxinerama1:armhf (2:1.1.4-3) ...
Setting up libxrandr2:armhf (2:1.5.2-2) ...
Setting up libxt6:armhf (1:1.2.1-1) ...
Setting up libcups2:armhf (2.4.2-1+b1) ...
Setting up libxss1:armhf (1:1.2.3-1) ...
Setting up libxmu6:armhf (2:1.1.3-3) ...
Setting up libxi6:armhf (2:1.8-1) ...
Setting up libxcursor1:armhf (1:1.2.1-1) ...
Setting up debhelper (13.11.4) ...
Setting up dconf-service (0.40.0-4) ...
Setting up libxaw7:armhf (2:1.0.14-1) ...
Setting up libatspi2.0-0:armhf (2.46.0-4) ...
Setting up libatk-bridge2.0-0:armhf (2.46.0-4) ...
Setting up dconf-gsettings-backend:armhf (0.40.0-4) ...
Setting up libgtk-3-common (3.24.36-1) ...
Setting up emacs-el (1:28.2+1-9) ...
Setting up emacs-common (1:28.2+1-9) ...
Setting up emacs-bin-common (1:28.2+1-9) ...
update-alternatives: using /usr/bin/ctags.emacs to provide /usr/bin/ctags (ctags) in auto mode
update-alternatives: using /usr/bin/ebrowse.emacs to provide /usr/bin/ebrowse (ebrowse) in auto mode
update-alternatives: using /usr/bin/emacsclient.emacs to provide /usr/bin/emacsclient (emacsclient) in auto mode
update-alternatives: using /usr/bin/etags.emacs to provide /usr/bin/etags (etags) in auto mode
Processing triggers for sgml-base (1.31) ...
Setting up libfontconfig1:armhf (2.14.1-3) ...
Processing triggers for install-info (6.8-6+b1) ...
Setting up fontconfig (2.14.1-3) ...
Regenerating fonts cache... done.
Setting up libxft2:armhf (2.3.6-1) ...
Setting up libtk8.6:armhf (8.6.13-1) ...
Processing triggers for libc-bin (2.36-6+rpi1) ...
Setting up libpango-1.0-0:armhf (1.50.12+ds-1) ...
Setting up libcairo2:armhf (1.16.0-7) ...
Setting up libgd3:armhf (2.3.3-7+b1) ...
Setting up texlive-binaries (2022.20220321.62855-5) ...
update-alternatives: using /usr/bin/xdvi-xaw to provide /usr/bin/xdvi.bin (xdvi.bin) in auto mode
update-alternatives: using /usr/bin/bibtex.original to provide /usr/bin/bibtex (bibtex) in auto mode
Setting up libcairo-gobject2:armhf (1.16.0-7) ...
Setting up libpangoft2-1.0-0:armhf (1.50.12+ds-1) ...
Setting up texlive-base (2022.20221123-1) ...
tl-paper: setting paper size for dvips to a4: /var/lib/texmf/dvips/config/config-paper.ps
tl-paper: setting paper size for dvipdfmx to a4: /var/lib/texmf/dvipdfmx/dvipdfmx-paper.cfg
tl-paper: setting paper size for xdvi to a4: /var/lib/texmf/xdvi/XDvi-paper
tl-paper: setting paper size for pdftex to a4: /var/lib/texmf/tex/generic/tex-ini-files/pdftexconfig.tex
Setting up libpangocairo-1.0-0:armhf (1.50.12+ds-1) ...
Setting up libgtk-3-0:armhf (3.24.36-1) ...
Setting up libm17n-0:armhf (1.8.0-5) ...
Setting up librsvg2-2:armhf (2.54.5+dfsg-1) ...
Setting up texlive-latex-base (2022.20221123-1) ...
Setting up emacs-gtk (1:28.2+1-9) ...
update-alternatives: using /usr/bin/emacs-gtk to provide /usr/bin/emacs (emacs) in auto mode
Install emacsen-common for emacs
emacsen-common: Handling install of emacsen flavor emacs
Setting up gcl (2.6.14-1+rpi1) ...
Creating config file /etc/default/gcl with new version
Install gcl for emacs
Setting up emacs (1:28.2+1-9) ...
Setting up sbuild-build-depends-hol88-dummy (0.invalid.0) ...
Processing triggers for libc-bin (2.36-6+rpi1) ...
Processing triggers for tex-common (6.18) ...
Running updmap-sys. This may take some time... done.
Running mktexlsr /var/lib/texmf ... done.
Building format(s) --all.
This may take some time... done.
W: No sandbox user '_apt' on the system, can not drop privileges
+------------------------------------------------------------------------------+
| Build environment |
+------------------------------------------------------------------------------+
Kernel: Linux 4.9.0-0.bpo.6-armmp armhf (armv7l)
Toolchain package versions: binutils_2.39.50.20221208-5+rpi1 dpkg-dev_1.21.9+rpi1 g++-12_12.2.0-10+rpi1 gcc-12_12.2.0-10+rpi1 libc6-dev_2.36-6+rpi1 libstdc++-12-dev_12.2.0-10+rpi1 libstdc++6_12.2.0-10+rpi1 linux-libc-dev_6.0.12-1+rpi1
Package versions: adduser_3.129 adwaita-icon-theme_43-1 apt_2.5.4 aptitude_0.8.13-5 aptitude-common_0.8.13-5 at-spi2-common_2.46.0-4 autoconf_2.71-2 automake_1:1.16.5-1.3 autopoint_0.21-10 autotools-dev_20220109.1 base-files_12.3+rpi1 base-passwd_3.6.1 bash_5.2-2 binutils_2.39.50.20221208-5+rpi1 binutils-arm-linux-gnueabihf_2.39.50.20221208-5+rpi1 binutils-common_2.39.50.20221208-5+rpi1 bsdextrautils_2.38.1-4 bsdutils_1:2.38.1-4 build-essential_12.9 bzip2_1.0.8-5+b2 coreutils_9.1-1 cpp_4:12.2.0-1+rpi1 cpp-12_12.2.0-10+rpi1 dash_0.5.11+git20210903+057cd650a4ed-9 dbus_1.14.4-1 dbus-bin_1.14.4-1 dbus-daemon_1.14.4-1 dbus-session-bus-common_1.14.4-1 dbus-system-bus-common_1.14.4-1 dbus-user-session_1.14.4-1 dconf-gsettings-backend_0.40.0-4 dconf-service_0.40.0-4 debconf_1.5.80 debhelper_13.11.4 debianutils_5.7-0.4 dh-autoreconf_20 dh-strip-nondeterminism_1.13.1-1 diffutils_1:3.8-1 dirmngr_2.2.40-1 dmsetup_2:1.02.185-2 dpkg_1.21.9+rpi1 dpkg-dev_1.21.9+rpi1 dwz_0.15-1 e2fsprogs_1.46.6~rc1-1 emacs_1:28.2+1-9 emacs-bin-common_1:28.2+1-9 emacs-common_1:28.2+1-9 emacs-el_1:28.2+1-9 emacs-gtk_1:28.2+1-9 emacsen-common_3.0.5 fakeroot_1.29-1 file_1:5.41-4 findutils_4.9.0-3 fontconfig_2.14.1-3 fontconfig-config_2.14.1-3 fonts-dejavu-core_2.37-2 fonts-lmodern_2.005-1 g++_4:12.2.0-1+rpi1 g++-12_12.2.0-10+rpi1 gcc_4:12.2.0-1+rpi1 gcc-12_12.2.0-10+rpi1 gcc-12-base_12.2.0-10+rpi1 gcc-7-base_7.5.0-6+rpi1+b2 gcc-8-base_8.4.0-7+rpi1 gcc-9-base_9.4.0-2+rpi1 gcl_2.6.14-1+rpi1 gettext_0.21-10 gettext-base_0.21-10 gnupg_2.2.40-1 gnupg-l10n_2.2.40-1 gnupg-utils_2.2.40-1 gpg_2.2.40-1 gpg-agent_2.2.40-1 gpg-wks-client_2.2.40-1 gpg-wks-server_2.2.40-1 gpgconf_2.2.40-1 gpgsm_2.2.40-1 gpgv_2.2.40-1 grep_3.8-3 groff-base_1.22.4-9 gtk-update-icon-cache_3.24.36-1 gzip_1.12-1 hicolor-icon-theme_0.17-2 hostname_3.23 init-system-helpers_1.64 install-info_6.8-6+b1 intltool-debian_0.35.0+20060710.6 iputils-ping_3:20221126-1 krb5-locales_1.20.1-1 libabsl20220623_20220623.1-1+rpi1 libacl1_2.3.1-2 libaom3_3.5.0-1 libapparmor1_3.0.8-1 libapt-pkg6.0_2.5.4 libarchive-zip-perl_1.68-1 libargon2-1_0~20171227-0.3 libasan8_12.2.0-10+rpi1 libasound2_1.2.8-1 libasound2-data_1.2.8-1 libassuan0_2.5.5-5 libatk-bridge2.0-0_2.46.0-4 libatk1.0-0_2.46.0-4 libatomic1_12.2.0-10+rpi1 libatspi2.0-0_2.46.0-4 libattr1_1:2.5.1-3 libaudit-common_1:3.0.7-1.1 libaudit1_1:3.0.7-1.1 libavahi-client3_0.8-7 libavahi-common-data_0.8-7 libavahi-common3_0.8-7 libavif15_0.11.1-1 libbinutils_2.39.50.20221208-5+rpi1 libblkid1_2.38.1-4 libboost-iostreams1.74.0_1.74.0-17+b1 libbrotli1_1.0.9-2+b2 libbsd0_0.11.7-1 libbz2-1.0_1.0.8-5+b2 libc-bin_2.36-6+rpi1 libc-dev-bin_2.36-6+rpi1 libc6_2.36-6+rpi1 libc6-dev_2.36-6+rpi1 libcairo-gobject2_1.16.0-7 libcairo2_1.16.0-7 libcap-ng0_0.8.3-1 libcap2_1:2.44-1 libcap2-bin_1:2.44-1 libcc1-0_12.2.0-10+rpi1 libcolord2_1.4.6-2.1 libcom-err2_1.46.6~rc1-1 libcrypt-dev_1:4.4.33-1 libcrypt1_1:4.4.33-1 libcryptsetup12_2:2.6.0-2 libctf-nobfd0_2.39.50.20221208-5+rpi1 libctf0_2.39.50.20221208-5+rpi1 libcups2_2.4.2-1+b1 libcwidget4_0.5.18-6 libdatrie1_0.2.13-2+b2 libdav1d6_1.0.0-2+rpi1 libdb5.3_5.3.28+dfsg1-0.10 libdbus-1-3_1.14.4-1 libdconf1_0.40.0-4 libde265-0_1.0.9-1+rpi1 libdebconfclient0_0.265 libdebhelper-perl_13.11.4 libdeflate0_1.14-1 libdevmapper1.02.1_2:1.02.185-2 libdpkg-perl_1.21.9+rpi1 libedit2_3.1-20221030-2 libelf1_0.187-2+rpi2 libepoxy0_1.5.10-1 libexpat1_2.5.0-1 libext2fs2_1.46.6~rc1-1 libfakeroot_1.29-1 libfdisk1_2.38.1-4 libffi8_3.4.4-1 libfile-stripnondeterminism-perl_1.13.1-1 libfontconfig1_2.14.1-3 libfreetype6_2.12.1+dfsg-4 libfribidi0_1.0.8-2.1 libgav1-1_0.18.0-1+rpi1+b1 libgcc-12-dev_12.2.0-10+rpi1 libgcc-s1_12.2.0-10+rpi1 libgccjit0_12.2.0-10+rpi1 libgcrypt20_1.10.1-3 libgd3_2.3.3-7+b1 libgdbm-compat4_1.23-3 libgdbm6_1.23-3 libgdk-pixbuf-2.0-0_2.42.10+dfsg-1+b1 libgdk-pixbuf2.0-common_2.42.10+dfsg-1 libgif7_5.2.1-2.5 libglib2.0-0_2.74.4-1 libgmp10_2:6.2.1+dfsg1-1.1 libgnutls30_3.7.8-4 libgomp1_12.2.0-10+rpi1 libgpg-error0_1.46-1 libgpm2_1.20.7-10+b2 libgraphite2-3_1.3.14-1 libgssapi-krb5-2_1.20.1-1 libgtk-3-0_3.24.36-1 libgtk-3-common_3.24.36-1 libharfbuzz0b_6.0.0-1 libheif1_1.13.0-1 libhogweed6_3.8.1-2 libice6_2:1.0.10-1 libicu72_72.1-3 libidn2-0_2.3.3-1 libip4tc2_1.8.8-1 libisl23_0.25-1 libjansson4_2.14-2 libjbig0_2.1-6.1 libjpeg62-turbo_1:2.1.2-1 libjson-c5_0.16-2 libk5crypto3_1.20.1-1 libkeyutils1_1.6.3-1 libkmod2_30+20221128-1 libkpathsea6_2022.20220321.62855-5 libkrb5-3_1.20.1-1 libkrb5support0_1.20.1-1 libksba8_1.6.2-4 liblcms2-2_2.14-1+b1 libldap-2.4-2_2.4.59+dfsg-1+b1 libldap-2.5-0_2.5.13+dfsg-2+rpi1+b1 libldap-common_2.5.13+dfsg-2+rpi1 liblerc4_4.0.0+ds-2 liblz4-1_1.9.4-1+rpi1 liblzma5_5.4.0-0.1 libm17n-0_1.8.0-5 libmagic-mgc_1:5.41-4 libmagic1_1:5.41-4 libmd0_1.0.4-2 libmount1_2.38.1-4 libmpc3_1.2.1-2 libmpfr6_4.1.0-3 libncursesw6_6.3+20220423-2 libnettle8_3.8.1-2 libnpth0_1.6-3 libnsl-dev_1.3.0-2 libnsl2_1.3.0-2 libotf1_0.9.16-3 libp11-kit0_0.24.1-1 libpam-cap_1:2.44-1 libpam-modules_1.5.2-5 libpam-modules-bin_1.5.2-5 libpam-runtime_1.5.2-5 libpam-systemd_252.4-1+rpi1 libpam0g_1.5.2-5 libpango-1.0-0_1.50.12+ds-1 libpangocairo-1.0-0_1.50.12+ds-1 libpangoft2-1.0-0_1.50.12+ds-1 libpaper-utils_1.1.28 libpaper1_1.1.28 libpcre2-8-0_10.40-3 libpcre3_2:8.39-14 libperl5.36_5.36.0-6 libpipeline1_1.5.7-1 libpixman-1-0_0.42.2-1 libpng16-16_1.6.39-2 libproc2-0_2:4.0.2-3 libptexenc1_2022.20220321.62855-5 librav1e0_0.5.1-6 libreadline8_8.2-1.2 librsvg2-2_2.54.5+dfsg-1 libsasl2-2_2.1.28+dfsg-10 libsasl2-modules-db_2.1.28+dfsg-10 libseccomp2_2.5.4-1+rpi1 libselinux1_3.4-1 libsemanage-common_3.4-1 libsemanage2_3.4-1 libsepol1_3.1-1 libsepol2_3.4-2 libsigc++-2.0-0v5_2.10.8-1 libsm6_2:1.2.3-1 libsmartcols1_2.38.1-4 libsqlite3-0_3.40.0-1 libss2_1.46.6~rc1-1 libssl1.1_1.1.1o-1 libssl3_3.0.7-1 libstdc++-12-dev_12.2.0-10+rpi1 libstdc++6_12.2.0-10+rpi1 libsub-override-perl_0.09-4 libsvtav1enc1_1.4.1+dfsg-1 libsynctex2_2022.20220321.62855-5 libsystemd-shared_252.4-1+rpi1 libsystemd0_252.4-1+rpi1 libtasn1-6_4.19.0-2 libtcl8.6_8.6.13+dfsg-1 libteckit0_2.5.11+ds1-1 libtexlua53-5_2022.20220321.62855-5 libtexluajit2_2022.20220321.62855-5 libthai-data_0.1.29-1 libthai0_0.1.29-1 libtiff5_4.4.0-6 libtiff6_4.5.0-3 libtinfo6_6.3+20220423-2 libtirpc-common_1.3.3+ds-1 libtirpc-dev_1.3.3+ds-1 libtirpc3_1.3.3+ds-1 libtk8.6_8.6.13-1 libtool_2.4.7-5 libubsan1_12.2.0-10+rpi1 libuchardet0_0.0.7-1 libudev1_252.4-1+rpi1 libunistring2_1.0-2 libuuid1_2.38.1-4 libwayland-client0_1.21.0-1 libwayland-cursor0_1.21.0-1 libwayland-egl1_1.21.0-1 libwebp7_1.2.2-2+b2 libx11-6_2:1.8.3-3 libx11-data_2:1.8.3-3 libx265-199_3.5-2 libxapian30_1.4.21-1 libxau6_1:1.0.9-1 libxaw7_2:1.0.14-1 libxcb-render0_1.15-1 libxcb-shm0_1.15-1 libxcb1_1.15-1 libxcomposite1_1:0.4.5-1 libxcursor1_1:1.2.1-1 libxdamage1_1:1.1.6-1 libxdmcp6_1:1.1.2-3 libxext6_2:1.3.4-1 libxfixes3_1:6.0.0-2 libxft2_2.3.6-1 libxi6_2:1.8-1 libxinerama1_2:1.1.4-3 libxkbcommon0_1.5.0-1 libxml2_2.9.14+dfsg-1.1 libxmu6_2:1.1.3-3 libxpm4_1:3.5.12-1 libxrandr2_2:1.5.2-2 libxrender1_1:0.9.10-1.1 libxss1_1:1.2.3-1 libxt6_1:1.2.1-1 libxxhash0_0.8.1-1 libyuv0_0.0~git20230104.6e4b0ac-1 libzstd1_1.5.2+dfsg-1 libzzip-0-13_0.13.72+dfsg.1-1.1 linux-libc-dev_6.0.12-1+rpi1 login_1:4.13+dfsg1-1 logsave_1.46.6~rc1-1 lsb-base_11.4+rpi1 m17n-db_1.8.0-3 m4_1.4.19-2 make_4.3-4.1 man-db_2.11.2-1 mawk_1.3.4.20200120-3.1 mount_2.38.1-4 nano_7.1-1 ncurses-base_6.3+20220423-2 ncurses-bin_6.3+20220423-2 netbase_6.4 passwd_1:4.13+dfsg1-1 patch_2.7.6-7 perl_5.36.0-6 perl-base_5.36.0-6 perl-modules-5.36_5.36.0-6 pinentry-curses_1.2.1-1 po-debconf_1.0.21+nmu1 procps_2:4.0.2-3 raspbian-archive-keyring_20120528.2 readline-common_8.2-1.2 rpcsvc-proto_1.4.3-1 sbuild-build-depends-core-dummy_0.invalid.0 sbuild-build-depends-hol88-dummy_0.invalid.0 sed_4.8-1 sensible-utils_0.0.17 sgml-base_1.31 shared-mime-info_2.2-1 systemd_252.4-1+rpi1 systemd-sysv_252.4-1+rpi1 sysvinit-utils_3.05-7 t1utils_1.41-4 tar_1.34+dfsg-1 tex-common_6.18 texlive-base_2022.20221123-1 texlive-binaries_2022.20220321.62855-5 texlive-latex-base_2022.20221123-1 tzdata_2022f-1 ucf_3.0043 util-linux_2.38.1-4 util-linux-extra_2.38.1-4 x11-common_1:7.7+23 xdg-utils_1.1.3-4.1 xkb-data_2.35.1-1 xz-utils_5.4.0-0.1 zlib1g_1:1.2.13.dfsg-1
+------------------------------------------------------------------------------+
| Build |
+------------------------------------------------------------------------------+
Unpack source
-------------
gpgv: unknown type of key resource 'trustedkeys.kbx'
gpgv: keyblock resource '/tmp/dpkg-verify-sig.3SoENuB1/trustedkeys.kbx': General error
gpgv: Signature made Sat Jan 14 00:00:45 2023 UTC
gpgv: using RSA key FE214F363697773242E816ECB845CE510F9B714D
gpgv: Can't check signature: No public key
dpkg-source: warning: cannot verify signature ./hol88_2.02.19940316dfsg-5.dsc
dpkg-source: info: extracting hol88 in /<<PKGBUILDDIR>>
dpkg-source: info: unpacking hol88_2.02.19940316dfsg.orig.tar.gz
dpkg-source: info: unpacking hol88_2.02.19940316dfsg-5.debian.tar.xz
dpkg-source: info: using patch list from debian/patches/series
dpkg-source: info: applying quilt-source-init
dpkg-source: info: applying FTBFS_detection_fix
Check disc space
----------------
Sufficient free space for build
User Environment
----------------
APT_CONFIG=/var/lib/sbuild/apt.conf
DEB_BUILD_OPTIONS=parallel=4
HOME=/sbuild-nonexistent
LC_ALL=POSIX
LOGNAME=buildd
PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games
SCHROOT_ALIAS_NAME=bookworm-staging-armhf-sbuild
SCHROOT_CHROOT_NAME=bookworm-staging-armhf-sbuild
SCHROOT_COMMAND=env
SCHROOT_GID=109
SCHROOT_GROUP=buildd
SCHROOT_SESSION_ID=bookworm-staging-armhf-sbuild-2b0bf318-a64c-4702-90d8-a4ecf95f17e4
SCHROOT_UID=104
SCHROOT_USER=buildd
SHELL=/bin/sh
TERM=xterm
USER=buildd
dpkg-buildpackage
-----------------
dpkg-buildpackage: info: source package hol88
dpkg-buildpackage: info: source version 2.02.19940316dfsg-5
dpkg-buildpackage: info: source distribution unstable
dpkg-source --before-build .
dpkg-buildpackage: info: host architecture armhf
fakeroot debian/rules clean
dh_testdir
dh_testroot
rm -f build-arch-stamp build-indep-stamp configure-stamp
[ ! -f Makefile ] || /usr/bin/make clean
make[1]: Entering directory '/<<PKGBUILDDIR>>'
/bin/rm -f ml/*_ml.o ml/*_ml.l ml/site.ml lisp/*.o
/bin/rm -f hol-lcf basic-hol hol
/usr/bin/make clean-library
make[2]: Entering directory '/<<PKGBUILDDIR>>'
(cd /<<PKGBUILDDIR>>/Library; /usr/bin/make Obj=o clean; cd ..)
make[3]: Entering directory '/<<PKGBUILDDIR>>/Library'
for lib in unwind taut sets reduce arith pred_sets string finite_sets res_quan wellorder abs_theory reals window pair word record_proof parser prettyp trs latex-hol more_arithmetic numeral ind_defs ; \
do (cd $lib; /usr/bin/make Obj=o clean; cd ..) ; \
done
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/unwind'
rm -f *_ml.o *_ml.l
===> library unwind: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/unwind'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/taut'
rm -f taut_check_ml.o taut_check_ml.l
===> library taut: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/taut'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/sets'
rm -f *_ml.o
===> library sets: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/reduce'
rm -f boolconv_ml.o arithconv_ml.o reduce_ml.o
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/reduce'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/arith'
rm -f *_ml.l *_ml.o
===> library arith: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/arith'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/pred_sets'
rm -f *_ml.o
===> library pred_sets: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/pred_sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/string'
rm -f *_ml.o
===> library string: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/string'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/finite_sets'
rm -f *_ml.o
===> library finite_sets: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/finite_sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/res_quan'
rm -f *_ml.o
===> library res_quan: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/res_quan'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/wellorder'
make[4]: 'clean' is up to date.
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/wellorder'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/abs_theory'
/bin/rm -f *_ml.o
===> abs_theory. All object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/abs_theory'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/reals'
cd theories; make clean
make[5]: Entering directory '/<<PKGBUILDDIR>>/Library/reals/theories'
rm -f *_ml.o
make[5]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals/theories'
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/window'
rm -f *.l *.c *.o *.h *.data
===> library window: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/window'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/pair'
rm -f *.l *.c *.o *.h *.data *.i *.s *.ir
===> library pair: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/pair'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/word'
rm -f *_ml.o
===> library word: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/word'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/record_proof'
rm -f *_ml.o
===> library record_proof: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/record_proof'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/parser'
rm -f *_ml.o *_ml.l *.o
===> library parser: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/parser'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/prettyp'
rm -f PP_printer/*_ml.o PP_printer/*_ml.l
rm -f PP_parser/*_ml.o PP_parser/*_ml.l
rm -f PP_hol/*_ml.o PP_hol/*_ml.l
===> library prettyp: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/prettyp'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/trs'
rm -f *_ml.l *_ml.o
===> library trs: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/trs'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/latex-hol'
rm -f *.o
===> library latex-hol: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/latex-hol'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/more_arithmetic'
rm -f *_ml.o
===> library more_arithmetic: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/more_arithmetic'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/numeral'
rm -f numeral_rules_ml.o
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/numeral'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/ind_defs'
rm -f *_ml.o
===> library ind_defs: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/ind_defs'
===> all library object code deleted
make[3]: Leaving directory '/<<PKGBUILDDIR>>/Library'
make[2]: Leaving directory '/<<PKGBUILDDIR>>'
=======> all hol and lisp object code deleted
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
[ ! -f Makefile ] || /usr/bin/make clobber
make[1]: Entering directory '/<<PKGBUILDDIR>>'
/bin/rm -f ml/*_ml.o ml/*_ml.l ml/site.ml lisp/*.o
/bin/rm -f /<<PKGBUILDDIR>>/theories/*.th hol-lcf basic-hol hol
/usr/bin/make clobber-library
make[2]: Entering directory '/<<PKGBUILDDIR>>'
(cd /<<PKGBUILDDIR>>/Library; /usr/bin/make Obj=o clobber; cd ..)
make[3]: Entering directory '/<<PKGBUILDDIR>>/Library'
for lib in unwind taut sets reduce arith pred_sets string finite_sets res_quan wellorder abs_theory reals window pair word record_proof parser prettyp trs latex-hol more_arithmetic numeral ind_defs ; \
do (cd $lib; /usr/bin/make Obj=o clobber; cd ..) ; \
done
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/unwind'
rm -f *_ml.o *_ml.l
===> library unwind: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/unwind'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/taut'
rm -f taut_check_ml.o taut_check_ml.l
===> library taut: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/taut'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/sets'
rm -f *_ml.o *_ml.l *.th
===> library sets: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/reduce'
rm -f boolconv_ml.o arithconv_ml.o reduce_ml.o
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/reduce'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/arith'
rm -f *_ml.l *_ml.o
===> library arith: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/arith'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/pred_sets'
rm -f *_ml.o *_ml.l *.th
===> library pred_sets: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/pred_sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/string'
rm -f *_ml.o *_ml.l *.th
===> library string: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/string'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/finite_sets'
rm -f *_ml.o *_ml.l *.th
===> library finite_sets: object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/finite_sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/res_quan'
rm -f *_ml.o *_ml.l *.th
===> library res_quan: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/res_quan'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/wellorder'
rm -f WELLORDER.th
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/wellorder'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/abs_theory'
/bin/rm -f *_ml.o *.th print
===> abs_theory: All object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/abs_theory'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/reals'
cd theories; make clobber
make[5]: Entering directory '/<<PKGBUILDDIR>>/Library/reals/theories'
rm -f *_ml.o
rm -f *.th
make[5]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals/theories'
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/window'
rm -f *.l *.c *.o *.th *.h *.data
===> library window: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/window'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/pair'
rm -f *.l *.c *.o *.th *.h *.data *.i *.s *.ir
===> library pair: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/pair'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/word'
rm -f *_ml.o *_ml.l *.th
===> library word: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/word'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/record_proof'
rm -f *_ml.o *_ml.l *.th
===> library record_proof: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/record_proof'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/parser'
rm -f *_ml.o *_ml.l *.o
===> library parser: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/parser'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/prettyp'
rm -f PP_printer/*_ml.o PP_printer/*_ml.l
rm -f PP_parser/*_ml.o PP_parser/*_ml.l PP_parser/*_pp.ml
rm -f PP_hol/*_ml.o PP_hol/*_ml.l PP_hol/*_pp.ml
===> library prettyp: all object code and _pp.ml files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/prettyp'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/trs'
rm -f *_ml.l *_ml.o
===> library trs: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/trs'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/latex-hol'
rm -f latex_*_pp.ml *.o
===> library latex-hol: all object code and _pp.ml file deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/latex-hol'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/more_arithmetic'
rm -f *_ml.o *_ml.l *.th
===> library more_arithmetic: all object code and theory files deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/more_arithmetic'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/numeral'
rm -f numeral_rules_ml.o
rm -f numeral.th
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/numeral'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/ind_defs'
rm -f *_ml.o *_ml.l
===> library ind_defs: all object code deleted
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/ind_defs'
===> all library object code and theory files deleted
make[3]: Leaving directory '/<<PKGBUILDDIR>>/Library'
make[2]: Leaving directory '/<<PKGBUILDDIR>>'
=======> all object code and theory files deleted
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
for i in $(find Library -name index.tex) Library/pred_sets/Manual/theorems.tex Library/record_proof/Manual/record_proof.ind ; do\
[ -e $i.sve ] || cp $i $i.sve ; done
[ ! -f Makefile ] || /usr/bin/make -C Manual clean
make[1]: Entering directory '/<<PKGBUILDDIR>>/Manual'
for i in Tutorial Description Reference Libraries Covers ; do /usr/bin/make -C $i clean ; done
make[2]: Entering directory '/<<PKGBUILDDIR>>/Manual/Tutorial'
rm -f *.dvi *.aux *.toc *.log
make[2]: Leaving directory '/<<PKGBUILDDIR>>/Manual/Tutorial'
make[2]: Entering directory '/<<PKGBUILDDIR>>/Manual/Description'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[2]: Leaving directory '/<<PKGBUILDDIR>>/Manual/Description'
make[2]: Entering directory '/<<PKGBUILDDIR>>/Manual/Reference'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[2]: Leaving directory '/<<PKGBUILDDIR>>/Manual/Reference'
make[2]: Entering directory '/<<PKGBUILDDIR>>/Manual/Libraries'
rm -f *.dvi *.aux *.toc *.log
make[2]: Leaving directory '/<<PKGBUILDDIR>>/Manual/Libraries'
make[2]: Entering directory '/<<PKGBUILDDIR>>/Manual/Covers'
rm -f *.log core *.aux *~ #* LOG
===> Fancy end and title pages cleaned up
make[2]: Leaving directory '/<<PKGBUILDDIR>>/Manual/Covers'
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Manual'
[ ! -f Makefile ] || for i in $(find Library -name Manual); do /usr/bin/make -C $i clean ; done
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/reduce/Manual'
\
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/reduce/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/pred_sets/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/pred_sets/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/res_quan/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/res_quan/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/word/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/word/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/taut/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/taut/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/unwind/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/unwind/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/window/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex *.bak; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/window/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/more_arithmetic/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/more_arithmetic/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/latex-hol/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/latex-hol/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/record_proof/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/record_proof/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/pair/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex theorems.tex; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/pair/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/wellorder/Manual'
\
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/wellorder/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/reals/Manual'
\
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/finite_sets/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/finite_sets/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/arith/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/arith/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/string/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/string/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/prettyp/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/prettyp/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/sets/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/sets/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/trs/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/trs/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/abs_theory/Manual'
\
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/abs_theory/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/numeral/Manual'
\
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg entries.tex; \
printf '\\begin{theindex}' >index.tex; \
printf '\\mbox{}' >>index.tex; \
printf '\\end{theindex}' >>index.tex
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/numeral/Manual'
make[1]: Entering directory '/<<PKGBUILDDIR>>/Library/parser/Manual'
rm -f *.dvi *.aux *.toc *.log *.idx *.ilg
make[1]: Leaving directory '/<<PKGBUILDDIR>>/Library/parser/Manual'
find -name X.tex -exec rm -rf {} \;
dh_clean -X./ml/site.ml.orig -X./contrib/tooltool/Makefile.orig \
-X./contrib/tooltool/events.c.orig -X./contrib/tooltool/func_fix.c.orig \
-X./contrib/tooltool/lex.c.orig -X./contrib/tooltool/parse.y.orig \
-X./contrib/tooltool/patchlevel.h.orig -X./contrib/tooltool/windows.c.orig \
-X./contrib/Xhelp/hol_apro.orig -X./contrib/Xhelp/hol_ref.orig \
-X./contrib/Xhelp/xholhelp.h.orig -X./contrib/Xhelp/hol_thm.orig
dh_clean: warning: Compatibility levels before 10 are deprecated (level 9 in use)
for i in $(find Library -name "*.sve") ; do mv $i $(echo $i | sed "s,\.sve,,1"); done
rm -f debian/hol88.install debian/hol88-library.install debian/hol88-source.install debian/hol88-help.install debian/hol88-library-source.install debian/hol88-library-help.install debian/hol88-contrib-source.install debian/hol88-contrib-help.install debian/hol88-doc.install debian/hol88.links debian/hol88-library.links debian/hol88.sh
find -name "*.dvi" -exec rm {} \;
rm -f Manual/Tutorial/ack.tex Manual/Reference/ack.tex Manual/Description/ack.tex
rm -f Manual/Covers/titlepages.ps Manual/Covers/endpages.ps
rm -f bm.l foo* gcl ./lisp/f-ol-syntax.data
cp debian/site_ml_orig ml/site.ml.orig
rm -f Library/finite_sets/Manual/entries.tex \
Library/finite_sets/Manual/theorems.tex \
Library/more_arithmetic/Manual/theorems.tex \
Library/numeral/Manual/theorems.tex \
Library/pred_sets/Manual/entries.tex \
Library/prettyp/Manual/entries.tex \
Library/reals/Manual/theorems.tex \
Library/res_quan/Manual/entries.tex \
Library/sets/Manual/entries.tex \
Library/sets/Manual/theorems.tex \
Library/string/Manual/theorems.tex \
Library/wellorder/Manual/theorems.tex \
Library/word/Manual/theorems.tex \
Manual/Reference/entries.tex \
Manual/Reference/theorems.tex
debian/rules build-arch
dh_testdir
touch configure-stamp
echo '#-native-reloc(bye -1)' | gcl || cat debian/gcl_patch.l debian/gcl_save.l | gcl
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>PATH=$(pwd):$PATH /usr/bin/make all
make[1]: Entering directory '/<<PKGBUILDDIR>>'
date
Thu Jan 19 17:40:35 UTC 2023
/usr/bin/make hol
make[2]: Entering directory '/<<PKGBUILDDIR>>'
if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(compile-file "lisp/f-cl.l") (quit)'\
| gcl; else\
lisp/f-franz; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>
Compiling lisp/f-cl.l.
; (DEFUN SET-FASL-FLAG ...) is being compiled.
;; The variable |%print_fasl-flag| is undefined.
;; The compiler will assume this variable is a global.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-cl.o.
#p"/<<PKGBUILDDIR>>/lisp/f-cl.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-macro.l") (quit)'\
| gcl; else\
lisp/f-macro; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-macro.l.
; (DEFUN EXISTS ...) is being compiled.
;; Warning: The variable IGNORE is not used.
; (DEFUN FORALL ...) is being compiled.
;; Warning: The variable IGNORE is not used.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-macro.o.
#p"/<<PKGBUILDDIR>>/lisp/f-macro.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-system.l") (quit)'\
| gcl; else\
lisp/f-system; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-system.l.
;;; Including lisp/f-macrostart address -T 0x77f550
; (DEFUN FILETOKP ...) is being compiled.
;; Warning: The variable KIND is not used.
;; Warning: The variable TOK is not used.
; (DEFUN COMPILE-LISP ...) is being compiled.
;; Warning: The variable X is not used.
;; Warning: The variable X is not used.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-system.o.
#p"/<<PKGBUILDDIR>>/lisp/f-system.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-help.l") (quit)'\
| gcl; else\
lisp/f-help; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-help.l.
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-help.o.
#p"/<<PKGBUILDDIR>>/lisp/f-help.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-ol-rec.l") (quit)'\
| gcl; else\
lisp/f-ol-rec; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-ol-rec.l.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-ol-rec.o.
#p"/<<PKGBUILDDIR>>/lisp/f-ol-rec.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/genmacs.l") (quit)'\
| gcl; else\
lisp/genmacs; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/genmacs.l.
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x78eed8
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/genmacs.o.
#p"/<<PKGBUILDDIR>>/lisp/genmacs.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/mk-ml.l") (quit)'\
| gcl; else\
lisp/mk-ml; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/mk-ml.l.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/mk-ml.o.
#p"/<<PKGBUILDDIR>>/lisp/mk-ml.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/mk-hol-lcf.l") (quit)'\
| gcl; else\
lisp/mk-hol-lcf; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/mk-hol-lcf.l.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/mk-hol-lcf.o.
#p"/<<PKGBUILDDIR>>/lisp/mk-hol-lcf.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-constants.l") (quit)'\
| gcl; else\
lisp/f-constants; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-constants.l.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-constants.o.
#p"/<<PKGBUILDDIR>>/lisp/f-constants.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-site.l") (quit)'\
| gcl; else\
lisp/f-site; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-site.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-site.o.
#p"/<<PKGBUILDDIR>>/lisp/f-site.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-gp.l") (quit)'\
| gcl; else\
lisp/f-gp; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-gp.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-gp.o.
#p"/<<PKGBUILDDIR>>/lisp/f-gp.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-parser.l") (quit)'\
| gcl; else\
lisp/f-parser; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-parser.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
;; Note: Tail-recursive call of GNC was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-parser.o.
#p"/<<PKGBUILDDIR>>/lisp/f-parser.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-parsml.l") (quit)'\
| gcl; else\
lisp/f-parsml; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-parsml.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
;; Note: Tail-recursive call of ULTABSTR was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-parsml.o.
#p"/<<PKGBUILDDIR>>/lisp/f-parsml.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-mlprin.l") (quit)'\
| gcl; else\
lisp/f-mlprin; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-mlprin.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-mlprin.o.
#p"/<<PKGBUILDDIR>>/lisp/f-mlprin.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-typeml.l") (quit)'\
| gcl; else\
lisp/f-typeml; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-typeml.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
;; Note: Tail-recursive call of TYPING was replaced by iteration.
;; Note: Tail-recursive call of TYPING was replaced by iteration.
;; Note: Tail-recursive call of TYPING was replaced by iteration.
;; Note: Tail-recursive call of TYPING was replaced by iteration.
;; Note: Tail-recursive call of ADJUST-FUNDEF was replaced by iteration.
;; Note: Tail-recursive call of ADJUST-FUNDEF was replaced by iteration.
;; Note: Tail-recursive call of ADJUST-ABSTRACTION was replaced by iteration.
;; Note: Tail-recursive call of IS-LOCAL-CONSTRUCTOR was replaced by iteration.
;; Note: Tail-recursive call of LAYER was replaced by iteration.
;; Note: Tail-recursive call of GETTYPEID was replaced by iteration.
;; Note: Tail-recursive call of MUTANT1 was replaced by iteration.
;; Note: Tail-recursive call of IMMUT was replaced by iteration.
;; Note: Tail-recursive call of ATCH was replaced by iteration.
;; Note: Tail-recursive call of TIDYUP was replaced by iteration.
;; Note: Tail-recursive call of PRINTTYTAIL was replaced by iteration.
;; Note: Tail-recursive call of PRUNE was replaced by iteration.
;; Note: Tail-recursive call of UNIFYTL was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-typeml.o.
#p"/<<PKGBUILDDIR>>/lisp/f-typeml.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-dml.l") (quit)'\
| gcl; else\
lisp/f-dml; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-dml.l.
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-constantsstart address -T 0x799010
End of Pass 1.
;; Note: Tail-recursive call of ML-ORD was replaced by iteration.
;; Note: Tail-recursive call of ML-ORD was replaced by iteration.
End of Pass 2.
/<<PKGBUILDDIR>>/lisp/f-dml.c: In function 'L2':
/<<PKGBUILDDIR>>/lisp/f-dml.c:1129:26: warning: unused variable 'V12' [-Wunused-variable]
1129 | {register object V12;
| ^~~
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-dml.o.
#p"/<<PKGBUILDDIR>>/lisp/f-dml.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-format.l") (quit)'\
| gcl; else\
lisp/f-format; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-format.l.
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-constantsstart address -T 0x799010
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-format.o.
#p"/<<PKGBUILDDIR>>/lisp/f-format.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-tran.l") (quit)'\
| gcl; else\
lisp/f-tran; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-tran.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
;; Note: Tail-recursive call of STORST was replaced by iteration.
;; Note: Tail-recursive call of VARPAT was replaced by iteration.
;; Note: Tail-recursive call of TRE was replaced by iteration.
;; Note: Tail-recursive call of TRE was replaced by iteration.
;; Note: Tail-recursive call of TRE was replaced by iteration.
;; Note: Tail-recursive call of TRE was replaced by iteration.
;; Note: Tail-recursive call of TRE was replaced by iteration.
;; Note: Tail-recursive call of INSERTTRANSFUN was replaced by iteration.
;; Note: Tail-recursive call of FAP was replaced by iteration.
;; Note: Tail-recursive call of CHECKS was replaced by iteration.
End of Pass 2.
/<<PKGBUILDDIR>>/lisp/f-tran.c: In function 'L44':
/<<PKGBUILDDIR>>/lisp/f-tran.c:4173:26: warning: unused variable 'V248' [-Wunused-variable]
4173 | {register object V248;
| ^~~~
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-tran.o.
#p"/<<PKGBUILDDIR>>/lisp/f-tran.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-iox-stand.l") (quit)'\
| gcl; else\
lisp/f-iox-stand; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-iox-stand.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
End of Pass 2.
/<<PKGBUILDDIR>>/lisp/f-iox-stand.c: In function 'L2':
/<<PKGBUILDDIR>>/lisp/f-iox-stand.c:1140:26: warning: unused variable 'V6' [-Wunused-variable]
1140 | {register object V6;
| ^~
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-iox-stand.o.
#p"/<<PKGBUILDDIR>>/lisp/f-iox-stand.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-writml.l") (quit)'\
| gcl; else\
lisp/f-writml; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-writml.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
; (DEFUN ML-PRINT_VOID ...) is being compiled.
;; Warning: The variable IGNORE is not used.
; (DEFUN PRINT_PROD ...) is being compiled.
;; Warning: The variable CL is not used.
; (DEFUN PRINT_CONC ...) is being compiled.
;; Warning: The variable TY is not used.
End of Pass 1.
;; Note: Tail-recursive call of PRLET was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-writml.o.
#p"/<<PKGBUILDDIR>>/lisp/f-writml.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-tml.l") (quit)'\
| gcl; else\
lisp/f-tml; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-tml.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
; (DEFUN HOL-ERR ...) is being compiled.
;; Warning: The variable X is not used.
; (DEFUN OKPASS ...) is being compiled.
;; Warning: The variable ERRTOK is not used.
; (DEFUN ML-COMPILE ...) is being compiled.
;; Warning: The variable $GCPRINT is not used.
End of Pass 1.
;; Note: Tail-recursive call of EXTEND-ENV was replaced by iteration.
;; Note: Tail-recursive call of SETBINDINGS was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-tml.o.
#p"/<<PKGBUILDDIR>>/lisp/f-tml.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-lis.l") (quit)'\
| gcl; else\
lisp/f-lis; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-lis.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-lis.o.
#p"/<<PKGBUILDDIR>>/lisp/f-lis.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-parsol.l") (quit)'\
| gcl; else\
lisp/f-parsol; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-parsol.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
; (DEFUN OLVARINFIX ...) is being compiled.
;; The variable HOL-VAR-BINOPS is undefined.
;; The compiler will assume this variable is a global.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-parsol.o.
#p"/<<PKGBUILDDIR>>/lisp/f-parsol.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-typeol.l") (quit)'\
| gcl; else\
lisp/f-typeol; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-typeol.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
;; Note: Tail-recursive call of HOL-TRUNC was replaced by iteration.
;; Note: Tail-recursive call of HOL-TRUNC was replaced by iteration.
;; Note: Tail-recursive call of CANON-TY was replaced by iteration.
End of Pass 2.
/<<PKGBUILDDIR>>/lisp/f-typeol.c: In function 'L3':
/<<PKGBUILDDIR>>/lisp/f-typeol.c:1217:17: warning: unused variable 'V10' [-Wunused-variable]
1217 | {object V10;
| ^~~
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-typeol.o.
#p"/<<PKGBUILDDIR>>/lisp/f-typeol.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-writol.l") (quit)'\
| gcl; else\
lisp/f-writol; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-writol.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
;;; Including lisp/genmacsstart address -T 0x791d10
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-writol.o.
#p"/<<PKGBUILDDIR>>/lisp/f-writol.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-thyfns.l") (quit)'\
| gcl; else\
lisp/f-thyfns; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-thyfns.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
; (DEFUN OPEN-THY-FILE ...) is being compiled.
;; Warning: The variable ERTOK is not used.
; (DEFUN THY-READ ...) is being compiled.
;; Warning: The variable ERTOK is not used.
; (DEFUN GET-PARENT ...) is being compiled.
;; Warning: The variable PARDATA is not used.
; (DEFUN UNLOAD-THEORY ...) is being compiled.
;; Warning: The variable TOK is not used.
; (DEFUN WRITE-THY-FILE ...) is being compiled.
;; Warning: The variable $GCPRINT is not used.
End of Pass 1.
;; Note: Tail-recursive call of ABS-TYPE was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-thyfns.o.
#p"/<<PKGBUILDDIR>>/lisp/f-thyfns.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-freadth.l") (quit)'\
| gcl; else\
touch lisp/f-freadth.o; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-freadth.l.
;;; Including lisp/f-macrostart address -T 0x77f550
; (DEFUN THY-READ ...) is being compiled.
;; The variable %FAILTOK is undefined.
;; The compiler will assume this variable is a global.
;; Warning: The variable ERTOK is not used.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-freadth.o.
#p"/<<PKGBUILDDIR>>/lisp/f-freadth.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-ol-syntax.l") (quit)'\
| gcl; else\
lisp/f-ol-syntax; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-ol-syntax.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
; (DEFUN Q-MK_EQUIV ...) is being compiled.
;; Warning: The variable TOK is not used.
; (DEFUN Q-MK_INEQUIV ...) is being compiled.
;; Warning: The variable TOK is not used.
; (DEFUN ML-MK_COMB ...) is being compiled.
;; Warning: The variable TOK is not used.
End of Pass 1.
;; Note: Tail-recursive call of PREP-TERM-FN was replaced by iteration.
;; Note: Tail-recursive call of ADD-TERM-LINKS was replaced by iteration.
;; Note: Tail-recursive call of ADD-TYPE-LINKS was replaced by iteration.
;; Note: Tail-recursive call of GET-TYPE-LINKS was replaced by iteration.
;; Note: Tail-recursive call of GET-TERM-LINKS was replaced by iteration.
;; Note: Tail-recursive call of PREP-TY-FN was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-ol-syntax.o.
#p"/<<PKGBUILDDIR>>/lisp/f-ol-syntax.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-subst.l") (quit)'\
| gcl; else\
lisp/f-subst; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-subst.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
;; Note: Tail-recursive call of ALPHA-FM was replaced by iteration.
;; Note: Tail-recursive call of ALPHA-TM was replaced by iteration.
;; Note: Tail-recursive call of VARS-FM was replaced by iteration.
;; Note: Tail-recursive call of VARS-FM was replaced by iteration.
;; Note: Tail-recursive call of VARS-TM was replaced by iteration.
;; Note: Tail-recursive call of VARS-TM was replaced by iteration.
;; Note: Tail-recursive call of VARFILTER was replaced by iteration.
;; Note: Tail-recursive call of FREEIN-FM was replaced by iteration.
;; Note: Tail-recursive call of FREEIN-FM was replaced by iteration.
;; Note: Tail-recursive call of FREEIN-TM was replaced by iteration.
;; Note: Tail-recursive call of FREEIN-TM was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-subst.o.
#p"/<<PKGBUILDDIR>>/lisp/f-subst.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-inst.l") (quit)'\
| gcl; else\
lisp/f-inst; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-inst.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
;; Note: Tail-recursive call of TYPE-IN-FM was replaced by iteration.
;; Note: Tail-recursive call of TYPE-IN-FM was replaced by iteration.
;; Note: Tail-recursive call of TYPE-IN-TM was replaced by iteration.
;; Note: Tail-recursive call of TYPE-IN-TM was replaced by iteration.
;; Note: Tail-recursive call of TYVARS-FM was replaced by iteration.
;; Note: Tail-recursive call of TYVARS-FM was replaced by iteration.
;; Note: Tail-recursive call of TYVARS-TM was replaced by iteration.
;; Note: Tail-recursive call of TYVARS-TM was replaced by iteration.
;; Note: Tail-recursive call of STRIP-PRIMES-AUX was replaced by iteration.
;; Note: Tail-recursive call of TYPEL-IN-TM was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-inst.o.
#p"/<<PKGBUILDDIR>>/lisp/f-inst.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-simpl.l") (quit)'\
| gcl; else\
lisp/f-simpl; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-simpl.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
;; Note: Tail-recursive call of TERM-MATCH was replaced by iteration.
;; Note: Tail-recursive call of PREPARE-SUBSTL was replaced by iteration.
;; Note: Tail-recursive call of PREPARE-INSTTYL was replaced by iteration.
End of Pass 2.
/<<PKGBUILDDIR>>/lisp/f-simpl.c: In function 'L3':
/<<PKGBUILDDIR>>/lisp/f-simpl.c:1402:17: warning: unused variable 'V27' [-Wunused-variable]
1402 | {object V27;
| ^~~
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-simpl.o.
#p"/<<PKGBUILDDIR>>/lisp/f-simpl.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/f-ol-net.l") (quit)'\
| gcl; else\
lisp/f-ol-net; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/f-ol-net.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
;; Note: Tail-recursive call of FOLLOW-FM was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/f-ol-net.o.
#p"/<<PKGBUILDDIR>>/lisp/f-ol-net.o"
NIL
NIL
>echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/mk-ml")'\
'(load "lisp/mk-hol-lcf")'\
'(setq %system-name "HOL-LCF")'\
'(setq %liszt "")'\
'(setq %version "2.02 (GCL)")'\
'(set-make)'\
'(tml)'\
'compile(`ml/ml-curry`,true);;'\
'quit();;'\
| gcl
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/mk-ml"
;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
;; Loading "lisp/f-system"
start address -T 0x76ed08 ;; Finished loading "lisp/f-system"
;; Loading "lisp/f-constants"
start address -T 0x799010 ;; Finished loading "lisp/f-constants"
;; Loading "lisp/f-site"
start address -T 0x7d7f50 ;; Finished loading "lisp/f-site"
;; Loading "lisp/f-gp"
start address -T 0x786b00 ;; Finished loading "lisp/f-gp"
;; Loading "lisp/f-parser"
start address -T 0x7ca0c8 ;; Finished loading "lisp/f-parser"
;; Loading "lisp/f-parsml"
start address -T 0x7713b8 ;; Finished loading "lisp/f-parsml"
;; Loading "lisp/f-mlprin"
start address -T 0x75c9c8 ;; Finished loading "lisp/f-mlprin"
;; Loading "lisp/f-typeml"
start address -T 0x7af1c0 ;; Finished loading "lisp/f-typeml"
;; Loading "lisp/f-dml"
start address -T 0x762538 ;; Finished loading "lisp/f-dml"
;; Loading "lisp/f-format"
start address -T 0x74f300 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-tran"
start address -T 0x8e0008 ;; Finished loading "lisp/f-tran"
;; Loading "lisp/f-iox-stand"
start address -T 0x754fc8 ;; Finished loading "lisp/f-iox-stand"
;; Loading "lisp/f-writml"
start address -T 0x8ea2f0 ;; Finished loading "lisp/f-writml"
;; Loading "lisp/f-tml"
start address -T 0x8edb38 ;; Finished loading "lisp/f-tml"
;; Loading "lisp/f-lis"
start address -T 0x8f7cf8 ;; Finished loading "lisp/f-lis"
;; Loading "lisp/f-ol-rec"
start address -T 0x770378 ;; Finished loading "lisp/f-ol-rec"
;; Loading "lisp/f-help"
start address -T 0x78c368 ;; Finished loading "lisp/f-help"
start address -T 0x7d7a98 ;; Finished loading "lisp/mk-ml"
583
>;; Loading "lisp/mk-hol-lcf"
;; Loading "lisp/f-parsol"
start address -T 0x900ca8 ;; Finished loading "lisp/f-parsol"
;; Loading "lisp/f-typeol"
start address -T 0x905470 ;; Finished loading "lisp/f-typeol"
;; Loading "lisp/f-help"
start address -T 0x7cf8c8 ;; Finished loading "lisp/f-help"
;; Loading "lisp/f-format"
start address -T 0x90b5d0 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-writol"
start address -T 0x90f298 ;; Finished loading "lisp/f-writol"
;; Loading "lisp/f-thyfns"
start address -T 0x914608 ;; Finished loading "lisp/f-thyfns"
;; Loading "lisp/f-freadth"
Warning: lisp/f-freadth.l is redefining function THY-READ
start address -T 0x91f3a8 ;; Finished loading "lisp/f-freadth"
;; Loading "lisp/f-ol-syntax"
start address -T 0x922b78 ;; Finished loading "lisp/f-ol-syntax"
;; Loading "lisp/f-subst"
start address -T 0x92a710 ;; Finished loading "lisp/f-subst"
;; Loading "lisp/f-inst"
start address -T 0x92fc58 ;; Finished loading "lisp/f-inst"
;; Loading "lisp/f-simpl"
start address -T 0x9349b8 ;; Finished loading "lisp/f-simpl"
;; Loading "lisp/f-ol-net"
start address -T 0x937d20 ;; Finished loading "lisp/f-ol-net"
start address -T 0x764650 ;; Finished loading "lisp/mk-hol-lcf"
583
>
"HOL-LCF"
>
""
>
"2.02 (GCL)"
>
NIL
>
HOL-LCF version 2.02 (GCL) created 19/1/23
#
mem = - : (* -> * list -> bool)
map = - : ((* -> **) -> * list -> ** list)
exists = - : ((* -> bool) -> * list -> bool)
forall = - : ((* -> bool) -> * list -> bool)
find = - : ((* -> bool) -> * list -> *)
tryfind = - : ((* -> **) -> * list -> **)
filter = - : ((* -> bool) -> * list -> * list)
mapfilter = - : ((* -> **) -> * list -> ** list)
rev_itlist = - : ((* -> ** -> **) -> * list -> ** -> **)
compiling = false : bool
compiling_stack = [] : bool list
load = - : ((string # bool) -> void)
compile = - : ((string # bool) -> void)
Calling Lisp compiler
File ml/ml-curry compiled
() : void
#echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/mk-ml")'\
'(load "lisp/mk-hol-lcf")'\
'(setq %system-name "HOL-LCF")'\
'(setq %liszt "")'\
'(setq %version "2.02 (GCL)")'\
'(set-make)'\
'(tml)'\
'load(`ml/ml-curry`,false);;'\
'compile(`ml/lis`,true);;'\
'quit();;'\
| gcl
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/mk-ml"
;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
;; Loading "lisp/f-system"
start address -T 0x76ed08 ;; Finished loading "lisp/f-system"
;; Loading "lisp/f-constants"
start address -T 0x799010 ;; Finished loading "lisp/f-constants"
;; Loading "lisp/f-site"
start address -T 0x7d7f50 ;; Finished loading "lisp/f-site"
;; Loading "lisp/f-gp"
start address -T 0x786b00 ;; Finished loading "lisp/f-gp"
;; Loading "lisp/f-parser"
start address -T 0x7ca0c8 ;; Finished loading "lisp/f-parser"
;; Loading "lisp/f-parsml"
start address -T 0x7713b8 ;; Finished loading "lisp/f-parsml"
;; Loading "lisp/f-mlprin"
start address -T 0x75c9c8 ;; Finished loading "lisp/f-mlprin"
;; Loading "lisp/f-typeml"
start address -T 0x7af1c0 ;; Finished loading "lisp/f-typeml"
;; Loading "lisp/f-dml"
start address -T 0x762538 ;; Finished loading "lisp/f-dml"
;; Loading "lisp/f-format"
start address -T 0x74f300 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-tran"
start address -T 0x8e0008 ;; Finished loading "lisp/f-tran"
;; Loading "lisp/f-iox-stand"
start address -T 0x754fc8 ;; Finished loading "lisp/f-iox-stand"
;; Loading "lisp/f-writml"
start address -T 0x8ea2f0 ;; Finished loading "lisp/f-writml"
;; Loading "lisp/f-tml"
start address -T 0x8edb38 ;; Finished loading "lisp/f-tml"
;; Loading "lisp/f-lis"
start address -T 0x8f7cf8 ;; Finished loading "lisp/f-lis"
;; Loading "lisp/f-ol-rec"
start address -T 0x770378 ;; Finished loading "lisp/f-ol-rec"
;; Loading "lisp/f-help"
start address -T 0x78c368 ;; Finished loading "lisp/f-help"
start address -T 0x7d7a98 ;; Finished loading "lisp/mk-ml"
583
>;; Loading "lisp/mk-hol-lcf"
;; Loading "lisp/f-parsol"
start address -T 0x900ca8 ;; Finished loading "lisp/f-parsol"
;; Loading "lisp/f-typeol"
start address -T 0x905470 ;; Finished loading "lisp/f-typeol"
;; Loading "lisp/f-help"
start address -T 0x7cf8c8 ;; Finished loading "lisp/f-help"
;; Loading "lisp/f-format"
start address -T 0x90b5d0 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-writol"
start address -T 0x90f298 ;; Finished loading "lisp/f-writol"
;; Loading "lisp/f-thyfns"
start address -T 0x914608 ;; Finished loading "lisp/f-thyfns"
;; Loading "lisp/f-freadth"
Warning: lisp/f-freadth.l is redefining function THY-READ
start address -T 0x91f3a8 ;; Finished loading "lisp/f-freadth"
;; Loading "lisp/f-ol-syntax"
start address -T 0x922b78 ;; Finished loading "lisp/f-ol-syntax"
;; Loading "lisp/f-subst"
start address -T 0x92a710 ;; Finished loading "lisp/f-subst"
;; Loading "lisp/f-inst"
start address -T 0x92fc58 ;; Finished loading "lisp/f-inst"
;; Loading "lisp/f-simpl"
start address -T 0x9349b8 ;; Finished loading "lisp/f-simpl"
;; Loading "lisp/f-ol-net"
start address -T 0x937d20 ;; Finished loading "lisp/f-ol-net"
start address -T 0x764650 ;; Finished loading "lisp/mk-hol-lcf"
583
>
"HOL-LCF"
>
""
>
"2.02 (GCL)"
>
NIL
>
HOL-LCF version 2.02 (GCL) created 19/1/23
#.............start address -T 0x93f490 () : void
append = - : (* list -> * list -> * list)
itlist = - : ((* -> ** -> **) -> * list -> ** -> **)
end_itlist = - : ((* -> * -> *) -> * list -> *)
assoc = - : (* -> (* # **) list -> (* # **))
rev_assoc = - : (* -> (** # *) list -> (** # *))
intersect = - : (* list -> * list -> * list)
subtract = - : (* list -> * list -> * list)
union = - : (* list -> * list -> * list)
setify = - : (* list -> * list)
split = - : ((* # **) list -> (* list # ** list))
combine = - : ((* list # ** list) -> (* # **) list)
() : void
com = - : ((* list # ** list) -> (* # **) list)
distinct = - : (* list -> bool)
chop_list = - : (int -> * list -> (* list # * list))
last = - : (* list -> *)
butlast = - : (* list -> * list)
partition = - : ((* -> bool) -> * list -> (* list # * list))
replicate = - : (* -> int -> * list)
sort = - : (((* # *) -> bool) -> * list -> * list)
splitp = - : ((* -> bool) -> * list -> (* list # * list))
remove = - : ((* -> bool) -> * list -> (* # * list))
Calling Lisp compiler
File ml/lis compiled
() : void
#echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/mk-ml")'\
'(load "lisp/mk-hol-lcf")'\
'(setq %system-name "HOL-LCF")'\
'(setq %liszt "")'\
'(setq %version "2.02 (GCL)")'\
'(set-make)'\
'(tml)'\
'load(`ml/ml-curry`,false);;'\
'load(`ml/lis`,false);;'\
'compile(`ml/gen`,true);;'\
'quit();;'\
| gcl
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/mk-ml"
;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
;; Loading "lisp/f-system"
start address -T 0x76ed08 ;; Finished loading "lisp/f-system"
;; Loading "lisp/f-constants"
start address -T 0x799010 ;; Finished loading "lisp/f-constants"
;; Loading "lisp/f-site"
start address -T 0x7d7f50 ;; Finished loading "lisp/f-site"
;; Loading "lisp/f-gp"
start address -T 0x786b00 ;; Finished loading "lisp/f-gp"
;; Loading "lisp/f-parser"
start address -T 0x7ca0c8 ;; Finished loading "lisp/f-parser"
;; Loading "lisp/f-parsml"
start address -T 0x7713b8 ;; Finished loading "lisp/f-parsml"
;; Loading "lisp/f-mlprin"
start address -T 0x75c9c8 ;; Finished loading "lisp/f-mlprin"
;; Loading "lisp/f-typeml"
start address -T 0x7af1c0 ;; Finished loading "lisp/f-typeml"
;; Loading "lisp/f-dml"
start address -T 0x762538 ;; Finished loading "lisp/f-dml"
;; Loading "lisp/f-format"
start address -T 0x74f300 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-tran"
start address -T 0x8e0008 ;; Finished loading "lisp/f-tran"
;; Loading "lisp/f-iox-stand"
start address -T 0x754fc8 ;; Finished loading "lisp/f-iox-stand"
;; Loading "lisp/f-writml"
start address -T 0x8ea2f0 ;; Finished loading "lisp/f-writml"
;; Loading "lisp/f-tml"
start address -T 0x8edb38 ;; Finished loading "lisp/f-tml"
;; Loading "lisp/f-lis"
start address -T 0x8f7cf8 ;; Finished loading "lisp/f-lis"
;; Loading "lisp/f-ol-rec"
start address -T 0x770378 ;; Finished loading "lisp/f-ol-rec"
;; Loading "lisp/f-help"
start address -T 0x78c368 ;; Finished loading "lisp/f-help"
start address -T 0x7d7a98 ;; Finished loading "lisp/mk-ml"
583
>;; Loading "lisp/mk-hol-lcf"
;; Loading "lisp/f-parsol"
start address -T 0x900ca8 ;; Finished loading "lisp/f-parsol"
;; Loading "lisp/f-typeol"
start address -T 0x905470 ;; Finished loading "lisp/f-typeol"
;; Loading "lisp/f-help"
start address -T 0x7cf8c8 ;; Finished loading "lisp/f-help"
;; Loading "lisp/f-format"
start address -T 0x90b5d0 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-writol"
start address -T 0x90f298 ;; Finished loading "lisp/f-writol"
;; Loading "lisp/f-thyfns"
start address -T 0x914608 ;; Finished loading "lisp/f-thyfns"
;; Loading "lisp/f-freadth"
Warning: lisp/f-freadth.l is redefining function THY-READ
start address -T 0x91f3a8 ;; Finished loading "lisp/f-freadth"
;; Loading "lisp/f-ol-syntax"
start address -T 0x922b78 ;; Finished loading "lisp/f-ol-syntax"
;; Loading "lisp/f-subst"
start address -T 0x92a710 ;; Finished loading "lisp/f-subst"
;; Loading "lisp/f-inst"
start address -T 0x92fc58 ;; Finished loading "lisp/f-inst"
;; Loading "lisp/f-simpl"
start address -T 0x9349b8 ;; Finished loading "lisp/f-simpl"
;; Loading "lisp/f-ol-net"
start address -T 0x937d20 ;; Finished loading "lisp/f-ol-net"
start address -T 0x764650 ;; Finished loading "lisp/mk-hol-lcf"
583
>
"HOL-LCF"
>
""
>
"2.02 (GCL)"
>
NIL
>
HOL-LCF version 2.02 (GCL) created 19/1/23
#.............start address -T 0x93f490 () : void
......................start address -T 0x9431d0 () : void
words2 = - : (string -> string -> string list)
words = - : (string -> string list)
maptok = - : ((string -> *) -> string -> * list)
loadt = - : (string -> void)
loadf = - : (string -> void)
compilet = - : (string -> void)
compilef = - : (string -> void)
concat = - : (string -> string -> string)
concatl = - : (string list -> string)
() : void
^ = - : (string -> string -> string)
message = - : (string -> void)
() : void
() : void
() : void
() : void
o = - : (((* -> **) # (*** -> *)) -> *** -> **)
CB = - : ((* -> **) -> (** -> ***) -> * -> ***)
# = - : (((* -> **) # (*** -> ****)) -> (* # ***) -> (** # ****))
oo =
-
: ((((* # **) -> ***) # (**** -> *) # (**** -> **)) -> **** -> ***)
I = - : (* -> *)
K = - : (* -> ** -> *)
KI = - : (* -> ** -> **)
C = - : ((* -> ** -> ***) -> ** -> * -> ***)
W = - : ((* -> * -> **) -> * -> **)
B = - : ((* -> **) -> (*** -> *) -> *** -> **)
S = - : ((* -> ** -> ***) -> (* -> **) -> * -> ***)
() : void
Co = - : (((* -> ** -> ***) # (**** -> *)) -> ** -> **** -> ***)
pair = - : (* -> ** -> (* # **))
curry = - : (((* # **) -> ***) -> * -> ** -> ***)
can = - : ((* -> **) -> * -> bool)
assert = - : ((* -> bool) -> * -> *)
syserror = - : (string -> *)
set_fail_prefix = - : (string -> (* -> **) -> * -> **)
set_fail = - : (string -> (* -> **) -> * -> **)
funpow = - : (int -> (* -> *) -> * -> *)
() : void
install = - : (string -> void)
Calling Lisp compiler
File ml/gen compiled
() : void
#sed -e "s;ml/;/<<PKGBUILDDIR>>/ml/;g" \
-e "s;lisp/;/<<PKGBUILDDIR>>/lisp/;g" ml/site.ml.orig > ml/site.ml
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/mk-ml")'\
'(load "lisp/mk-hol-lcf")'\
'(setq %system-name "HOL-LCF")'\
'(setq %liszt "")'\
'(setq %version "2.02 (GCL)")'\
'(set-make)'\
'(tml)'\
'compile(`ml/site`,true);;'\
'quit();;'\
| gcl
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/mk-ml"
;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
;; Loading "lisp/f-system"
start address -T 0x76ed08 ;; Finished loading "lisp/f-system"
;; Loading "lisp/f-constants"
start address -T 0x799010 ;; Finished loading "lisp/f-constants"
;; Loading "lisp/f-site"
start address -T 0x7d7f50 ;; Finished loading "lisp/f-site"
;; Loading "lisp/f-gp"
start address -T 0x786b00 ;; Finished loading "lisp/f-gp"
;; Loading "lisp/f-parser"
start address -T 0x7ca0c8 ;; Finished loading "lisp/f-parser"
;; Loading "lisp/f-parsml"
start address -T 0x7713b8 ;; Finished loading "lisp/f-parsml"
;; Loading "lisp/f-mlprin"
start address -T 0x75c9c8 ;; Finished loading "lisp/f-mlprin"
;; Loading "lisp/f-typeml"
start address -T 0x7af1c0 ;; Finished loading "lisp/f-typeml"
;; Loading "lisp/f-dml"
start address -T 0x762538 ;; Finished loading "lisp/f-dml"
;; Loading "lisp/f-format"
start address -T 0x74f300 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-tran"
start address -T 0x8e0008 ;; Finished loading "lisp/f-tran"
;; Loading "lisp/f-iox-stand"
start address -T 0x754fc8 ;; Finished loading "lisp/f-iox-stand"
;; Loading "lisp/f-writml"
start address -T 0x8ea2f0 ;; Finished loading "lisp/f-writml"
;; Loading "lisp/f-tml"
start address -T 0x8edb38 ;; Finished loading "lisp/f-tml"
;; Loading "lisp/f-lis"
start address -T 0x8f7cf8 ;; Finished loading "lisp/f-lis"
;; Loading "lisp/f-ol-rec"
start address -T 0x770378 ;; Finished loading "lisp/f-ol-rec"
;; Loading "lisp/f-help"
start address -T 0x78c368 ;; Finished loading "lisp/f-help"
start address -T 0x7d7a98 ;; Finished loading "lisp/mk-ml"
583
>;; Loading "lisp/mk-hol-lcf"
;; Loading "lisp/f-parsol"
start address -T 0x900ca8 ;; Finished loading "lisp/f-parsol"
;; Loading "lisp/f-typeol"
start address -T 0x905470 ;; Finished loading "lisp/f-typeol"
;; Loading "lisp/f-help"
start address -T 0x7cf8c8 ;; Finished loading "lisp/f-help"
;; Loading "lisp/f-format"
start address -T 0x90b5d0 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-writol"
start address -T 0x90f298 ;; Finished loading "lisp/f-writol"
;; Loading "lisp/f-thyfns"
start address -T 0x914608 ;; Finished loading "lisp/f-thyfns"
;; Loading "lisp/f-freadth"
Warning: lisp/f-freadth.l is redefining function THY-READ
start address -T 0x91f3a8 ;; Finished loading "lisp/f-freadth"
;; Loading "lisp/f-ol-syntax"
start address -T 0x922b78 ;; Finished loading "lisp/f-ol-syntax"
;; Loading "lisp/f-subst"
start address -T 0x92a710 ;; Finished loading "lisp/f-subst"
;; Loading "lisp/f-inst"
start address -T 0x92fc58 ;; Finished loading "lisp/f-inst"
;; Loading "lisp/f-simpl"
start address -T 0x9349b8 ;; Finished loading "lisp/f-simpl"
;; Loading "lisp/f-ol-net"
start address -T 0x937d20 ;; Finished loading "lisp/f-ol-net"
start address -T 0x764650 ;; Finished loading "lisp/mk-hol-lcf"
583
>
"HOL-LCF"
>
""
>
"2.02 (GCL)"
>
NIL
>
HOL-LCF version 2.02 (GCL) created 19/1/23
#
concat = - : (string -> string -> string)
ml_dir_pathname =
`/<<PKGBUILDDIR>>/ml/`
: string
lisp_dir_pathname =
`/<<PKGBUILDDIR>>/lisp/`
: string
Calling Lisp compiler
File ml/site compiled
() : void
#echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/mk-ml")'\
'(load "lisp/mk-hol-lcf")'\
'(setq %version "2.02 (GCL)")'\
'(set-make)'\
'(tml)'\
'load(`ml/site`,false);;'\
'load(`ml/ml-curry`,false);;'\
'load(`ml/lis`,false);;'\
'load(`ml/gen`,false);;'\
'load(`ml/killpp`,false);;'\
'lisp `(setq %system-name "HOL-LCF")`;;'\
'lisp `(setq %liszt "")`;;'\
'lisp `(setup)`;;' >foo
echo '#+native-reloc(progn (load "foo")(ml-save "hol-lcf"))#-native-reloc(let ((si::*collect-binary-modules* t)(si::*binary-modules* nil)) (load "foo")(compiler::link (remove-duplicates si::*binary-modules* :test (function equal)) "hol-lcf" "(load \"debian/gcl_patch.l\")(load \"foo\")(ml-save \"hol-lcf\")" "" nil)(with-open-file (s "bm.l" :direction :output) (prin1 si::*binary-modules* s)))(quit)' | gcl
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "foo"
;; Loading "lisp/mk-ml"
;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
;; Loading "lisp/f-system"
start address -T 0x759300 ;; Finished loading "lisp/f-system"
;; Loading "lisp/f-constants"
start address -T 0x799010 ;; Finished loading "lisp/f-constants"
;; Loading "lisp/f-site"
start address -T 0x7d8088 ;; Finished loading "lisp/f-site"
;; Loading "lisp/f-gp"
start address -T 0x788b00 ;; Finished loading "lisp/f-gp"
;; Loading "lisp/f-parser"
start address -T 0x7ca0c8 ;; Finished loading "lisp/f-parser"
;; Loading "lisp/f-parsml"
start address -T 0x7713b8 ;; Finished loading "lisp/f-parsml"
;; Loading "lisp/f-mlprin"
start address -T 0x75e9c8 ;; Finished loading "lisp/f-mlprin"
;; Loading "lisp/f-typeml"
start address -T 0x7af1c0 ;; Finished loading "lisp/f-typeml"
;; Loading "lisp/f-dml"
start address -T 0x74d300 ;; Finished loading "lisp/f-dml"
;; Loading "lisp/f-format"
start address -T 0x751418 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-tran"
start address -T 0x8e0008 ;; Finished loading "lisp/f-tran"
;; Loading "lisp/f-iox-stand"
start address -T 0x8e82f0 ;; Finished loading "lisp/f-iox-stand"
;; Loading "lisp/f-writml"
start address -T 0x8ec2f8 ;; Finished loading "lisp/f-writml"
;; Loading "lisp/f-tml"
start address -T 0x8efb40 ;; Finished loading "lisp/f-tml"
;; Loading "lisp/f-lis"
start address -T 0x776990 ;; Finished loading "lisp/f-lis"
;; Loading "lisp/f-ol-rec"
start address -T 0x8fbd00 ;; Finished loading "lisp/f-ol-rec"
;; Loading "lisp/f-help"
start address -T 0x764538 ;; Finished loading "lisp/f-help"
start address -T 0x7d7bd0 ;; Finished loading "lisp/mk-ml"
;; Loading "lisp/mk-hol-lcf"
;; Loading "lisp/f-parsol"
start address -T 0x902b38 ;; Finished loading "lisp/f-parsol"
;; Loading "lisp/f-typeol"
start address -T 0x907300 ;; Finished loading "lisp/f-typeol"
;; Loading "lisp/f-help"
start address -T 0x7cf8c8 ;; Finished loading "lisp/f-help"
;; Loading "lisp/f-format"
start address -T 0x90d460 ;; Finished loading "lisp/f-format"
;; Loading "lisp/f-writol"
start address -T 0x911128 ;; Finished loading "lisp/f-writol"
;; Loading "lisp/f-thyfns"
start address -T 0x916498 ;; Finished loading "lisp/f-thyfns"
;; Loading "lisp/f-freadth"
Warning: lisp/f-freadth.l is redefining function THY-READ
start address -T 0x921238 ;; Finished loading "lisp/f-freadth"
;; Loading "lisp/f-ol-syntax"
start address -T 0x924a08 ;; Finished loading "lisp/f-ol-syntax"
;; Loading "lisp/f-subst"
start address -T 0x92c5a0 ;; Finished loading "lisp/f-subst"
;; Loading "lisp/f-inst"
start address -T 0x931c20 ;; Finished loading "lisp/f-inst"
;; Loading "lisp/f-simpl"
start address -T 0x936ab8 ;; Finished loading "lisp/f-simpl"
;; Loading "lisp/f-ol-net"
start address -T 0x939e20 ;; Finished loading "lisp/f-ol-net"
start address -T 0x777ce8 ;; Finished loading "lisp/mk-hol-lcf"
<system name> version 2.02 (GCL) created 19/1/23
#...start address -T 0x941590 () : void
.............start address -T 0x943bc0 () : void
......................start address -T 0x947900 () : void
..................................start address -T 0x94e8c0 () : void
............() : void
#() : void
() : void
() : void
#;; Finished loading "foo"
=======> hol-lcf made
if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/genfns.l") (quit)'\
| gcl; else\
lisp/genfns; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/genfns.l.
;;; Including lisp/f-macrostart address -T 0x77f550
End of Pass 1.
;; Note: Tail-recursive call of SEG was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/genfns.o.
#p"/<<PKGBUILDDIR>>/lisp/genfns.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/gnt.l") (quit)'\
| gcl; else\
lisp/gnt; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/gnt.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/gnt.o.
#p"/<<PKGBUILDDIR>>/lisp/gnt.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/hol-pars.l") (quit)'\
| gcl; else\
lisp/hol-pars; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/hol-pars.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
;;; Including lisp/genmacsstart address -T 0x791d10
; (DEFUN LAMQ-RTN ...) is being compiled.
;; Warning: The variable CONSTR is not used.
End of Pass 1.
;; Note: Tail-recursive call of BUILD-LAM-STRUC was replaced by iteration.
;; Note: Tail-recursive call of BUILD-LAM-STRUC was replaced by iteration.
;; Note: Tail-recursive call of DISTINCTP was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/hol-pars.o.
#p"/<<PKGBUILDDIR>>/lisp/hol-pars.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/parslist.l") (quit)'\
| gcl; else\
lisp/parslist; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/parslist.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
;;; Including lisp/genmacsstart address -T 0x791d10
; (DEFUN HOL-SCOLONSETUP ...) is being compiled.
;; The variable %HOL-LIST-DEPTH is undefined.
;; The compiler will assume this variable is a global.
; (DEFUN ML-DEFINE_FINITE_SET_SYNTAX ...) is being compiled.
;; The variable |%print_set-flag| is undefined.
;; The compiler will assume this variable is a global.
;; Warning: The variable SET-PROP is not used.
; (DEFUN ML-DEFINE_SET_ABSTRACTION_SYNTAX ...) is being compiled.
;; Warning: The variable SET-PROP is not used.
End of Pass 1.
;; Note: Tail-recursive call of GET-FREES-IN-PT was replaced by iteration.
;; Note: Tail-recursive call of INTERSECT was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/parslist.o.
#p"/<<PKGBUILDDIR>>/lisp/parslist.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/parslet.l") (quit)'\
| gcl; else\
lisp/parslet; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/parslet.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/parslet.o.
#p"/<<PKGBUILDDIR>>/lisp/parslet.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/constp.l") (quit)'\
| gcl; else\
lisp/constp; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/constp.l.
End of Pass 1.
;; Note: Tail-recursive call of TEST-LIST-ELS was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/constp.o.
#p"/<<PKGBUILDDIR>>/lisp/constp.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/hol-writ.l") (quit)'\
| gcl; else\
lisp/hol-writ; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/hol-writ.l.
;;; Including lisp/f-constantsstart address -T 0x798fe8
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x790ed8
;;; Including lisp/genmacsstart address -T 0x791d10
; (DEFUN PREP-TM ...) is being compiled.
;; The variable %EMPTY-SET is undefined.
;; The compiler will assume this variable is a global.
; (DEFUN PRINT-TM ...) is being compiled.
;; The variable HOL-VAR-BINOPS is undefined.
;; The compiler will assume this variable is a global.
; (DEFUN IS-OL-SET-CONS ...) is being compiled.
;; The variable %FINITE-SET-CONSTRUCTOR is undefined.
;; The compiler will assume this variable is a global.
; (DEFUN PREP-OL-SET-ABSTRACTION ...) is being compiled.
;; The variable %SET-ABSTRACTION-CONSTRUCTOR is undefined.
;; The compiler will assume this variable is a global.
; (DEFUN PREP-OL-QUANT ...) is being compiled.
;; Warning: The variable TY is not used.
; (DEFUN PREP-OL-RESTRICT ...) is being compiled.
;; Warning: The variable TY is not used.
; (DEFUN PREP-OL-UNOP ...) is being compiled.
;; Warning: The variable TY is not used.
; (DEFUN PREP-OL-BINOP ...) is being compiled.
;; Warning: The variable TY is not used.
; (DEFUN ML-PRINT_THM ...) is being compiled.
;; Warning: The variable X is not used.
;; The variable %MARGIN is undefined.
;; The compiler will assume this variable is a global.
End of Pass 1.
;; Note: Tail-recursive call of SUBTRACT was replaced by iteration.
;; Note: Tail-recursive call of IS-SUBSET was replaced by iteration.
;; Note: Tail-recursive call of IS-OL-LIST was replaced by iteration.
;; Note: Tail-recursive call of IS-OL-FINITE-SET was replaced by iteration.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/hol-writ.o.
#p"/<<PKGBUILDDIR>>/lisp/hol-writ.o"
NIL
NIL
>if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/mk_pp_thm.l") (quit)'\
| gcl; else\
lisp/mk_pp_thm; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/mk_pp_thm.l.
;;; Including lisp/f-macrostart address -T 0x77f550
;;; Including lisp/f-ol-recstart address -T 0x78eed8
;;; Including lisp/genmacsstart address -T 0x791d10
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/mk_pp_thm.o.
#p"/<<PKGBUILDDIR>>/lisp/mk_pp_thm.o"
NIL
NIL
>cd /<<PKGBUILDDIR>>/theories; rm -f PPLAMB.th;\
/<<PKGBUILDDIR>>/hol-lcf < /<<PKGBUILDDIR>>/theories/mk_PPLAMB.ml;\
cd /<<PKGBUILDDIR>>
HOL-LCF version 2.02 (GCL) created 19/1/23
###########################() : void
##() : void
##() : void
##=======> theory PPLAMB built
cd /<<PKGBUILDDIR>>/theories; rm -f bool.th;\
/<<PKGBUILDDIR>>/hol-lcf < /<<PKGBUILDDIR>>/theories/mk_bool.ml;\
cd /<<PKGBUILDDIR>>
HOL-LCF version 2.02 (GCL) created 19/1/23
################################################################################################() : void
##Theory PPLAMB loaded
() : void
##() : void
##() : void
##() : void
#####|-"HOL_ASSERT $= = $=" : thm
###
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
........() : void
...................................................................................................................................() : void
File /<<PKGBUILDDIR>>/ml/hol-in-out loaded
() : void
###() : void
##() : void
##() : void
##() : void
##############() : void
##|- T = ((\x. x) = (\x. x))
##() : void
##|- $! = (\P. P = (\x. T))
###########|- $? = (\P. P($@ P))
##() : void
##|- $/\ = (\t1 t2. !t. (t1 ==> t2 ==> t) ==> t)
##() : void
##|- $\/ = (\t1 t2. !t. (t1 ==> t) ==> (t2 ==> t) ==> t)
############|- F = (!t. t)
##() : void
##|- $~ = (\t. t ==> F)
##() : void
####|- $?! = (\P. $? P /\ (!x y. P x /\ P y ==> (x = y)))
##|- LET = (\f x. f x)
###|- COND =
(\t t1 t2. @x. ((t = T) ==> (x = t1)) /\ ((t = F) ==> (x = t2)))
#######|- !P B. RES_FORALL P B = (!x. P x ==> B x)
###|- !P B. RES_EXISTS P B = (?x. P x /\ B x)
###|- !P B. RES_SELECT P B = (@x. P x /\ B x)
###|- ARB = (@x. T)
###|- !P B. RES_ABSTRACT P B = (\x. (P x => B x | ARB))
###########|- !f. ONE_ONE f = (!x1 x2. (f x1 = f x2) ==> (x1 = x2))
###|- !f. ONTO f = (!y. ?x. y = f x)
###############[|- !t. (t = T) \/ (t = F);
|- !t1 t2. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 = t2);
|- !t. (\x. t x) = t;
|- !P x. P x ==> P($@ P)]
: thm list
#########|- !t1 t2. t1 IS_ASSUMPTION_OF t2 = t1 ==> t2
##########|- !P rep.
TYPE_DEFINITION P rep =
(!x' x''. (rep x' = rep x'') ==> (x' = x'')) /\
(!x. P x = (?x'. x = rep x'))
######MK_PAIR_DEF = |- !x y. MK_PAIR x y = (\a b. (a = x) /\ (b = y))
###IS_PAIR_DEF = |- !p. IS_PAIR p = (?x y. p = MK_PAIR x y)
#########################################PAIR_EXISTS = |- ?p. IS_PAIR p
####|- ?rep. TYPE_DEFINITION IS_PAIR rep
###########|- REP_prod =
(@rep.
(!p' p''. (rep p' = rep p'') ==> (p' = p'')) /\
(!p. IS_PAIR p = (?p'. p = rep p')))
##() : void
###|- !x y. x,y = (@p. REP_prod p = MK_PAIR x y)
###|- !p. FST p = (@x. ?y. MK_PAIR x y = REP_prod p)
###|- !p. SND p = (@y. ?x. MK_PAIR x y = REP_prod p)
##########[|- !x. FST x,SND x = x; |- !x y. FST(x,y) = x; |- !x y. SND(x,y) = y]
: thm list
#############################PAIR_EQ = |- !x y a b. (x,y = a,b) = (x = a) /\ (y = b)
#####|- !f x y. UNCURRY f(x,y) = f x y
###|- !f x y. CURRY f x y = f(x,y)
##() : void
##=======> theory bool built
cd /<<PKGBUILDDIR>>/theories; rm -f ind.th;\
/<<PKGBUILDDIR>>/hol-lcf < /<<PKGBUILDDIR>>/theories/mk_ind.ml;\
cd /<<PKGBUILDDIR>>
HOL-LCF version 2.02 (GCL) created 19/1/23
############################() : void
##Theory bool loaded
() : void
##() : void
##
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
........() : void
...................................................................................................................................() : void
File /<<PKGBUILDDIR>>/ml/hol-in-out loaded
() : void
##|- ?f. ONE_ONE f /\ ~ONTO f
##() : void
##=======> theory ind built
cd /<<PKGBUILDDIR>>/theories; rm -f BASIC-HOL.th;\
/<<PKGBUILDDIR>>/hol-lcf < /<<PKGBUILDDIR>>/theories/mk_BASIC-HOL.ml;\
cd /<<PKGBUILDDIR>>
HOL-LCF version 2.02 (GCL) created 19/1/23
############################Theory ind loaded
() : void
###.....................................................................................................................................................() : void
####.............() : void
#...................................................................................() : void
#............................() : void
##() : void
#####() : void
##################TYPE_DEFINITION =
|- !P rep.
TYPE_DEFINITION P rep =
(!x' x''. (rep x' = rep x'') ==> (x' = x'')) /\
(!x. P x = (?x'. x = rep x'))
#############################ABS_REP_THM =
|- !P.
(?rep. TYPE_DEFINITION P rep) ==>
(?rep abs. (!a. abs(rep a) = a) /\ (!r. P r = (rep(abs r) = r)))
###|- !P.
(?rep. TYPE_DEFINITION P rep) ==>
(?rep abs. (!a. abs(rep a) = a) /\ (!r. P r = (rep(abs r) = r)))
##=======> theory BASIC-HOL built
echo 'compilet `ml/genfns`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#
map2 = - : (((* # **) -> ***) -> (* list # ** list) -> *** list)
itlist2 =
-
: (((* # **) -> *** -> ***) -> (* list # ** list) -> *** -> ***)
set_equal = - : (* list -> * list -> bool)
el = - : (int -> * list -> *)
word_separators = [` `; `
`] : string list
words = - : (string -> string list)
maptok = - : ((string -> *) -> string -> * list)
uncurry = - : ((* -> ** -> ***) -> (* # **) -> ***)
Calling Lisp compiler
File ml/genfns compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'lisp `(load "lisp/genfns")`;;'\
'lisp `(load "lisp/gnt")`;;'\
'lisp `(load "lisp/hol-pars")`;;'\
'lisp `(load "lisp/parslist")`;;'\
'lisp `(load "lisp/parslet")`;;'\
'lisp `(load "lisp/constp")`;;'\
'lisp `(load "lisp/hol-writ")`;;'\
'lisp `(load "lisp/mk_pp_thm")`;;'\
'compilet `ml/hol-syn`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
New constructors declared:
AssumeStep : (term -> step)
ReflStep : (term -> step)
SubstStep : (((thm # term) list # term # thm) -> step)
BetaConvStep : (term -> step)
AbsStep : ((term # thm) -> step)
InstTypeStep : (((type # type) list # thm) -> step)
DischStep : ((term # thm) -> step)
MpStep : ((thm # thm) -> step)
MkCombStep : ((thm # thm) -> step)
MkAbsStep : (thm -> step)
AlphaStep : ((term # term) -> step)
AddAssumStep : ((term # thm) -> step)
SymStep : (thm -> step)
TransStep : ((thm # thm) -> step)
ImpTransStep : ((thm # thm) -> step)
ApTermStep : ((term # thm) -> step)
ApThmStep : ((thm # term) -> step)
EqMpStep : ((thm # thm) -> step)
EqImpRuleStep : (thm -> step)
SpecStep : ((term # thm) -> step)
EqtIntroStep : (thm -> step)
GenStep : ((term # thm) -> step)
EtaConvStep : (term -> step)
ExtStep : (thm -> step)
ExistsStep : (((term # term) # thm) -> step)
ChooseStep : (((term # thm) # thm) -> step)
ImpAntisymRuleStep : ((thm # thm) -> step)
MkExistsStep : (thm -> step)
SubsStep : ((thm list # thm) -> step)
SubsOccsStep : (((int list # thm) list # thm) -> step)
SubstConvStep : (((thm # term) list # term # term) -> step)
ConjStep : ((thm # thm) -> step)
Conjunct1Step : (thm -> step)
Conjunct2Step : (thm -> step)
Disj1Step : ((thm # term) -> step)
Disj2Step : ((term # thm) -> step)
DisjCasesStep : ((thm # thm # thm) -> step)
NotIntroStep : (thm -> step)
NotElimStep : (thm -> step)
ContrStep : ((term # thm) -> step)
CcontrStep : ((term # thm) -> step)
InstStep : (((term # term) list # thm) -> step)
StoreDefinitionStep : ((string # term) -> step)
DefinitionStep : ((string # string) -> step)
DefExistsRuleStep : (term -> step)
NewAxiomStep : ((string # term) -> step)
AxiomStep : ((string # string) -> step)
TheoremStep : ((string # string) -> step)
NewConstantStep : ((string # type) -> step)
NewTypeStep : ((int # string) -> step)
NumConvStep : (term -> step)
steplist = [] : step list
record_proof_flag = false : bool
suspended = false : bool
is_recording_proof = - : (void -> bool)
record_proof = - : (bool -> void)
suspend_recording = - : (* -> void)
resume_recording = - : (* -> void)
RecordStep = - : (step -> void)
get_steps = - : (void -> step list)
((-), (-), (-), (-), (-), -)
: ((bool -> void) #
(void -> bool) #
(step -> void) #
(void -> step list) #
(* -> void) #
(** -> void))
record_proof = - : (bool -> void)
is_recording_proof = - : (void -> bool)
RecordStep = - : (step -> void)
get_steps = - : (void -> step list)
suspend_recording = - : (* -> void)
resume_recording = - : (* -> void)
new_constant = - : ((string # type) -> void)
arb_term = "arb" : term
ARB_THM = |- $= = $=
falsity = "F" : term
bool_ty = ":bool" : type
mk_forall = - : ((term # term) -> term)
mk_exists = - : ((term # term) -> term)
mk_select = - : ((term # term) -> term)
mk_conj = - : ((term # term) -> term)
mk_disj = - : ((term # term) -> term)
mk_imp = - : ((term # term) -> term)
mk_eq = - : ((term # term) -> term)
mk_pair = - : ((term # term) -> term)
mk_neg = - : (term -> term)
dest_forall = - : (term -> (term # term))
dest_exists = - : (term -> (term # term))
dest_select = - : (term -> (term # term))
dest_conj = - : (term -> (term # term))
dest_disj = - : (term -> (term # term))
dest_eq = - : (term -> (term # term))
dest_pair = - : (term -> (term # term))
dest_imp = - : (term -> (term # term))
dest_neg = - : (term -> term)
dest_neg_imp = - : (term -> (term # term))
dest_form = - : (form -> term)
mk_form = - : (term -> form)
mk_thm = - : ((term list # term) -> thm)
dest_thm = - : (thm -> (term list # term))
hyp = - : (thm -> term list)
concl = - : (thm -> term)
hyp_union = - : (thm list -> term list)
is_forall = - : (term -> bool)
is_exists = - : (term -> bool)
is_select = - : (term -> bool)
is_conj = - : (term -> bool)
is_disj = - : (term -> bool)
is_imp = - : (term -> bool)
is_eq = - : (term -> bool)
is_pair = - : (term -> bool)
is_neg = - : (term -> bool)
is_neg_imp = - : (term -> bool)
aconv = - : (term -> term -> bool)
subst = - : ((term # term) list -> term -> term)
subst_occs = - : (int list list -> (term # term) list -> term -> term)
free_in = - : (term -> term -> bool)
variant = - : (term list -> term -> term)
type_in_type = - : (type -> type -> bool)
type_in = - : (type -> term -> bool)
inst_type = - : ((type # type) list -> type -> type)
inst = - : (term list -> (type # type) list -> term -> term)
match = - : (term -> term -> ((term # term) list # (type # type) list))
freesl = - : (term list -> term list)
varsl = - : (term list -> term list)
tyvarsl = - : (term list -> type list)
thm_frees = - : (thm -> term list)
disch = - : ((term # term list) -> term list)
is_pred = - : (term -> bool)
mk_pred = - : ((string # term) -> term)
dest_pred = - : (term -> (string # term))
list_mk_abs = - : ((term list # term) -> term)
list_mk_comb = - : ((term # term list) -> term)
list_mk_conj = - : (term list -> term)
list_mk_disj = - : (term list -> term)
list_mk_imp = - : ((term list # term) -> term)
list_mk_forall = - : ((term list # term) -> term)
list_mk_exists = - : ((term list # term) -> term)
list_mk_pair = - : (term list -> term)
strip_abs = - : (term -> (term list # term))
strip_comb = - : (term -> (term # term list))
conjuncts = - : (term -> term list)
disjuncts = - : (term -> term list)
strip_imp = - : (term -> (term list # term))
strip_forall = - : (term -> (term list # term))
strip_exists = - : (term -> (term list # term))
strip_pair = - : (term -> term list)
mk_cond = - : ((term # term # term) -> term)
is_cond = - : (term -> bool)
dest_cond = - : (term -> (term # term # term))
dest_let = - : (term -> (term # term))
mk_let = - : ((term # term) -> term)
is_let = - : (term -> bool)
mk_cons = - : ((term # term) -> term)
dest_cons = - : (term -> (term # term))
is_cons = - : (term -> bool)
mk_list = - : ((term list # type) -> term)
dest_list = - : (term -> (term list # type))
is_list = - : (term -> bool)
mk_pabs = - : ((term # term) -> term)
dest_pabs = - : (term -> (term # term))
is_pabs = - : (term -> bool)
lhs = - : (term -> term)
rhs = - : (term -> term)
find_term = - : ((term -> bool) -> term -> term)
rator = - : (term -> term)
rand = - : (term -> term)
bndvar = - : (term -> term)
body = - : (term -> term)
find_terms = - : ((term -> bool) -> term -> term list)
mk_primed_var = - : ((string # type) -> term)
new_axiom = - : ((string # term) -> thm)
new_open_axiom = - : ((string # term) -> thm)
new_predicate = - : ((string # type) -> void)
mk_definition = - : (term -> term)
dest_definition = - : (term -> term)
is_definition = - : (term -> bool)
store_definition = - : ((string # term) -> thm)
theorem = - : (string -> string -> thm)
new_type = - : (int -> string -> void)
delete_thm = - : (string -> string -> thm)
pp_axiom = - : (string -> string -> thm)
axiom = - : (string -> string -> thm)
definition = - : (string -> string -> thm)
new_infix = - : ((string # type) -> void)
store_binders = - : (term list -> thm)
list_of_binders = [] : term list
new_binder = - : ((string # type) -> void)
n_strip_quant = - : ((* -> (** # *)) -> int -> * -> (** list # *))
is_infix_type = - : (type -> bool)
is_binder_type = - : (type -> bool)
check_specification =
-
: (* -> (string # string) list -> thm -> (term list # term))
new_specification = - : (string -> (string # string) list -> thm -> thm)
check_varstruct = - : (term -> term list)
check_lhs = - : (term -> term list)
get_type = - : (term -> type -> type)
DEF_EXISTS_RULE = - : (term -> thm)
new_gen_definition = - : (string -> (string # term) -> thm)
new_definition = - : ((string # term) -> thm)
new_infix_definition = - : ((string # term) -> thm)
new_theory = - : (string -> void)
close_theory = - : (void -> void)
binders = - : (string -> term list)
activate_binders = - : (string -> string list)
ancestors = - : (string -> string list)
thy_chked = [] : string list
activate_all_binders = - : (string -> string list)
load_theory = - : (string -> void)
extend_theory = - : (string -> void)
new_parent = - : (string -> void)
((-), (-), -) : ((string -> void) # (string -> void) # (string -> void))
load_theory = - : (string -> void)
extend_theory = - : (string -> void)
new_parent = - : (string -> void)
new_binder_definition = - : ((string # term) -> thm)
new_type_definition = - : ((string # term # thm) -> thm)
ML_eval = - : (string -> void)
New constructors declared:
preterm_var : (string -> preterm)
preterm_const : (string -> preterm)
preterm_comb : ((preterm # preterm) -> preterm)
preterm_abs : ((preterm # preterm) -> preterm)
preterm_typed : ((preterm # type) -> preterm)
preterm_antiquot : (term -> preterm)
preterm_to_term = - : (preterm -> term)
Calling Lisp compiler
File ml/hol-syn compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/hol-rule`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
T_DEF = |- T = ((\x. x) = (\x. x))
F_DEF = |- F = (!t. t)
FORALL_DEF = |- $! = (\P. P = (\x. T))
AND_DEF = |- $/\ = (\t1 t2. !t. (t1 ==> t2 ==> t) ==> t)
OR_DEF = |- $\/ = (\t1 t2. !t. (t1 ==> t) ==> (t2 ==> t) ==> t)
EXISTS_DEF = |- $? = (\P. P($@ P))
NOT_DEF = |- $~ = (\t. t ==> F)
EXISTS_UNIQUE_DEF = |- ?! = (\P. $? P /\ (!x y. P x /\ P y ==> (x = y)))
LET_DEF = |- LET = (\f x. f x)
UNCURRY_DEF = |- !f x y. UNCURRY f(x,y) = f x y
CURRY_DEF = |- !f x y. CURRY f x y = f(x,y)
COND_DEF =
|- COND =
(\t t1 t2. @x. ((t = T) ==> (x = t1)) /\ ((t = F) ==> (x = t2)))
TYPE_DEFINITION =
|- !P rep.
TYPE_DEFINITION P rep =
(!x' x''. (rep x' = rep x'') ==> (x' = x'')) /\
(!x. P x = (?x'. x = rep x'))
BOOL_CASES_AX = |- !t. (t = T) \/ (t = F)
IMP_ANTISYM_AX = |- !t1 t2. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 = t2)
ETA_AX = |- !t. (\x. t x) = t
SELECT_AX = |- !P x. P x ==> P($@ P)
PAIR = |- !x. FST x,SND x = x
FST = |- !x y. FST(x,y) = x
SND = |- !x y. SND(x,y) = y
PAIR_EQ = |- !x y a b. (x,y = a,b) = (x = a) /\ (y = b)
ASSUME = - : (term -> thm)
REFL = - : (term -> thm)
SUBST = - : ((thm # term) list -> term -> thm -> thm)
BETA_CONV = - : (term -> thm)
ABS = - : (term -> thm -> thm)
INST_TYPE = - : ((type # type) list -> thm -> thm)
DISCH = - : (term -> thm -> thm)
MP = - : (thm -> thm -> thm)
Calling Lisp compiler
File ml/hol-rule compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/hol-drule`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
ADD_ASSUM = - : (term -> thm -> thm)
SYM = - : (thm -> thm)
() : void
TRANS = - : (thm -> thm -> thm)
IMP_TRANS = - : (thm -> thm -> thm)
AP_TERM = - : (term -> thm -> thm)
AP_THM = - : (thm -> term -> thm)
EQ_MP = - : (thm -> thm -> thm)
EQ_IMP_RULE = - : (thm -> (thm # thm))
TRUTH = |- T
EQT_ELIM = - : (thm -> thm)
SPEC = - : (term -> thm -> thm)
SPECL = - : (term list -> thm -> thm)
EQT_INTRO = - : (thm -> thm)
GEN = - : (term -> thm -> thm)
GENL = - : (term list -> thm -> thm)
ETA_CONV = - : (term -> thm)
EXT = - : (thm -> thm)
SELECT_INTRO = - : (thm -> thm)
SELECT_ELIM = - : (thm -> (term # thm) -> thm)
EXISTS = - : ((term # term) -> thm -> thm)
CHOOSE = - : ((term # thm) -> thm -> thm)
SELECT_RULE = - : (thm -> thm)
IMP_ANTISYM_RULE = - : (thm -> thm -> thm)
MK_EXISTS = - : (thm -> thm)
LIST_MK_EXISTS = - : (term list -> thm -> thm)
FORALL_EQ = - : (term -> thm -> thm)
EXISTS_EQ = - : (term -> thm -> thm)
SELECT_EQ = - : (term -> thm -> thm)
SUBS = - : (thm list -> thm -> thm)
SUBS_OCCS = - : ((int list # thm) list -> thm -> thm)
SUBST_CONV = - : ((thm # term) list -> term -> term -> thm)
RIGHT_BETA = - : (thm -> thm)
LIST_BETA_CONV = - : (term -> thm)
RIGHT_LIST_BETA = - : (thm -> thm)
AND_INTRO_THM = |- !t1 t2. t1 ==> t2 ==> t1 /\ t2
CONJ = - : (thm -> thm -> thm)
AND1_THM = |- !t1 t2. t1 /\ t2 ==> t1
CONJUNCT1 = - : (thm -> thm)
AND2_THM = |- !t1 t2. t1 /\ t2 ==> t2
CONJUNCT2 = - : (thm -> thm)
CONJ_SYM = |- !t1 t2. t1 /\ t2 = t2 /\ t1
CONJ_ASSOC = |- !t1 t2 t3. t1 /\ t2 /\ t3 = (t1 /\ t2) /\ t3
CONJUNCTS_CONV = - : ((term # term) -> thm)
CONJ_SET_CONV = - : (term list -> term list -> thm)
FRONT_CONJ_CONV = - : (term list -> term -> thm)
CONJ_DISCH = - : (term -> thm -> thm)
CONJ_DISCHL = - : (term list -> thm -> thm)
OR_INTRO_THM1 = |- !t1 t2. t1 ==> t1 \/ t2
DISJ1 = - : (thm -> term -> thm)
OR_INTRO_THM2 = |- !t1 t2. t2 ==> t1 \/ t2
DISJ2 = - : (term -> thm -> thm)
OR_ELIM_THM = |- !t t1 t2. t1 \/ t2 ==> (t1 ==> t) ==> (t2 ==> t) ==> t
DISJ_CASES = - : (thm -> thm -> thm -> thm)
FALSITY = |- !t. F ==> t
IMP_F = |- !t. (t ==> F) ==> ~t
NOT_INTRO = - : (thm -> thm)
NEG_DISCH = - : (term -> thm -> thm)
F_IMP = |- !t. ~t ==> t ==> F
NOT_MP = - : (thm -> thm -> thm)
UNDISCH = - : (thm -> thm)
NOT_ELIM = - : (thm -> thm)
NOT_EQ_SYM = - : (thm -> thm)
AND_CLAUSES =
|- !t.
(T /\ t = t) /\
(t /\ T = t) /\
(F /\ t = F) /\
(t /\ F = F) /\
(t /\ t = t)
OR_CLAUSES =
|- !t.
(T \/ t = T) /\
(t \/ T = T) /\
(F \/ t = t) /\
(t \/ F = t) /\
(t \/ t = t)
IMP_CLAUSES =
|- !t.
(T ==> t = t) /\
(t ==> T = T) /\
(F ==> t = T) /\
(t ==> t = T) /\
(t ==> F = ~t)
CONTR = - : (term -> thm -> thm)
EQF_INTRO = - : (thm -> thm)
EQF_ELIM = - : (thm -> thm)
EXCLUDED_MIDDLE = |- !t. t \/ ~t
CCONTR = - : (term -> thm -> thm)
INST = - : ((term # term) list -> thm -> thm)
NOT_F = |- !t. ~t ==> (t = F)
NOT_AND = |- ~(t /\ ~t)
OR_IMP_THM = |- !t1 t2. (t1 = t2 \/ t1) = t2 ==> t1
NOT_IMP = |- !t1 t2. ~(t1 ==> t2) = t1 /\ ~t2
DISJ_ASSOC = |- !t1 t2 t3. t1 \/ t2 \/ t3 = (t1 \/ t2) \/ t3
DISJ_SYM = |- !t1 t2. t1 \/ t2 = t2 \/ t1
DE_MORGAN_THM =
|- !t1 t2. (~(t1 /\ t2) = ~t1 \/ ~t2) /\ (~(t1 \/ t2) = ~t1 /\ ~t2)
ISPEC = - : (term -> thm -> thm)
ISPECL = - : (term list -> thm -> thm)
SELECT_REFL = |- !x. (@y. y = x) = x
SELECT_UNIQUE = |- !P x. (!y. P y = (y = x)) ==> ($@ P = x)
Calling Lisp compiler
File ml/hol-drule compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/drul`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
GEN_ALL = - : (thm -> thm)
DISCH_ALL = - : (thm -> thm)
SPEC_VAR = - : (thm -> (term # thm))
UNDISCH_ALL = - : (thm -> thm)
SPEC_ALL = - : (thm -> thm)
PROVE_HYP = - : (thm -> thm -> thm)
CONJ_PAIR = - : (thm -> (thm # thm))
LIST_CONJ = - : (thm list -> thm)
CONJ_LIST = - : (int -> thm -> thm list)
CONJUNCTS = - : (thm -> thm list)
BODY_CONJUNCTS = - : (thm -> thm list)
IMP_CANON = - : (thm -> thm list)
LIST_MP = - : (thm list -> thm -> thm)
CONTRAPOS = - : (thm -> thm)
DISJ_IMP = - : (thm -> thm)
IMP_ELIM = - : (thm -> thm)
NOT_CLAUSES = |- (!t. ~~t = t) /\ (~T = F) /\ (~F = T)
DISJ_CASES_UNION = - : (thm -> thm -> thm -> thm)
EQ_REFL = |- !x. x = x
REFL_CLAUSE = |- !x. (x = x) = T
EQ_SYM = |- !x y. (x = y) ==> (y = x)
EQ_SYM_EQ = |- !x y. (x = y) = (y = x)
EQ_EXT = |- !f g. (!x. f x = g x) ==> (f = g)
EQ_TRANS = |- !x y z. (x = y) /\ (y = z) ==> (x = z)
BOOL_EQ_DISTINCT = |- ~(T = F) /\ ~(F = T)
EQ_CLAUSES =
|- !t.
((T = t) = t) /\ ((t = T) = t) /\ ((F = t) = ~t) /\ ((t = F) = ~t)
MK_COMB = - : ((thm # thm) -> thm)
MK_ABS = - : (thm -> thm)
HALF_MK_ABS = - : (thm -> thm)
ALPHA_CONV = - : (term -> term -> thm)
ALPHA = - : (term -> term -> thm)
GEN_ALPHA_CONV = - : (term -> term -> thm)
COND_CLAUSES = |- !t1 t2. ((T => t1 | t2) = t1) /\ ((F => t1 | t2) = t2)
COND_ID = |- !b t. (b => t | t) = t
IMP_CONJ = - : (thm -> thm -> thm)
EXISTS_IMP = - : (term -> thm -> thm)
LEFT_AND_OVER_OR = |- !t1 t2 t3. t1 /\ (t2 \/ t3) = t1 /\ t2 \/ t1 /\ t3
RIGHT_AND_OVER_OR =
|- !t1 t2 t3. (t2 \/ t3) /\ t1 = t2 /\ t1 \/ t3 /\ t1
LEFT_OR_OVER_AND =
|- !t1 t2 t3. t1 \/ t2 /\ t3 = (t1 \/ t2) /\ (t1 \/ t3)
RIGHT_OR_OVER_AND =
|- !t1 t2 t3. t2 /\ t3 \/ t1 = (t2 \/ t1) /\ (t3 \/ t1)
IMP_DISJ_THM = |- !t1 t2. t1 ==> t2 = ~t1 \/ t2
IMP_F_EQ_F = |- !t. t ==> F = (t = F)
AND_IMP_INTRO = |- !t1 t2 t3. t1 ==> t2 ==> t3 = t1 /\ t2 ==> t3
EQ_IMP_THM = |- !t1 t2. (t1 = t2) = (t1 ==> t2) /\ (t2 ==> t1)
EQ_EXPAND = |- !t1 t2. (t1 = t2) = t1 /\ t2 \/ ~t1 /\ ~t2
COND_RATOR = |- !b f g x. (b => f | g)x = (b => f x | g x)
COND_RAND = |- !f b x y. f(b => x | y) = (b => f x | f y)
COND_ABS = |- !b f g. (\x. (b => f x | g x)) = (b => f | g)
COND_EXPAND = |- !b t1 t2. (b => t1 | t2) = (~b \/ t1) /\ (b \/ t2)
Calling Lisp compiler
File ml/drul compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/hol-thyfn`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
IS_ASSUMPTION_OF = |- !t1 t2. t1 IS_ASSUMPTION_OF t2 = t1 ==> t2
ASSUMPTION_DISCH = - : (term -> thm -> thm)
ASSUMPTION_DISCH_ALL = - : (thm -> thm)
ASSUMPTION_UNDISCH = - : (thm -> thm)
ASSUMPTION_UNDISCH_ALL = - : (thm -> thm)
save_thm = - : ((string # thm) -> thm)
theorem = - : (string -> string -> thm)
delete_thm = - : (string -> string -> thm)
theorems = - : (string -> (string # thm) list)
((-), (-), (-), -)
: (((string # thm) -> thm) #
(string -> string -> thm) #
(string -> string -> thm) #
(string -> (string # thm) list))
save_thm = - : ((string # thm) -> thm)
theorem = - : (string -> string -> thm)
delete_thm = - : (string -> string -> thm)
theorems = - : (string -> (string # thm) list)
constants = - : (string -> term list)
axioms = - : (string -> (string # thm) list)
definition = - : (string -> string -> thm)
definitions = - : (string -> (string # thm) list)
print_list = - : (bool -> string -> (* -> **) -> * list -> void)
print_theory = - : (string -> void)
theorem_lfn = - : (string list -> thm)
theorem_msg_lfn = - : (string list -> thm)
load_theorem = - : (string -> string -> void)
load_theorems = - : (string -> void list)
definition_lfn = - : (string list -> thm)
definition_msg_lfn = - : (string list -> thm)
load_definition = - : (string -> string -> void)
load_definitions = - : (string -> void list)
axiom_lfn = - : (string list -> thm)
axiom_msg_lfn = - : (string list -> thm)
load_axiom = - : (string -> string -> void)
load_axioms = - : (string -> void list)
Calling Lisp compiler
File ml/hol-thyfn compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/tacticals`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
type proof defined
type goal defined
type tactic defined
TAC_PROOF = - : ((goal # tactic) -> thm)
prove = - : ((term # tactic) -> thm)
ASSUM_LIST = - : ((thm list -> tactic) -> tactic)
POP_ASSUM = - : ((thm -> tactic) -> tactic)
POP_ASSUM_LIST = - : ((thm list -> tactic) -> tactic)
() : void
() : void
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
THEN = - : (tactic -> tactic -> tactic)
THENL = - : (tactic -> tactic list -> tactic)
((-), -)
: ((tactic -> tactic -> tactic) # (tactic -> tactic list -> tactic))
THEN = - : (tactic -> tactic -> tactic)
THENL = - : (tactic -> tactic list -> tactic)
() : void
ORELSE = - : (tactic -> tactic -> tactic)
FAIL_TAC = - : (string -> tactic)
NO_TAC = - : tactic
ALL_TAC = - : tactic
TRY = - : (tactic -> tactic)
REPEAT = - : (tactic -> tactic)
achieves = - : (thm -> goal -> bool)
chktac = - : ((goal list # proof) -> thm)
check_valid = - : (goal -> (goal list # proof) -> bool)
VALID = - : (tactic -> tactic)
EVERY = - : (tactic list -> tactic)
FIRST = - : (tactic list -> tactic)
MAP_EVERY = - : ((* -> tactic) -> * list -> tactic)
MAP_FIRST = - : ((* -> tactic) -> * list -> tactic)
EVERY_ASSUM = - : ((thm -> tactic) -> tactic)
FIRST_ASSUM = - : ((thm -> tactic) -> tactic)
SUBGOAL_THEN = - : (term -> (thm -> tactic) -> tactic)
CHANGED_TAC = - : (tactic -> tactic)
Calling Lisp compiler
File ml/tacticals compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/tacont`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
type thm_tactic defined
type thm_tactical defined
() : void
() : void
THEN_TCL = - : (thm_tactical -> thm_tactical -> thm_tactical)
ORELSE_TCL = - : (thm_tactical -> thm_tactical -> thm_tactical)
REPEAT_TCL = - : (thm_tactical -> thm_tactical)
REPEAT_GTCL = - : (thm_tactical -> thm_tactical)
ALL_THEN = - : thm_tactical
NO_THEN = - : thm_tactical
EVERY_TCL = - : (thm_tactical list -> thm_tactical)
FIRST_TCL = - : (thm_tactical list -> thm_tactical)
CONJUNCTS_THEN2 = - : (thm_tactic -> thm_tactical)
CONJUNCTS_THEN = - : thm_tactical
DISJ_CASES_THEN2 = - : (thm_tactic -> thm_tactical)
DISJ_CASES_THEN = - : thm_tactical
DISJ_CASES_THENL = - : (thm_tactic list -> thm_tactic)
DISCH_THEN = - : (thm_tactic -> tactic)
X_CHOOSE_THEN = - : (term -> thm_tactical)
CHOOSE_THEN = - : thm_tactical
X_CASES_THENL = - : (term list list -> thm_tactic list -> thm_tactic)
X_CASES_THEN = - : (term list list -> thm_tactical)
CASES_THENL = - : (thm_tactic list -> thm_tactic)
STRIP_THM_THEN = - : thm_tactical
Calling Lisp compiler
File ml/tacont compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/tactics`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
ACCEPT_TAC = - : thm_tactic
DISCARD_TAC = - : thm_tactic
CONTR_TAC = - : thm_tactic
ASSUME_TAC = - : thm_tactic
FREEZE_THEN = - : thm_tactical
CONJ_TAC = - : tactic
DISJ1_TAC = - : tactic
DISJ2_TAC = - : tactic
MP_TAC = - : thm_tactic
EQ_TAC = - : tactic
X_GEN_TAC = - : (term -> tactic)
GEN_TAC = - : tactic
SPEC_TAC = - : ((term # term) -> tactic)
EXISTS_TAC = - : (term -> tactic)
GSUBST_TAC =
-
: (((term # term) list -> term -> term) -> thm list -> tactic)
SUBST_TAC = - : (thm list -> tactic)
SUBST_OCCS_TAC = - : ((int list # thm) list -> tactic)
SUBST1_TAC = - : thm_tactic
RULE_ASSUM_TAC = - : ((thm -> thm) -> tactic)
SUBST_ALL_TAC = - : thm_tactic
CHECK_ASSUME_TAC = - : thm_tactic
STRIP_ASSUME_TAC = - : thm_tactic
STRUCT_CASES_TAC = - : thm_tactic
COND_CASES_TAC = - : tactic
BOOL_CASES_TAC = - : (term -> tactic)
STRIP_GOAL_THEN = - : (thm_tactic -> tactic)
FILTER_GEN_TAC = - : (term -> tactic)
FILTER_DISCH_THEN = - : (thm_tactic -> term -> tactic)
FILTER_STRIP_THEN = - : (thm_tactic -> term -> tactic)
DISCH_TAC = - : tactic
DISJ_CASES_TAC = - : thm_tactic
CHOOSE_TAC = - : thm_tactic
X_CHOOSE_TAC = - : (term -> thm_tactic)
STRIP_TAC = - : tactic
FILTER_DISCH_TAC = - : (term -> tactic)
FILTER_STRIP_TAC = - : (term -> tactic)
ASM_CASES_TAC = - : (term -> tactic)
REFL_TAC = - : tactic
UNDISCH_TAC = - : (term -> tactic)
AP_TERM_TAC = - : tactic
AP_THM_TAC = - : tactic
Calling Lisp compiler
File ml/tactics compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/conv`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
type conv defined
INST_TY_TERM =
-
: (((term # term) list # (type # type) list) -> thm -> thm)
GSPEC = - : (thm -> thm)
PART_MATCH = - : ((term -> term) -> thm -> conv)
MATCH_MP = - : (thm -> thm -> thm)
REWR_CONV = - : (thm -> conv)
NO_CONV = - : conv
ALL_CONV = - : conv
() : void
() : void
THENC = - : (conv -> conv -> conv)
ORELSEC = - : (conv -> conv -> conv)
FIRST_CONV = - : (conv list -> conv)
EVERY_CONV = - : (conv list -> conv)
REPEATC = - : (conv -> conv)
CHANGED_CONV = - : (conv -> conv)
TRY_CONV = - : (conv -> conv)
SUB_CONV = - : (conv -> conv)
qconv = `QCONV` : string
QCONV = - : (conv -> conv)
ALL_QCONV = - : conv
THENQC = - : (conv -> conv -> conv)
ORELSEQC = - : ((term -> *) -> (term -> *) -> term -> *)
REPEATQC = - : (conv -> conv)
CHANGED_QCONV = - : (conv -> conv)
TRY_QCONV = - : (conv -> conv)
SUB_QCONV = - : (conv -> conv)
SUB_ALPHA_QCONV = - : (conv -> conv)
DEPTH_QCONV = - : ((conv -> conv) -> conv -> conv)
DEPTH_CONV = - : (conv -> conv)
REDEPTH_QCONV = - : ((conv -> conv) -> conv -> conv)
REDEPTH_CONV = - : (conv -> conv)
TOP_DEPTH_QCONV = - : ((conv -> conv) -> conv -> conv)
TOP_DEPTH_CONV = - : (conv -> conv)
ONCE_DEPTH_QCONV = - : ((conv -> conv) -> conv -> conv)
ONCE_DEPTH_CONV = - : (conv -> conv)
REW_DEPTH_CONV = - : (conv -> conv)
ONCE_REW_DEPTH_CONV = - : (conv -> conv)
((-), (-), (-), (-), (-), -)
: ((conv -> conv) #
(conv -> conv) #
(conv -> conv) #
(conv -> conv) #
(conv -> conv) #
(conv -> conv))
DEPTH_CONV = - : (conv -> conv)
REDEPTH_CONV = - : (conv -> conv)
TOP_DEPTH_CONV = - : (conv -> conv)
ONCE_DEPTH_CONV = - : (conv -> conv)
REW_DEPTH_CONV = - : (conv -> conv)
ONCE_REW_DEPTH_CONV = - : (conv -> conv)
CONV_RULE = - : (conv -> thm -> thm)
CONV_TAC = - : (conv -> tactic)
BETA_RULE = - : (thm -> thm)
BETA_TAC = - : tactic
NOT_FORALL_CONV = - : conv
NOT_EXISTS_CONV = - : conv
EXISTS_NOT_CONV = - : conv
FORALL_NOT_CONV = - : conv
FORALL_AND_CONV = - : conv
EXISTS_OR_CONV = - : conv
AND_FORALL_CONV = - : conv
LEFT_AND_FORALL_CONV = - : conv
RIGHT_AND_FORALL_CONV = - : conv
OR_EXISTS_CONV = - : conv
LEFT_OR_EXISTS_CONV = - : conv
RIGHT_OR_EXISTS_CONV = - : conv
EXISTS_AND_CONV = - : conv
AND_EXISTS_CONV = - : conv
LEFT_AND_EXISTS_CONV = - : conv
RIGHT_AND_EXISTS_CONV = - : conv
FORALL_OR_CONV = - : conv
OR_FORALL_CONV = - : conv
LEFT_OR_FORALL_CONV = - : conv
RIGHT_OR_FORALL_CONV = - : conv
FORALL_IMP_CONV = - : conv
LEFT_IMP_EXISTS_CONV = - : conv
RIGHT_IMP_FORALL_CONV = - : conv
EXISTS_IMP_CONV = - : conv
LEFT_IMP_FORALL_CONV = - : conv
RIGHT_IMP_EXISTS_CONV = - : conv
X_SKOLEM_CONV = - : (term -> conv)
SKOLEM_CONV = - : conv
SYM_CONV = - : conv
RIGHT_CONV_RULE = - : (conv -> thm -> thm)
FUN_EQ_CONV = - : conv
X_FUN_EQ_CONV = - : (term -> conv)
CONTRAPOS_CONV = - : conv
ANTE_CONJ_CONV = - : conv
SWAP_EXISTS_CONV = - : conv
RAND_CONV = - : (conv -> conv)
RATOR_CONV = - : (conv -> conv)
ABS_CONV = - : (conv -> conv)
SELECT_CONV = - : conv
bool_EQ_CONV = - : conv
EXISTS_UNIQUE_CONV = - : conv
COND_CONV = - : conv
PAIRED_BETA_CONV = - : conv
PAIRED_ETA_CONV = - : conv
GEN_BETA_CONV = - : conv
ITER_BETA_CONV = - : conv
ARGS_CONV = - : (conv list -> conv)
RED_WHERE = - : (term -> term -> conv)
REDUCE = - : (term -> term -> thm -> thm)
let_CONV = - : conv
- : conv
let_CONV = - : conv
EXISTENCE = - : (thm -> thm)
AC_CONV = - : ((thm # thm) -> conv)
GSYM = - : (thm -> thm)
Calling Lisp compiler
File ml/conv compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/hol-net`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
nil_term_net = - : * term_net
enter_term = - : ((term # *) -> * term_net -> * term_net)
lookup_term = - : (* term_net -> term -> * list)
merge_term_nets = - : (* term_net -> * term_net -> * term_net)
Calling Lisp compiler
File ml/hol-net compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/rewrite`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
mk_rewrites = - : (thm -> thm list)
mk_rewritesl = - : (thm list -> thm list)
mk_conv_net = - : (thm list -> conv term_net)
- : (thm list -> conv term_net)
mk_conv_net = - : (thm list -> conv term_net)
FORALL_SIMP = |- !t. (!x. t) = t
EXISTS_SIMP = |- !t. (?x. t) = t
ABS_SIMP = |- !t1 t2. (\x. t1)t2 = t1
basic_rewrites =
[|- !x. (x = x) = T;
|- !t.
((T = t) = t) /\ ((t = T) = t) /\ ((F = t) = ~t) /\ ((t = F) = ~t);
|- (!t. ~~t = t) /\ (~T = F) /\ (~F = T);
|- !t.
(T /\ t = t) /\
(t /\ T = t) /\
(F /\ t = F) /\
(t /\ F = F) /\
(t /\ t = t);
|- !t.
(T \/ t = T) /\
(t \/ T = T) /\
(F \/ t = t) /\
(t \/ F = t) /\
(t \/ t = t);
|- !t.
(T ==> t = t) /\
(t ==> T = T) /\
(F ==> t = T) /\
(t ==> t = T) /\
(t ==> F = ~t);
|- !t1 t2. ((T => t1 | t2) = t1) /\ ((F => t1 | t2) = t2);
|- !t. (!x. t) = t;
|- !t. (?x. t) = t;
|- !t1 t2. (\x. t1)t2 = t1;
|- !x. FST x,SND x = x;
|- !x y. FST(x,y) = x;
|- !x y. SND(x,y) = y]
: thm list
GEN_REWRITE_CONV = - : ((conv -> conv) -> thm list -> thm list -> conv)
PURE_REWRITE_CONV = - : (thm list -> conv)
REWRITE_CONV = - : (thm list -> conv)
PURE_ONCE_REWRITE_CONV = - : (thm list -> conv)
ONCE_REWRITE_CONV = - : (thm list -> conv)
GEN_REWRITE_RULE =
-
: ((conv -> conv) -> thm list -> thm list -> thm -> thm)
PURE_REWRITE_RULE = - : (thm list -> thm -> thm)
REWRITE_RULE = - : (thm list -> thm -> thm)
PURE_ONCE_REWRITE_RULE = - : (thm list -> thm -> thm)
ONCE_REWRITE_RULE = - : (thm list -> thm -> thm)
PURE_ASM_REWRITE_RULE = - : (thm list -> thm -> thm)
ASM_REWRITE_RULE = - : (thm list -> thm -> thm)
PURE_ONCE_ASM_REWRITE_RULE = - : (thm list -> thm -> thm)
ONCE_ASM_REWRITE_RULE = - : (thm list -> thm -> thm)
FILTER_PURE_ASM_REWRITE_RULE =
-
: ((term -> bool) -> thm list -> thm -> thm)
FILTER_ASM_REWRITE_RULE = - : ((term -> bool) -> thm list -> thm -> thm)
FILTER_PURE_ONCE_ASM_REWRITE_RULE =
-
: ((term -> bool) -> thm list -> thm -> thm)
FILTER_ONCE_ASM_REWRITE_RULE =
-
: ((term -> bool) -> thm list -> thm -> thm)
GEN_REWRITE_TAC = - : ((conv -> conv) -> thm list -> thm list -> tactic)
PURE_REWRITE_TAC = - : (thm list -> tactic)
REWRITE_TAC = - : (thm list -> tactic)
PURE_ONCE_REWRITE_TAC = - : (thm list -> tactic)
ONCE_REWRITE_TAC = - : (thm list -> tactic)
PURE_ASM_REWRITE_TAC = - : (thm list -> tactic)
ASM_REWRITE_TAC = - : (thm list -> tactic)
PURE_ONCE_ASM_REWRITE_TAC = - : (thm list -> tactic)
ONCE_ASM_REWRITE_TAC = - : (thm list -> tactic)
FILTER_PURE_ASM_REWRITE_TAC = - : ((term -> bool) -> thm list -> tactic)
FILTER_ASM_REWRITE_TAC = - : ((term -> bool) -> thm list -> tactic)
FILTER_PURE_ONCE_ASM_REWRITE_TAC =
-
: ((term -> bool) -> thm list -> tactic)
FILTER_ONCE_ASM_REWRITE_TAC = - : ((term -> bool) -> thm list -> tactic)
find_match =
-
: (term -> term -> ((term # term) list # (type # type) list))
SUBST_MATCH = - : (thm -> thm -> thm)
Calling Lisp compiler
File ml/rewrite compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/resolve`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
MATCH_ACCEPT_TAC = - : thm_tactic
ANTE_RES_THEN = - : thm_tactical
RES_CANON = - : (thm -> thm list)
MATCH_MP = - : (thm -> thm -> thm)
check = - : (string -> * list -> * list)
IMP_RES_THEN = - : thm_tactical
RES_THEN = - : (thm_tactic -> tactic)
((-), -) : (thm_tactical # (thm_tactic -> tactic))
IMP_RES_THEN = - : thm_tactical
RES_THEN = - : (thm_tactic -> tactic)
IMP_RES_TAC = - : thm_tactic
RES_TAC = - : tactic
MATCH_MP_TAC = - : thm_tactic
Calling Lisp compiler
File ml/resolve compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/goals`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
assignable_print_term = - : (term -> void)
() : void
print_hyps = - : (term list -> void)
print_goal = - : (goal -> void)
PROVE = - : ((term # tactic) -> thm)
prove_thm = - : ((string # term # tactic) -> thm)
type subgoals defined
root_goal = - : tactic
attempt_first = - : (subgoals -> tactic -> subgoals)
rotate_goals = - : (subgoals -> subgoals)
achieve_first = - : (subgoals -> thm -> subgoals)
apply_proof = - : (subgoals -> thm)
() : void
print_subgoals = - : (subgoals -> void)
print_stack = - : (subgoals list -> int -> void)
pop_proofs = - : (subgoals list -> subgoals list)
pop_proofs_print = - : (subgoals list -> subgoals list)
push_print = - : (subgoals -> subgoals list -> subgoals list)
push_fsubgoals = - : (subgoals list -> tactic -> subgoals list)
push_subgoals = - : (subgoals list -> tactic -> subgoals list)
rotate_top = - : (int -> subgoals list -> subgoals list)
new_stack = - : (goal -> subgoals list)
top_proof = - : (subgoals list -> thm)
Calling Lisp compiler
File ml/goals compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `bool`;;'\
'compilet `ml/stack`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory bool loaded
() : void
() : void
abs_goals = - : (subgoals list -> goalstack)
rep_goals = - : (goalstack -> subgoals list)
goals = - : goalstack
backup_list = [] : goalstack list
backup_limit = 12 : int
print_state = - : (int -> void)
change_state = - : (goalstack -> void)
set_goal = - : (goal -> void)
expandf = - : (tactic -> void)
expand = - : (tactic -> void)
rotate = - : (int -> void)
backup = - : (void -> void)
top_thm = - : (void -> thm)
save_top_thm = - : (string -> thm)
top_goal = - : (void -> goal)
get_state = - : (void -> goalstack)
set_state = - : (goalstack -> void)
g = - : (term -> void)
e = - : (tactic -> void)
p = - : (int -> void)
b = - : (void -> void)
r = - : (int -> void)
Calling Lisp compiler
File ml/stack compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `BASIC-HOL`;;'\
'compilet `ml/abs-rep`;;'\
'quit();;'\
| hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory BASIC-HOL loaded
() : void
() : void
ABS_REP_THM =
|- !P.
(?rep. TYPE_DEFINITION P rep) ==>
(?rep abs. (!a. abs(rep a) = a) /\ (!r. P r = (rep(abs r) = r)))
define_new_type_bijections =
-
: (string -> string -> string -> thm -> thm)
prove_rep_fn_one_one = - : (thm -> thm)
prove_rep_fn_onto = - : (thm -> thm)
prove_abs_fn_onto = - : (thm -> thm)
prove_abs_fn_one_one = - : (thm -> thm)
Calling Lisp compiler
File ml/abs-rep compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `BASIC-HOL`;;'\
'loadf `ml/hol-in-out`;;'\
'loadf `ml/hol-rule`;;'\
'loadf `ml/hol-drule`;;'\
'loadf `ml/drul`;;'\
'loadf `ml/tacticals`;;'\
'loadf `ml/tacont`;;'\
'loadf `ml/tactics`;;'\
'loadf `ml/conv`;;'\
'loadf `ml/hol-net`;;'\
'loadf `ml/rewrite`;;'\
'loadf `ml/resolve`;;'\
'loadf `ml/hol-thyfn`;;'\
'loadf `ml/goals`;;'\
'loadf `ml/stack`;;'\
'loadf `ml/abs-rep`;;'\
'activate_binders `bool`;;'\
'lisp `(setq %liszt "")`;;'\
'lisp `(setq %version "2.02 (GCL)")`;;'\
'lisp `(setq %system-name "BASIC-HOL")`;;'\
'lisp `(setup)`;;' >foo1
echo 'lisp `(throw (quote eof) t)`;; #+native-reloc(progn (with-open-file (s "foo1") (let ((*standard-input* s)) (tml)))(ml-save "basic-hol")) #-native-reloc(let ((si::*collect-binary-modules* t)(si::*binary-modules* (with-open-file (s "bm.l") (read s)))) (with-open-file (s "foo1") (let ((*standard-input* s)) (tml)))(compiler::link (remove-duplicates si::*binary-modules* :test (function equal)) "basic-hol" "(progn (load \"debian/gcl_patch.l\")(load \"foo\")(with-open-file (s \"foo1\") (let ((*standard-input* s)) (tml)))(ml-save \"basic-hol\")(quit))" "" nil)(with-open-file (s "bm.l" :direction :output) (prin1 si::*binary-modules* s))(quit))`;;' | hol-lcf
HOL-LCF version 2.02 (GCL) created 19/1/23
#GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>
HOL-LCF version 2.02 (GCL) created 19/1/23
#() : void
Theory BASIC-HOL loaded
() : void
.....................................................................................................................................................() : void
#.............() : void
...................................................................................() : void
..................................................() : void
...................................() : void
.........................() : void
..........................................() : void
...................................................................................................() : void
..() : void
......................() : void
.............() : void
............................() : void
........................() : void
.................() : void
.......() : void
[`?!`; `!`; `?`; `@`] : string list
() : void
() : void
() : void
() : void
#=======> basic-hol88 made
cd /<<PKGBUILDDIR>>/theories; rm -f combin.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_combin.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
##########################() : void
#####o_DEF = |- !f g. f o g = (\x. f(g x))
###K_DEF = |- K = (\x y. x)
######S_DEF = |- S = (\f g x. f x(g x))
########I_DEF = |- I = S K K
###() : void
#########o_THM = |- !f g x. (f o g)x = f(g x)
########o_ASSOC = |- !f g h. f o (g o h) = (f o g) o h
########K_THM = |- !x y. K x y = x
########S_THM = |- !f g x. S f g x = f x(g x)
########I_THM = |- !x. I x = x
##########I_o_ID = |- !f. (I o f = f) /\ (f o I = f)
##=======> theory combin built
cd /<<PKGBUILDDIR>>/theories; rm -f num.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_num.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
##############################() : void
##INFINITY_AX = |- ?f. ONE_ONE f /\ ~ONTO f
##ONE_ONE_DEF = |- !f. ONE_ONE f = (!x1 x2. (f x1 = f x2) ==> (x1 = x2))
#ONTO_DEF = |- !f. ONTO f = (!y. ?x. y = f x)
######SUC_REP_DEF = |- SUC_REP = (@f. ONE_ONE f /\ ~ONTO f)
#####ZERO_REP_DEF = |- ZERO_REP = (@x. !y. ~(x = SUC_REP y))
##########IS_NUM_REP =
|- !m.
IS_NUM_REP m =
(!P. P ZERO_REP /\ (!n. P n ==> P(SUC_REP n)) ==> P m)
########EXISTS_NUM_REP = |- ?n. IS_NUM_REP n
####num_TY_DEF = |- ?rep. TYPE_DEFINITION IS_NUM_REP rep
##########num_ISO_DEF =
|- (!a. ABS_num(REP_num a) = a) /\
(!r. IS_NUM_REP r = (REP_num(ABS_num r) = r))
#####R_11 = |- !a a'. (REP_num a = REP_num a') = (a = a')
R_ONTO = |- !r. IS_NUM_REP r = (?a. r = REP_num a)
A_11 =
|- !r r'.
IS_NUM_REP r ==>
IS_NUM_REP r' ==>
((ABS_num r = ABS_num r') = (r = r'))
A_ONTO = |- !a. ?r. (a = ABS_num r) /\ IS_NUM_REP r
###############() : void
#() : void
###ZERO_DEF = |- 0 = ABS_num ZERO_REP
####SUC_DEF = |- !m. SUC m = ABS_num(SUC_REP(REP_num m))
##() : void
######IS_NUM_REP_ZERO = |- IS_NUM_REP ZERO_REP
#######IS_NUM_SUC_REP = |- !i. IS_NUM_REP i ==> IS_NUM_REP(SUC_REP i)
#######IS_NUM_REP_SUC_REP = |- !n. IS_NUM_REP(SUC_REP(REP_num n))
####thm1 = |- ONE_ONE SUC_REP /\ ~ONTO SUC_REP
#thm2 =
|- (!x1 x2. (SUC_REP x1 = SUC_REP x2) ==> (x1 = x2)) /\
~(!y. ?x. y = SUC_REP x)
####SUC_REP_11 = |- !x1 x2. (SUC_REP x1 = SUC_REP x2) ==> (x1 = x2)
########NOT_SUC_ZERO = |- !x. ~(SUC_REP x = ZERO_REP)
################NOT_SUC = |- !n. ~(SUC n = 0)
##############INV_SUC = |- !m n. (SUC m = SUC n) ==> (m = n)
###########ind_lemma1 =
|- !P.
P ZERO_REP /\ (!i. P i ==> P(SUC_REP i)) ==>
(!i. IS_NUM_REP i ==> P i)
####lemma = |- A ==> A /\ B = A ==> B
############ind_lemma2 =
|- !P.
P ZERO_REP /\ (!i. IS_NUM_REP i /\ P i ==> P(SUC_REP i)) ==>
(!i. IS_NUM_REP i ==> P i)
##########lemma1 = |- (!i. IS_NUM_REP i ==> P(ABS_num i)) = (!n. P n)
###############INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
##=======> theory num built
cd /<<PKGBUILDDIR>>/theories; rm -f prim_rec.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_prim_rec.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
#######################################################################() : void
##Theory num loaded
() : void
#####NOT_SUC = |- !n. ~(SUC n = 0)
INV_SUC = |- !m n. (SUC m = SUC n) ==> (m = n)
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
#####LESS = |- !m n. m < n = (?P. (!n'. P(SUC n') ==> P n') /\ P m /\ ~P n)
###########
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
####INDUCT_TAC = - : tactic
########INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
######LESS_REFL = |- !n. ~n < n
##########SUC_LESS = |- !m n. (SUC m) < n ==> m < n
#########NOT_LESS_0 = |- !n. ~n < 0
#########LESS_0_0 = |- 0 < (SUC 0)
#####################LESS_MONO = |- !m n. m < n ==> (SUC m) < (SUC n)
#########LESS_SUC_REFL = |- !n. n < (SUC n)
###########LESS_SUC = |- !m n. m < n ==> m < (SUC n)
#################LESS_LEMMA1 = |- !m n. m < (SUC n) ==> (m = n) \/ m < n
########LESS_LEMMA2 = |- !m n. (m = n) \/ m < n ==> m < (SUC n)
#######LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
#########LESS_SUC_IMP = |- !m n. m < (SUC n) ==> ~(m = n) ==> m < n
#######LESS_0 = |- !n. 0 < (SUC n)
##########EQ_LESS = |- !n. (SUC m = n) ==> m < n
#######SUC_ID = |- !n. ~(SUC n = n)
########NOT_LESS_EQ = |- !m n. (m = n) ==> ~m < n
###########LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
################################################SIMP_REC_REL =
|- !fun x f n.
SIMP_REC_REL fun x f n =
(fun 0 = x) /\ (!m. m < n ==> (fun(SUC m) = f(fun m)))
######SIMP_REC_FUN =
|- !x f n. SIMP_REC_FUN x f n = (@fun. SIMP_REC_REL fun x f n)
######SIMP_REC = |- !x f n. SIMP_REC x f n = SIMP_REC_FUN x f(SUC n)n
######################SIMP_REC_FUN_LEMMA =
|- (?fun. SIMP_REC_REL fun x f n) =
(SIMP_REC_FUN x f n 0 = x) /\
(!m. m < n ==> (SIMP_REC_FUN x f n(SUC m) = f(SIMP_REC_FUN x f n m)))
##################################SIMP_REC_EXISTS = |- !x f n. ?fun. SIMP_REC_REL fun x f n
#############SIMP_REC_FUN_THM =
|- !x f n.
(SIMP_REC_FUN x f n 0 = x) /\
(!m.
m < n ==> (SIMP_REC_FUN x f n(SUC m) = f(SIMP_REC_FUN x f n m)))
###SIMP_REC_FUN_THM1 = |- !x f n. SIMP_REC_FUN x f n 0 = x
###SIMP_REC_FUN_THM2 =
|- !n m. m < n ==> (SIMP_REC_FUN x f n(SUC m) = f(SIMP_REC_FUN x f n m))
###################SIMP_REC_UNIQUE =
|- !n m1 m2 x f.
n < m1 ==>
n < m2 ==>
(SIMP_REC_FUN x f m1 n = SIMP_REC_FUN x f m2 n)
#######LESS_SUC_SUC = |- !m. m < (SUC m) /\ m < (SUC(SUC m))
###############SIMP_REC_THM =
|- !x f.
(SIMP_REC x f 0 = x) /\
(!m. SIMP_REC x f(SUC m) = f(SIMP_REC x f m))
########################PRE_DEF = |- !m. PRE m = ((m = 0) => 0 | (@n. m = SUC n))
########SELECT_LEMMA = |- (@n. m = n) = m
#######PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
######PRIM_REC_FUN =
|- !x f. PRIM_REC_FUN x f = SIMP_REC(\n. x)(\fun n. f(fun(PRE n))n)
###########PRIM_REC_EQN =
|- !x f.
(!n. PRIM_REC_FUN x f 0 n = x) /\
(!m n. PRIM_REC_FUN x f(SUC m)n = f(PRIM_REC_FUN x f m(PRE n))n)
#####PRIM_REC = |- !x f m. PRIM_REC x f m = PRIM_REC_FUN x f m(PRE m)
###########PRIM_REC_THM =
|- !x f.
(PRIM_REC x f 0 = x) /\
(!m. PRIM_REC x f(SUC m) = f(PRIM_REC x f m)m)
####################num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
###() : void
##=======> theory prim_rec built
cd /<<PKGBUILDDIR>>/theories; rm -f fun.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_fun.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
###########################() : void
######ASSOC_DEF = |- !f. ASSOC f = (!x y z. f x(f y z) = f(f x y)z)
###COMM_DEF = |- !f. COMM f = (!x y. f x y = f y x)
####FCOMM_DEF = |- !f g. FCOMM f g = (!x y z. g x(f y z) = f(g x y)z)
###RIGHT_ID_DEF = |- !f e. RIGHT_ID f e = (!x. f x e = x)
###LEFT_ID_DEF = |- !f e. LEFT_ID f e = (!x. f e x = x)
###MONOID_DEF =
|- !f e. MONOID f e = ASSOC f /\ RIGHT_ID f e /\ LEFT_ID f e
###() : void
#######ASSOC_CONJ = |- ASSOC $/\
####ASSOC_DISJ = |- ASSOC $\/
####FCOMM_ASSOC = |- !f. FCOMM f f = ASSOC f
#####################MONOID_CONJ_T = |- MONOID $/\ T
####MONOID_DISJ_F = |- MONOID $\/ F
##=======> theory fun built
cd /<<PKGBUILDDIR>>/theories; rm -f arithmetic.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_arith.ml;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_arith_thms.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
#############################() : void
##Theory prim_rec loaded
Theory fun loaded
[(); ()] : void list
###########
Section prove_rec_fn_exists begun
derive_existence_thm = - : (thm -> conv)
mk_fn =
-
: ((term # term # term list # term # goal) -> (term # term list # thm))
instantiate_existence_thm = - : (thm -> conv)
closeup = - : (term -> term)
prove_rec_fn_exists = - : (thm -> conv)
- : (thm -> conv)
Section prove_rec_fn_exists ended
prove_rec_fn_exists = - : (thm -> conv)
new_recursive_definition = - : (bool -> thm -> string -> conv)
File /<<PKGBUILDDIR>>/ml/prim_rec.ml loaded
() : void
###num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
####ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
####SUB =
|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
####MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
####EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
########GREATER = |- !m n. m > n = n < m
###LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
###GREATER_OR_EQ = |- !m n. m >= n = m > n \/ (m = n)
########FACT = |- (FACT 0 = 1) /\ (!n. FACT(SUC n) = (SUC n) * (FACT n))
####EVEN = |- (EVEN 0 = T) /\ (!n. EVEN(SUC n) = ~EVEN n)
####ODD = |- (ODD 0 = F) /\ (!n. ODD(SUC n) = ~ODD n)
#################() : void
##
BASIC-HOL version 2.02 (GCL) created 19/1/23
###########################Theory arithmetic loaded
() : void
##########ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
SUB =
|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
FACT = |- (FACT 0 = 1) /\ (!n. FACT(SUC n) = (SUC n) * (FACT n))
EVEN = |- (EVEN 0 = T) /\ (!n. EVEN(SUC n) = ~EVEN n)
ODD = |- (ODD 0 = F) /\ (!n. ODD(SUC n) = ~ODD n)
####GREATER = |- !m n. m > n = n < m
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
GREATER_OR_EQ = |- !m n. m >= n = m > n \/ (m = n)
##################INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
LESS_REFL = |- !n. ~n < n
SUC_LESS = |- !m n. (SUC m) < n ==> m < n
NOT_LESS_0 = |- !n. ~n < 0
LESS_MONO = |- !m n. m < n ==> (SUC m) < (SUC n)
LESS_SUC_REFL = |- !n. n < (SUC n)
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
LESS_SUC_IMP = |- !m n. m < (SUC n) ==> ~(m = n) ==> m < n
LESS_0 = |- !n. 0 < (SUC n)
EQ_LESS = |- !n. (SUC m = n) ==> m < n
SUC_ID = |- !n. ~(SUC n = n)
NOT_LESS_EQ = |- !m n. (m = n) ==> ~m < n
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
LESS_SUC_SUC = |- !m. m < (SUC m) /\ m < (SUC(SUC m))
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
#####NOT_SUC = |- !n. ~(SUC n = 0)
INV_SUC = |- !m n. (SUC m = SUC n) ==> (m = n)
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
######ASSOC_DEF = |- !f. ASSOC f = (!x y z. f x(f y z) = f(f x y)z)
RIGHT_ID_DEF = |- !f e. RIGHT_ID f e = (!x. f x e = x)
LEFT_ID_DEF = |- !f e. LEFT_ID f e = (!x. f e x = x)
MONOID_DEF =
|- !f e. MONOID f e = ASSOC f /\ RIGHT_ID f e /\ LEFT_ID f e
#####
num_CONV = - : conv
File /<<PKGBUILDDIR>>/ml/numconv.ml loaded
() : void
###########
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
#####INDUCT_TAC = - : tactic
###########SUC_NOT = |- !n. ~(0 = SUC n)
########ADD_0 = |- !m. m + 0 = m
########ADD_SUC = |- !m n. SUC(m + n) = m + (SUC n)
#########ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
########ADD_SYM = |- !m n. m + n = n + m
#########num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
###########LESS_MONO_REV = |- !m n. (SUC m) < (SUC n) ==> m < n
#########LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
########SUC_SUB1 = |- !m. (SUC m) - 1 = m
########PRE_SUB1 = |- !m. PRE m = m - 1
###############LESS_ADD = |- !m n. n < m ==> (?p. p + n = m)
#######SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
###############LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
#######ADD1 = |- !m. SUC m = m + 1
###########LESS_ANTISYM = |- !m n. ~(m < n /\ n < m)
###########LESS_LESS_SUC = |- !m n. ~(m < n /\ n < (SUC m))
##########FUN_EQ_LEMMA = |- !f x1 x2. f x1 /\ ~f x2 ==> ~(x1 = x2)
############LESS_OR = |- !m n. m < n ==> (SUC m) <= n
###########OR_LESS = |- !m n. (SUC m) <= n ==> m < n
#######LESS_EQ = |- !m n. m < n = (SUC m) <= n
###########LESS_SUC_EQ_COR = |- !m n. m < n /\ ~(SUC m = n) ==> (SUC m) < n
###############LESS_NOT_SUC = |- !m n. m < n /\ ~(n = SUC m) ==> (SUC m) < n
#######LESS_0_CASES = |- !m. (0 = m) \/ 0 < m
#####################LESS_CASES_IMP = |- !m n. ~m < n /\ ~(m = n) ==> n < m
###########LESS_CASES = |- !m n. m < n \/ n <= m
#########ADD_INV_0 = |- !m n. (m + n = m) ==> (n = 0)
###############LESS_EQ_ADD = |- !m n. m <= (m + n)
#######LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
#############LESS_ADD_NONZERO = |- !m n. ~(n = 0) ==> m < (m + n)
############LESS_EQ_ANTISYM = |- !m n. ~(m < n /\ n <= m)
#############NOT_LESS = |- !m n. ~m < n = n <= m
######################SUB_EQ_0 = |- !m n. (m - n = 0) = m <= n
#######ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
#######MULT_0 = |- !m. m * 0 = 0
#######MULT_SUC = |- !m n. m * (SUC n) = m + (m * n)
#######MULT_LEFT_1 = |- !m. 1 * m = m
########MULT_RIGHT_1 = |- !m. m * 1 = m
###########MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
########MULT_SYM = |- !m n. m * n = n * m
############RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
###############LEFT_ADD_DISTRIB = |- !m n p. p * (m + n) = (p * m) + (p * n)
#######MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
###############SUB_ADD = |- !m n. n <= m ==> ((m - n) + n = m)
#############PRE_SUB = |- !m n. PRE(m - n) = (PRE m) - n
########ADD_EQ_0 = |- !m n. (m + n = 0) = (m = 0) /\ (n = 0)
##########ADD_INV_0_EQ = |- !m n. (m + n = m) = (n = 0)
########PRE_SUC_EQ = |- !m n. 0 < n ==> ((m = PRE n) = (SUC m = n))
########INV_PRE_EQ = |- !m n. 0 < m /\ 0 < n ==> ((PRE m = PRE n) = (m = n))
##########LESS_SUC_NOT = |- !m n. m < n ==> ~n < (SUC m)
##################TOTALLY_AD_HOC_LEMMA = |- !m n. (m + (SUC n) = n) = (SUC m = 0)
#######################ADD_EQ_SUB = |- !m n p. n <= p ==> ((m + n = p) = (m = p - n))
###########LESS_MONO_ADD = |- !m n p. m < n ==> (m + p) < (n + p)
#########LESS_MONO_ADD_INV = |- !m n p. (m + p) < (n + p) ==> m < n
########LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
#########EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
#########LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
###########LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
#############LESS_EQ_LESS_EQ_MONO =
|- !m n p q. m <= p /\ n <= q ==> (m + n) <= (p + q)
#######LESS_EQ_REFL = |- !m. m <= m
#######LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
##############LESS_MONO_MULT = |- !m n p. m <= n ==> (m * p) <= (n * p)
##################RIGHT_SUB_DISTRIB = |- !m n p. (m - n) * p = (m * p) - (n * p)
###########LEFT_SUB_DISTRIB = |- !m n p. p * (m - n) = (p * m) - (p * n)
################LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
#############EXP_ADD = |- !p q n. n EXP (p + q) = (n EXP p) * (n EXP q)
##########NOT_ODD_EQ_EVEN = |- !n m. ~(SUC(n + n) = m + m)
#######################MULT_SUC_EQ = |- !p m n. (n * (SUC p) = m * (SUC p)) = (n = m)
########MULT_EXP_MONO =
|- !p q n m. (n * ((SUC q) EXP p) = m * ((SUC q) EXP p)) = (n = m)
#########LESS_EQUAL_ANTISYM = |- !n m. n <= m /\ m <= n ==> (n = m)
#########LESS_ADD_SUC = |- !m n. m < (m + (SUC n))
#########ZERO_LESS_EQ = |- !n. 0 <= n
######LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
#############LESS_OR_EQ_ADD = |- !n m. n < m \/ (?p. n = p + m)
############################lemma = |- ~(?n. P n /\ (!m. m < n ==> ~P m)) ==> (!n m. m < n ==> ~P m)
###############WOP = |- !P. (?n. P n) ==> (?n. P n /\ (!m. m < n ==> ~P m))
###################exists_lemma = |- ?r q. k = (q * n) + r
#############smallest_lemma =
|- ?n'.
(?q. k = (q * n) + n') /\ (!m. m < n' ==> (!q. ~(k = (q * n) + m)))
###########leq_add_lemma = |- !m n. n <= m ==> (?p. m = n + p)
#####k_expr_lemma = |- (k = (q * n) + (n + p)) ==> (k = ((q + 1) * n) + p)
########less_add = . |- p < (n + p)
#############DA = |- !k n. 0 < n ==> (?r q. (k = (q * n) + r) /\ r < n)
#########Theory arithmetic loaded
() : void
#############MOD_exists =
|- ?MOD.
!n. 0 < n ==> (!k. ?q. (k = (q * n) + (MOD k n)) /\ (MOD k n) < n)
################MOD_DIV_exist =
|- ?MOD DIV.
!n.
0 < n ==> (!k. (k = ((DIV k n) * n) + (MOD k n)) /\ (MOD k n) < n)
####DIVISION =
|- !n.
0 < n ==> (!k. (k = ((k DIV n) * n) + (k MOD n)) /\ (k MOD n) < n)
##() : void
#############MOD_ONE = |- !k. k MOD (SUC 0) = 0
################DIV_LESS_EQ = |- !n. 0 < n ==> (!k. (k DIV n) <= k)
###########################################################DIV_UNIQUE =
|- !n k q. (?r. (k = (q * n) + r) /\ r < n) ==> (k DIV n = q)
#########lemma = |- !n k q r. (k = (q * n) + r) /\ r < n ==> (k DIV n = q)
#################MOD_UNIQUE =
|- !n k r. (?q. (k = (q * n) + r) /\ r < n) ==> (k MOD n = r)
###############DIV_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) DIV n = q)
#########LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
###########MOD_EQ_0 = |- !n. 0 < n ==> (!k. (k * n) MOD n = 0)
########ZERO_MOD = |- !n. 0 < n ==> (0 MOD n = 0)
#########ZERO_DIV = |- !n. 0 < n ==> (0 DIV n = 0)
#########MOD_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) MOD n = r)
############MOD_TIMES = |- !n. 0 < n ==> (!q r. ((q * n) + r) MOD n = r MOD n)
#############MOD_PLUS =
|- !n. 0 < n ==> (!j k. ((j MOD n) + (k MOD n)) MOD n = (j + k) MOD n)
########MOD_MOD = |- !n. 0 < n ==> (!k. (k MOD n) MOD n = k MOD n)
###########SUB_MONO_EQ = |- !n m. (SUC n) - (SUC m) = n - m
##########SUB_PLUS = |- !a b c. a - (b + c) = (a - b) - c
######################INV_PRE_LESS = |- !m. 0 < m ==> (!n. (PRE m) < (PRE n) = m < n)
##########INV_PRE_LESS_EQ = |- !n. 0 < n ==> (!m. (PRE m) <= (PRE n) = m <= n)
########SUB_LESS_EQ = |- !n m. (n - m) <= n
##############SUB_EQ_EQ_0 = |- !m n. (m - n = m) = (m = 0) \/ (n = 0)
###########SUB_LESS_0 = |- !n m. m < n = 0 < (n - m)
#########SUB_LESS_OR = |- !m n. n < m ==> n <= (m - 1)
################LESS_SUB_ADD_LESS = |- !n m i. i < (n - m) ==> (i + m) < n
########TIMES2 = |- !n. 2 * n = n + n
#####################LESS_MULT_MONO = |- !m i n. ((SUC n) * m) < ((SUC n) * i) = m < i
#######################MULT_MONO_EQ = |- !m i n. ((SUC n) * m = (SUC n) * i) = (m = i)
###########ADD_SUB = |- !a c. (a + c) - c = a
###############LESS_EQ_ADD_SUB = |- !c b. c <= b ==> (!a. (a + b) - c = a + (b - c))
########SUB_EQUAL_0 = |- !c. c - c = 0
##################LESS_EQ_SUB_LESS = |- !a b. b <= a ==> (!c. (a - b) < c = a < (b + c))
######NOT_SUC_LESS_EQ = |- !n m. ~(SUC n) <= m = m <= n
###############SUB_SUB = |- !b c. c <= b ==> (!a. a - (b - c) = (a + c) - b)
###########LESS_IMP_LESS_ADD = |- !n m. n < m ==> (!p. n < (m + p))
########LESS_EQ_IMP_LESS_SUC = |- !n m. n <= m ==> n < (SUC m)
###############SUB_LESS_EQ_ADD = |- !m p. m <= p ==> (!n. (p - m) <= n = p <= (m + n))
#############################SUB_CANCEL = |- !p n m. n <= p /\ m <= p ==> ((p - n = p - m) = (n = m))
##########################CANCEL_SUB = |- !p n m. p <= n /\ p <= m ==> ((n - p = m - p) = (n = m))
###########NOT_EXP_0 = |- !m n. ~((SUC n) EXP m = 0)
##########ZERO_LESS_EXP = |- !m n. 0 < ((SUC n) EXP m)
##########ODD_OR_EVEN =
|- !n. ?m. (n = (SUC(SUC 0)) * m) \/ (n = ((SUC(SUC 0)) * m) + 1)
##########LESS_EXP_SUC_MONO =
|- !n m. ((SUC(SUC m)) EXP n) < ((SUC(SUC m)) EXP (SUC n))
#########LESS_LESS_CASES = |- !m n. (m = n) \/ m < n \/ n < m
#####GREATER_EQ = |- !n m. n >= m = m <= n
######LESS_EQ_CASES = |- !m n. m <= n \/ n <= m
#######LESS_EQUAL_ADD = |- !m n. m <= n ==> (?p. n = m + p)
######LESS_EQ_EXISTS = |- !m n. m <= n = (?p. n = m + p)
####NOT_LESS_EQUAL = |- !m n. ~m <= n = n < m
#######LESS_EQ_0 = |- !n. n <= 0 = (n = 0)
######MULT_EQ_0 = |- !m n. (m * n = 0) = (m = 0) \/ (n = 0)
#####LESS_MULT2 = |- !m n. 0 < m /\ 0 < n ==> 0 < (m * n)
#####LESS_EQ_LESS_TRANS = |- !m n p. m <= n /\ n < p ==> m < p
#####LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
#########FACT_LESS = |- !n. 0 < (FACT n)
########EVEN_ODD = |- !n. EVEN n = ~ODD n
####ODD_EVEN = |- !n. ODD n = ~EVEN n
####EVEN_OR_ODD = |- !n. EVEN n \/ ODD n
####EVEN_AND_ODD = |- !n. ~(EVEN n /\ ODD n)
#####EVEN_ADD = |- !m n. EVEN(m + n) = (EVEN m = EVEN n)
#####EVEN_MULT = |- !m n. EVEN(m * n) = EVEN m \/ EVEN n
#####ODD_ADD = |- !m n. ODD(m + n) = ~(ODD m = ODD n)
####ODD_MULT = |- !m n. ODD(m * n) = ODD m /\ ODD n
#####EVEN_DOUBLE = |- !n. EVEN(2 * n)
####ODD_DOUBLE = |- !n. ODD(SUC(2 * n))
###########EVEN_ODD_EXISTS =
|- !n. (EVEN n ==> (?m. n = 2 * m)) /\ (ODD n ==> (?m. n = SUC(2 * m)))
######EVEN_EXISTS = |- !n. EVEN n = (?m. n = 2 * m)
######ODD_EXISTS = |- !n. ODD n = (?m. n = SUC(2 * m))
############EQ_LESS_EQ = |- !m n. (m = n) = m <= n /\ n <= m
#######ADD_MONO_LESS_EQ = |- !m n p. (m + n) <= (m + p) = n <= p
######NOT_SUC_LESS_EQ_0 = |- !n. ~(SUC n) <= 0
###########NOT_LEQ = |- !m n. ~m <= n = (SUC n) <= m
#######NOT_NUM_EQ = |- !m n. ~(m = n) = (SUC m) <= n \/ (SUC n) <= m
######NOT_GREATER = |- !m n. ~m > n = m <= n
######NOT_GREATER_EQ = |- !m n. ~m >= n = (SUC m) <= n
########SUC_ONE_ADD = |- !n. SUC n = 1 + n
########SUC_ADD_SYM = |- !m n. SUC(m + n) = (SUC n) + m
########NOT_SUC_ADD_LESS_EQ = |- !m n. ~(SUC(m + n)) <= m
#########################MULT_LESS_EQ_SUC = |- !m n p. m <= n = ((SUC p) * m) <= ((SUC p) * n)
################SUB_LEFT_ADD = |- !m n p. m + (n - p) = (n <= p => m | (m + n) - p)
################SUB_RIGHT_ADD = |- !m n p. (m - n) + p = (m <= n => p | (m + p) - n)
##############SUB_LEFT_SUB = |- !m n p. m - (n - p) = (n <= p => m | (m + p) - n)
#########SUB_RIGHT_SUB = |- !m n p. (m - n) - p = m - (n + p)
###########SUB_LEFT_SUC = |- !m n. SUC(m - n) = (m <= n => SUC 0 | (SUC m) - n)
##########################SUB_LEFT_LESS_EQ = |- !m n p. m <= (n - p) = (m + p) <= n \/ m <= 0
#################SUB_RIGHT_LESS_EQ = |- !m n p. (m - n) <= p = m <= (n + p)
#########SUB_LEFT_LESS = |- !m n p. m < (n - p) = (m + p) < n
#################SUB_RIGHT_LESS = |- !m n p. (m - n) < p = m < (n + p) /\ 0 < p
############SUB_LEFT_GREATER_EQ = |- !m n p. m >= (n - p) = (m + p) >= n
############SUB_RIGHT_GREATER_EQ = |- !m n p. (m - n) >= p = m >= (n + p) \/ 0 >= p
#########SUB_LEFT_GREATER = |- !m n p. m > (n - p) = (m + p) > n /\ m > 0
#########SUB_RIGHT_GREATER = |- !m n p. (m - n) > p = m > (n + p)
#############SUB_LEFT_EQ = |- !m n p. (m = n - p) = (m + p = n) \/ m <= 0 /\ n <= p
##############SUB_RIGHT_EQ = |- !m n p. (m - n = p) = (m = n + p) \/ m <= n /\ p <= 0
#######ASSOC_ADD = |- ASSOC $+
####RIGHT_ID_ADD_0 = |- RIGHT_ID $+ 0
####LEFT_ID_ADD_0 = |- LEFT_ID $+ 0
#####MONOID_ADD_0 = |- MONOID $+ 0
####ASSOC_MULT = |- ASSOC $*
####RIGHT_ID_MULT_1 = |- RIGHT_ID $* 1
####LEFT_ID_MULT_1 = |- LEFT_ID $* 1
####MONOID_MULT_1 = |- MONOID $* 1
##=======> theory arithmetic built
cd /<<PKGBUILDDIR>>/theories; rm -f list.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_list.ml;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_list_defs.ml;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_list_thms.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
##################################() : void
###Theory arithmetic loaded
() : void
###NOT_LESS_0 = |- !n. ~n < 0
#PRIM_REC_THM =
|- !x f.
(PRIM_REC x f 0 = x) /\
(!m. PRIM_REC x f(SUC m) = f(PRIM_REC x f m)m)
#PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
#LESS_0 = |- !n. 0 < (SUC n)
###NOT_SUC = |- !n. ~(SUC n = 0)
#INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
###ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
#LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
#LESS_EQ = |- !m n. m < n = (SUC m) <= n
#NOT_LESS = |- !m n. ~m < n = n <= m
#LESS_EQ_ADD = |- !m n. m <= (m + n)
#num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
#LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
###########
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
#####INDUCT_TAC = - : tactic
####
num_CONV = - : conv
File /<<PKGBUILDDIR>>/ml/numconv.ml loaded
() : void
######IS_list_REP =
|- !r. IS_list_REP r = (?f n. r = (\m. (m < n => f m | (@x. T))),n)
########EXISTS_list_REP = |- ?p. IS_list_REP p
#####list_TY_DEF = |- ?rep. TYPE_DEFINITION IS_list_REP rep
##########list_ISO_DEF =
|- (!a. ABS_list(REP_list a) = a) /\
(!r. IS_list_REP r = (REP_list(ABS_list r) = r))
#####R_ONTO = |- !r. IS_list_REP r = (?a. r = REP_list a)
A_11 =
|- !r r'.
IS_list_REP r ==>
IS_list_REP r' ==>
((ABS_list r = ABS_list r') = (r = r'))
A_R = |- !a. ABS_list(REP_list a) = a
R_A = |- !r. IS_list_REP r = (REP_list(ABS_list r) = r)
########NIL_DEF = |- [] = ABS_list((\n. @e. T),0)
#######CONS_DEF =
|- !h t.
CONS h t =
ABS_list
((\m. ((m = 0) => h | FST(REP_list t)(PRE m))),SUC(SND(REP_list t)))
##() : void
#######################lemma1 =
|- !x f.
?fn.
(!g. fn(g,0) = x) /\
(!g n.
fn(g,n + 1) =
f(fn((\i. g(i + 1)),n))(g 0)(ABS_list((\i. g(i + 1)),n)))
######NIL_lemma = |- REP_list[] = (\n. @x. T),0
######REP_lemma = |- IS_list_REP(REP_list l)
########################CONS_lemma =
|- REP_list(CONS h t) =
(\m. ((m = 0) => h | FST(REP_list t)(PRE m))),SUC(SND(REP_list t))
#############exists_lemma =
|- !x f. ?fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
####A_11_lemma =
|- (IS_list_REP r' /\ IS_list_REP r) /\ (r = r') ==>
(ABS_list r = ABS_list r')
#########R_A_lemma =
|- REP_list(ABS_list((\m. (m < n => f(SUC m) | (@x. T))),n)) =
(\m. (m < n => f(SUC m) | (@x. T))),n
#####################cons_lemma =
|- ABS_list((\m. (m < (SUC n) => f m | (@x. T))),SUC n) =
CONS(f 0)(ABS_list((\m. (m < n => f(SUC m) | (@x. T))),n))
###########################list_Axiom =
|- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
##
BASIC-HOL version 2.02 (GCL) created 19/1/23
#################################Theory list loaded
() : void
#Theory combin loaded
() : void
#####list_Axiom =
|- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
##num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
#PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
##UNCURRY_DEF = |- !f x y. UNCURRY f(x,y) = f x y
#o_DEF = |- !f g. f o g = (\x. f(g x))
#################################
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
#####INDUCT_TAC = - : tactic
##########
Section prove_rec_fn_exists begun
derive_existence_thm = - : (thm -> conv)
mk_fn =
-
: ((term # term # term list # term # goal) -> (term # term list # thm))
instantiate_existence_thm = - : (thm -> conv)
closeup = - : (term -> term)
prove_rec_fn_exists = - : (thm -> conv)
- : (thm -> conv)
Section prove_rec_fn_exists ended
prove_rec_fn_exists = - : (thm -> conv)
new_recursive_definition = - : (bool -> thm -> string -> conv)
File /<<PKGBUILDDIR>>/ml/prim_rec.ml loaded
() : void
######
() : void
Section prove_induction_thm begun
UNIQUENESS = - : (thm -> thm)
DEPTH_FORALL_CONV = - : (conv -> conv)
CONJS_CONV = - : (conv -> conv)
CONJS_SIMP = - : (conv -> conv)
T_AND_CONV = - : conv
GENL_T = - : (term list -> thm)
SIMP_CONV = - : conv
HYP_SIMP = - : conv
ANTE_ALL_CONV = - : conv
CONCL_SIMP = - : conv
prove_induction_thm = - : (thm -> thm)
- : (thm -> thm)
Section prove_induction_thm ended
prove_induction_thm = - : (thm -> thm)
Section prove_cases_thm begun
NOT_ALL_THENC = - : (conv -> conv)
BASE_CONV = - : conv
STEP_CONV = - : conv
NOT_IN_CONV = - : conv
STEP_SIMP = - : conv
DISJS_CHAIN = - : (conv -> thm -> thm)
prove_cases_thm = - : (thm -> thm)
- : (thm -> thm)
Section prove_cases_thm ended
prove_cases_thm = - : (thm -> thm)
Section prove_constructors_one_one begun
PAIR_EQ_CONV = - : conv
list_variant = - : (term list -> term list -> term list)
prove_const_one_one = - : (thm -> conv)
prove_constructors_one_one = - : (thm -> thm)
- : (thm -> thm)
Section prove_constructors_one_one ended
prove_constructors_one_one = - : (thm -> thm)
prove_constructors_distinct = - : (thm -> thm)
File /<<PKGBUILDDIR>>/ml/tyfns.ml loaded
() : void
####LIST_INDUCT_TAC = - : tactic
##
num_CONV = - : conv
File /<<PKGBUILDDIR>>/ml/numconv.ml loaded
() : void
########NULL_DEF = |- (NULL[] = T) /\ (!h t. NULL(CONS h t) = F)
####HD = |- !h t. HD(CONS h t) = h
####TL = |- !h t. TL(CONS h t) = t
###new_list_rec_definition = - : ((string # term) -> thm)
########SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
##########FOLDR =
|- (!f e. FOLDR f e[] = e) /\
(!f e x l. FOLDR f e(CONS x l) = f x(FOLDR f e l))
####FOLDL =
|- (!f e. FOLDL f e[] = e) /\
(!f e x l. FOLDL f e(CONS x l) = FOLDL f(f e x)l)
###########FILTER =
|- (!P. FILTER P[] = []) /\
(!P x l.
FILTER P(CONS x l) = (P x => CONS x(FILTER P l) | FILTER P l))
############SCANL =
|- (!f e. SCANL f e[] = [e]) /\
(!f e x l. SCANL f e(CONS x l) = CONS e(SCANL f(f e x)l))
#####SCANR =
|- (!f e. SCANR f e[] = [e]) /\
(!f e x l.
SCANR f e(CONS x l) = CONS(f x(HD(SCANR f e l)))(SCANR f e l))
############REVERSE =
|- (REVERSE[] = []) /\ (!x l. REVERSE(CONS x l) = SNOC x(REVERSE l))
###########APPEND =
|- (!l. APPEND[]l = l) /\
(!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
###########FLAT = |- (FLAT[] = []) /\ (!h t. FLAT(CONS h t) = APPEND h(FLAT t))
##########LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
##########MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
#############################MAP2 =
|- (!f. MAP2 f[][] = []) /\
(!f h1 t1 h2 t2.
MAP2 f(CONS h1 t1)(CONS h2 t2) = CONS(f h1 h2)(MAP2 f t1 t2))
#################ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
#########SOME_EL =
|- (!P. SOME_EL P[] = F) /\
(!P x l. SOME_EL P(CONS x l) = P x \/ SOME_EL P l)
########IS_EL_DEF = |- !x l. IS_EL x l = SOME_EL($= x)l
###AND_EL_DEF = |- AND_EL = ALL_EL I
###OR_EL_DEF = |- OR_EL = SOME_EL I
#####################FIRSTN =
|- (!l. FIRSTN 0 l = []) /\
(!n x l. FIRSTN(SUC n)(CONS x l) = CONS x(FIRSTN n l))
###########BUTFIRSTN =
|- (!l. BUTFIRSTN 0 l = l) /\
(!n x l. BUTFIRSTN(SUC n)(CONS x l) = BUTFIRSTN n l)
###############SEG =
|- (!k l. SEG 0 k l = []) /\
(!m x l. SEG(SUC m)0(CONS x l) = CONS x(SEG m 0 l)) /\
(!m k x l. SEG(SUC m)(SUC k)(CONS x l) = SEG(SUC m)k l)
######LAST_DEF = |- !l. LAST l = HD(SEG 1(PRE(LENGTH l))l)
###BUTLAST_DEF = |- !l. BUTLAST l = SEG(PRE(LENGTH l))0 l
####LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
###########LAST = |- !x l. LAST(SNOC x l) = x
#########BUTLAST = |- !x l. BUTLAST(SNOC x l) = l
###########LASTN =
|- (!l. LASTN 0 l = []) /\
(!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
###########BUTLASTN =
|- (!l. BUTLASTN 0 l = l) /\
(!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
###########EL = |- (!l. EL 0 l = HD l) /\ (!l n. EL(SUC n)l = EL n(TL l))
####ELL =
|- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))
################################IS_PREFIX =
|- (!l. IS_PREFIX l[] = T) /\
(!x l. IS_PREFIX[](CONS x l) = F) /\
(!x1 l1 x2 l2.
IS_PREFIX(CONS x1 l1)(CONS x2 l2) = (x1 = x2) /\ IS_PREFIX l1 l2)
#####REVERSE_SNOC = |- !x l. REVERSE(SNOC x l) = CONS x(REVERSE l)
###REVERSE_REVERSE = |- !l. REVERSE(REVERSE l) = l
######forall_REVERSE = |- !P. (!l. P(REVERSE l)) = (!l. P l)
########f_REVERSE_lemma =
|- !f1 f2. ((\x. f1(REVERSE x)) = (\x. f2(REVERSE x))) = (f1 = f2)
#######################SNOC_Axiom =
|- !e f. ?! fn. (fn[] = e) /\ (!x l. fn(SNOC x l) = f(fn l)x l)
####################################IS_SUFFIX =
|- (!l. IS_SUFFIX l[] = T) /\
(!x l. IS_SUFFIX[](SNOC x l) = F) /\
(!x1 l1 x2 l2.
IS_SUFFIX(SNOC x1 l1)(SNOC x2 l2) = (x1 = x2) /\ IS_SUFFIX l1 l2)
################IS_SUBLIST =
|- (!l. IS_SUBLIST l[] = T) /\
(!x l. IS_SUBLIST[](CONS x l) = F) /\
(!x1 l1 x2 l2.
IS_SUBLIST(CONS x1 l1)(CONS x2 l2) =
(x1 = x2) /\ IS_PREFIX l1 l2 \/ IS_SUBLIST l1(CONS x2 l2))
######SPLITP =
|- (!P. SPLITP P[] = [],[]) /\
(!P x l.
SPLITP P(CONS x l) =
(P x => ([],CONS x l) | (CONS x(FST(SPLITP P l)),SND(SPLITP P l))))
###PREFIX_DEF = |- !P l. PREFIX P l = FST(SPLITP($~ o P)l)
###SUFFIX_DEF =
|- !P l. SUFFIX P l = FOLDL(\l' x. (P x => SNOC x l' | []))[]l
######################ZIP =
|- (ZIP([],[]) = []) /\
(!x1 l1 x2 l2. ZIP(CONS x1 l1,CONS x2 l2) = CONS(x1,x2)(ZIP(l1,l2)))
#####UNZIP =
|- (UNZIP[] = [],[]) /\
(!x l.
UNZIP(CONS x l) =
CONS(FST x)(FST(UNZIP l)),CONS(SND x)(SND(UNZIP l)))
###UNZIP_FST_DEF = |- !l. UNZIP_FST l = FST(UNZIP l)
###UNZIP_SND_DEF = |- !l. UNZIP_SND l = SND(UNZIP l)
#########SUM = |- (SUM[] = 0) /\ (!h t. SUM(CONS h t) = h + (SUM t))
##########GENLIST =
|- (!f. GENLIST f 0 = []) /\
(!f n. GENLIST f(SUC n) = SNOC(f n)(GENLIST f n))
####REPLICATE =
|- (!x. REPLICATE 0 x = []) /\
(!n x. REPLICATE(SUC n)x = CONS x(REPLICATE n x))
##() : void
##
BASIC-HOL version 2.02 (GCL) created 19/1/23
###############################Theory list loaded
() : void
#####list_Axiom =
|- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
#NULL_DEF = |- (NULL[] = T) /\ (!h t. NULL(CONS h t) = F)
#HD = |- !h t. HD(CONS h t) = h
#TL = |- !h t. TL(CONS h t) = t
#SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
#FOLDR =
|- (!f e. FOLDR f e[] = e) /\
(!f e x l. FOLDR f e(CONS x l) = f x(FOLDR f e l))
#FOLDL =
|- (!f e. FOLDL f e[] = e) /\
(!f e x l. FOLDL f e(CONS x l) = FOLDL f(f e x)l)
#FILTER =
|- (!P. FILTER P[] = []) /\
(!P x l.
FILTER P(CONS x l) = (P x => CONS x(FILTER P l) | FILTER P l))
#MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
#MAP2 =
|- (!f. MAP2 f[][] = []) /\
(!f h1 t1 h2 t2.
MAP2 f(CONS h1 t1)(CONS h2 t2) = CONS(f h1 h2)(MAP2 f t1 t2))
#SCANR =
|- (!f e. SCANR f e[] = [e]) /\
(!f e x l.
SCANR f e(CONS x l) = CONS(f x(HD(SCANR f e l)))(SCANR f e l))
#SCANL =
|- (!f e. SCANL f e[] = [e]) /\
(!f e x l. SCANL f e(CONS x l) = CONS e(SCANL f(f e x)l))
#SEG =
|- (!k l. SEG 0 k l = []) /\
(!m x l. SEG(SUC m)0(CONS x l) = CONS x(SEG m 0 l)) /\
(!m k x l. SEG(SUC m)(SUC k)(CONS x l) = SEG(SUC m)k l)
#REVERSE =
|- (REVERSE[] = []) /\ (!x l. REVERSE(CONS x l) = SNOC x(REVERSE l))
#APPEND =
|- (!l. APPEND[]l = l) /\
(!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
#FLAT = |- (FLAT[] = []) /\ (!h t. FLAT(CONS h t) = APPEND h(FLAT t))
#LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
#ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
#SOME_EL =
|- (!P. SOME_EL P[] = F) /\
(!P x l. SOME_EL P(CONS x l) = P x \/ SOME_EL P l)
#IS_EL_DEF = |- !x l. IS_EL x l = SOME_EL($= x)l
#AND_EL_DEF = |- AND_EL = ALL_EL I
#OR_EL_DEF = |- OR_EL = SOME_EL I
#FIRSTN =
|- (!l. FIRSTN 0 l = []) /\
(!n x l. FIRSTN(SUC n)(CONS x l) = CONS x(FIRSTN n l))
#BUTFIRSTN =
|- (!l. BUTFIRSTN 0 l = l) /\
(!n x l. BUTFIRSTN(SUC n)(CONS x l) = BUTFIRSTN n l)
#LASTN =
|- (!l. LASTN 0 l = []) /\
(!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
#BUTLASTN =
|- (!l. BUTLASTN 0 l = l) /\
(!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
#LAST_DEF = |- !l. LAST l = HD(SEG 1(PRE(LENGTH l))l)
#BUTLAST_DEF = |- !l. BUTLAST l = SEG(PRE(LENGTH l))0 l
#EL = |- (!l. EL 0 l = HD l) /\ (!l n. EL(SUC n)l = EL n(TL l))
#ELL =
|- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))
#IS_PREFIX =
|- (!l. IS_PREFIX l[] = T) /\
(!x l. IS_PREFIX[](CONS x l) = F) /\
(!x1 l1 x2 l2.
IS_PREFIX(CONS x1 l1)(CONS x2 l2) = (x1 = x2) /\ IS_PREFIX l1 l2)
#IS_SUFFIX =
|- (!l. IS_SUFFIX l[] = T) /\
(!x l. IS_SUFFIX[](SNOC x l) = F) /\
(!x1 l1 x2 l2.
IS_SUFFIX(SNOC x1 l1)(SNOC x2 l2) = (x1 = x2) /\ IS_SUFFIX l1 l2)
#IS_SUBLIST =
|- (!l. IS_SUBLIST l[] = T) /\
(!x l. IS_SUBLIST[](CONS x l) = F) /\
(!x1 l1 x2 l2.
IS_SUBLIST(CONS x1 l1)(CONS x2 l2) =
(x1 = x2) /\ IS_PREFIX l1 l2 \/ IS_SUBLIST l1(CONS x2 l2))
#SPLITP =
|- (!P. SPLITP P[] = [],[]) /\
(!P x l.
SPLITP P(CONS x l) =
(P x => ([],CONS x l) | (CONS x(FST(SPLITP P l)),SND(SPLITP P l))))
#PREFIX_DEF = |- !P l. PREFIX P l = FST(SPLITP($~ o P)l)
#SUFFIX_DEF =
|- !P l. SUFFIX P l = FOLDL(\l' x. (P x => SNOC x l' | []))[]l
#ZIP =
|- (ZIP([],[]) = []) /\
(!x1 l1 x2 l2. ZIP(CONS x1 l1,CONS x2 l2) = CONS(x1,x2)(ZIP(l1,l2)))
#UNZIP =
|- (UNZIP[] = [],[]) /\
(!x l.
UNZIP(CONS x l) =
CONS(FST x)(FST(UNZIP l)),CONS(SND x)(SND(UNZIP l)))
#UNZIP_FST_DEF = |- !l. UNZIP_FST l = FST(UNZIP l)
#UNZIP_SND_DEF = |- !l. UNZIP_SND l = SND(UNZIP l)
#SUM = |- (SUM[] = 0) /\ (!h t. SUM(CONS h t) = h + (SUM t))
#GENLIST =
|- (!f. GENLIST f 0 = []) /\
(!f n. GENLIST f(SUC n) = SNOC(f n)(GENLIST f n))
#REPLICATE =
|- (!x. REPLICATE 0 x = []) /\
(!n x. REPLICATE(SUC n)x = CONS x(REPLICATE n x))
#####NOT_SUC = |- !n. ~(SUC n = 0)
#INV_SUC = |- !m n. (SUC m = SUC n) ==> (m = n)
#INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
##############################[(); (); (); (); (); (); (); (); (); (); (); (); (); (); (); (); ()]
: void list
#####################################################################################################[();
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: void list
#######ASSOC_DEF = |- !f. ASSOC f = (!x y z. f x(f y z) = f(f x y)z)
#COMM_DEF = |- !f. COMM f = (!x y. f x y = f y x)
#FCOMM_DEF = |- !f g. FCOMM f g = (!x y z. g x(f y z) = f(g x y)z)
#RIGHT_ID_DEF = |- !f e. RIGHT_ID f e = (!x. f x e = x)
#LEFT_ID_DEF = |- !f e. LEFT_ID f e = (!x. f e x = x)
#MONOID_DEF =
|- !f e. MONOID f e = ASSOC f /\ RIGHT_ID f e /\ LEFT_ID f e
##ASSOC_CONJ = |- ASSOC $/\
#ASSOC_DISJ = |- ASSOC $\/
#FCOMM_ASSOC = |- !f. FCOMM f f = ASSOC f
#MONOID_CONJ_T = |- MONOID $/\ T
#MONOID_DISJ_F = |- MONOID $/\ T
####o_DEF = |- !f g. f o g = (\x. f(g x))
#o_THM = |- !f g x. (f o g)x = f(g x)
#I_THM = |- !x. I x = x
##UNCURRY_DEF = |- !f x y. UNCURRY f(x,y) = f x y
#########
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
#####INDUCT_TAC = - : tactic
##########
Section prove_rec_fn_exists begun
derive_existence_thm = - : (thm -> conv)
mk_fn =
-
: ((term # term # term list # term # goal) -> (term # term list # thm))
instantiate_existence_thm = - : (thm -> conv)
closeup = - : (term -> term)
prove_rec_fn_exists = - : (thm -> conv)
- : (thm -> conv)
Section prove_rec_fn_exists ended
prove_rec_fn_exists = - : (thm -> conv)
new_recursive_definition = - : (bool -> thm -> string -> conv)
File /<<PKGBUILDDIR>>/ml/prim_rec.ml loaded
() : void
######
() : void
Section prove_induction_thm begun
UNIQUENESS = - : (thm -> thm)
DEPTH_FORALL_CONV = - : (conv -> conv)
CONJS_CONV = - : (conv -> conv)
CONJS_SIMP = - : (conv -> conv)
T_AND_CONV = - : conv
GENL_T = - : (term list -> thm)
SIMP_CONV = - : conv
HYP_SIMP = - : conv
ANTE_ALL_CONV = - : conv
CONCL_SIMP = - : conv
prove_induction_thm = - : (thm -> thm)
- : (thm -> thm)
Section prove_induction_thm ended
prove_induction_thm = - : (thm -> thm)
Section prove_cases_thm begun
NOT_ALL_THENC = - : (conv -> conv)
BASE_CONV = - : conv
STEP_CONV = - : conv
NOT_IN_CONV = - : conv
STEP_SIMP = - : conv
DISJS_CHAIN = - : (conv -> thm -> thm)
prove_cases_thm = - : (thm -> thm)
- : (thm -> thm)
Section prove_cases_thm ended
prove_cases_thm = - : (thm -> thm)
Section prove_constructors_one_one begun
PAIR_EQ_CONV = - : conv
list_variant = - : (term list -> term list -> term list)
prove_const_one_one = - : (thm -> conv)
prove_constructors_one_one = - : (thm -> thm)
- : (thm -> thm)
Section prove_constructors_one_one ended
prove_constructors_one_one = - : (thm -> thm)
prove_constructors_distinct = - : (thm -> thm)
File /<<PKGBUILDDIR>>/ml/tyfns.ml loaded
() : void
##
num_CONV = - : conv
File /<<PKGBUILDDIR>>/ml/numconv.ml loaded
() : void
#########NULL = |- NULL[] /\ (!h t. ~NULL(CONS h t))
######list_INDUCT =
|- !P. P[] /\ (!t. P t ==> (!h. P(CONS h t))) ==> (!l. P l)
###LIST_INDUCT_TAC = - : tactic
####list_CASES = |- !l. (l = []) \/ (?t h. l = CONS h t)
####CONS_11 = |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
###NOT_NIL_CONS = |- !h t. ~([] = CONS h t)
####NOT_CONS_NIL = |- !h t. ~(CONS h t = [])
######LIST_NOT_EQ =
|- !l1 l2. ~(l1 = l2) ==> (!h1 h2. ~(CONS h1 l1 = CONS h2 l2))
######NOT_EQ_LIST =
|- !h1 h2. ~(h1 = h2) ==> (!l1 l2. ~(CONS h1 l1 = CONS h2 l2))
######EQ_LIST =
|- !h1 h2.
(h1 = h2) ==> (!l1 l2. (l1 = l2) ==> (CONS h1 l1 = CONS h2 l2))
#########CONS = |- !l. ~NULL l ==> (CONS(HD l)(TL l) = l)
########APPEND_ASSOC =
|- !l1 l2 l3. APPEND l1(APPEND l2 l3) = APPEND(APPEND l1 l2)l3
#######Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
LENGTH_APPEND =
|- !l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)
########MAP_APPEND =
|- !f l1 l2. MAP f(APPEND l1 l2) = APPEND(MAP f l1)(MAP f l2)
######LENGTH_MAP = |- !l f. LENGTH(MAP f l) = LENGTH l
#########################################LENGTH_NIL = |- !l. (LENGTH l = 0) = (l = [])
##############Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
LENGTH_CONS =
|- !l n.
(LENGTH l = SUC n) = (?h l'. (LENGTH l' = n) /\ (l = CONS h l'))
#################LENGTH_EQ_SUC =
|- !P n.
(!l. (LENGTH l = SUC n) ==> P l) =
(!l. (LENGTH l = n) ==> (\l. !x. P(CONS x l))l)
###########LENGTH_EQ_NIL = |- !P. (!l. (LENGTH l = 0) ==> P l) = P[]
####################Theorem SUC_NOT autoloading from theory `arithmetic` ...
SUC_NOT = |- !n. ~(0 = SUC n)
LENGTH_MAP2 =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(!f.
(LENGTH(MAP2 f l1 l2) = LENGTH l1) /\
(LENGTH(MAP2 f l1 l2) = LENGTH l2))
##
Section <string> begun
chk_var = - : (term list -> term -> bool)
FORALL_PERM_RULE = - : (term list -> thm -> thm)
FORALL_PERM_CONV = - : (term list -> conv)
FORALL_PERM_TAC = - : (term list -> tactic)
((-), (-), -)
: ((term list -> thm -> thm) #
(term list -> conv) #
(term list -> tactic))
Section <string> ended
FORALL_PERM_RULE = - : (term list -> thm -> thm)
FORALL_PERM_CONV = - : (term list -> conv)
FORALL_PERM_TAC = - : (term list -> tactic)
NULL_EQ_NIL = |- !l. NULL l = (l = [])
LENGTH_EQ = |- !x y. (x = y) ==> (LENGTH x = LENGTH y)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
LENGTH_NOT_NULL = |- !l. 0 < (LENGTH l) = ~NULL l
REVERSE_SNOC = |- !x l. REVERSE(SNOC x l) = CONS x(REVERSE l)
REVERSE_REVERSE = |- !l. REVERSE(REVERSE l) = l
forall_REVERSE = |- !P. (!l. P(REVERSE l)) = (!l. P l)
f_REVERSE_lemma =
|- !f1 f2. ((\x. f1(REVERSE x)) = (\x. f2(REVERSE x))) = (f1 = f2)
SNOC_Axiom =
|- !e f. ?! fn. (fn[] = e) /\ (!x l. fn(SNOC x l) = f(fn l)x l)
SNOC_INDUCT =
|- !P. P[] /\ (!l. P l ==> (!x. P(SNOC x l))) ==> (!l. P l)
SNOC_CASES = |- !l. (l = []) \/ (?l' x. l = SNOC x l')
LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
NOT_NULL_SNOC = |- !x l. ~NULL(SNOC x l)
NOT_NIL_SNOC = |- !x l. ~([] = SNOC x l)
NOT_SNOC_NIL = |- !x l. ~(SNOC x l = [])
SNOC_11 = |- !x l x' l'. (SNOC x l = SNOC x' l') = (x = x') /\ (l = l')
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
SNOC_EQ_LENGTH_EQ =
|- !x1 l1 x2 l2. (SNOC x1 l1 = SNOC x2 l2) ==> (LENGTH l1 = LENGTH l2)
SNOC_REVERSE_CONS = |- !x l. SNOC x l = REVERSE(CONS x(REVERSE l))
SNOC_APPEND = |- !x l. SNOC x l = APPEND l[x]
MAP_SNOC = |- !f x l. MAP f(SNOC x l) = SNOC(f x)(MAP f l)
FOLDR_SNOC = |- !f e x l. FOLDR f e(SNOC x l) = FOLDR f(f x e)l
FOLDL_SNOC = |- !f e x l. FOLDL f e(SNOC x l) = f(FOLDL f e l)x
SNOC_INDUCT_TAC = - : tactic
FOLDR_FOLDL = |- !f e. MONOID f e ==> (!l. FOLDR f e l = FOLDL f e l)
LENGTH_FOLDR = |- !l. LENGTH l = FOLDR(\x l'. SUC l')0 l
LENGTH_FOLDL = |- !l. LENGTH l = FOLDL(\l' x. SUC l')0 l
MAP_FOLDR = |- !f l. MAP f l = FOLDR(\x l'. CONS(f x)l')[]l
MAP_FOLDL = |- !f l. MAP f l = FOLDL(\l' x. SNOC(f x)l')[]l
MAP_o = |- !f g. MAP(f o g) = (MAP f) o (MAP g)
MAP_MAP_o = |- !f g l. MAP f(MAP g l) = MAP(f o g)l
FILTER_FOLDR =
|- !P l. FILTER P l = FOLDR(\x l'. (P x => CONS x l' | l'))[]l
FILTER_SNOC =
|- !P x l. FILTER P(SNOC x l) = (P x => SNOC x(FILTER P l) | FILTER P l)
FILTER_FOLDL =
|- !P l. FILTER P l = FOLDL(\l' x. (P x => SNOC x l' | l'))[]l
FILTER_COMM =
|- !f1 f2 l. FILTER f1(FILTER f2 l) = FILTER f2(FILTER f1 l)
FILTER_IDEM = |- !f l. FILTER f(FILTER f l) = FILTER f l
FILTER_MAP = |- !f1 f2 l. FILTER f1(MAP f2 l) = MAP f2(FILTER(f1 o f2)l)
Theorem ADD_SUC autoloading from theory `arithmetic` ...
ADD_SUC = |- !m n. SUC(m + n) = m + (SUC n)
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Theorem ADD_0 autoloading from theory `arithmetic` ...
ADD_0 = |- !m. m + 0 = m
LENGTH_SEG =
|- !n k l. (n + k) <= (LENGTH l) ==> (LENGTH(SEG n k l) = n)
APPEND_NIL = |- (!l. APPEND l[] = l) /\ (!l. APPEND[]l = l)
APPEND_SNOC = |- !l1 x l2. APPEND l1(SNOC x l2) = SNOC x(APPEND l1 l2)
REVERSE_APPEND =
|- !l1 l2. REVERSE(APPEND l1 l2) = APPEND(REVERSE l2)(REVERSE l1)
APPEND_FOLDR = |- !l1 l2. APPEND l1 l2 = FOLDR CONS l2 l1
APPEND_FOLDL = |- !l1 l2. APPEND l1 l2 = FOLDL(\l' x. SNOC x l')l1 l2
FOLDR_APPEND =
|- !f e l1 l2. FOLDR f e(APPEND l1 l2) = FOLDR f(FOLDR f e l2)l1
FOLDL_APPEND =
|- !f e l1 l2. FOLDL f e(APPEND l1 l2) = FOLDL f(FOLDL f e l1)l2
CONS_APPEND = |- !x l. CONS x l = APPEND[x]l
ASSOC_APPEND = |- ASSOC APPEND
RIGHT_ID_APPEND_NIL = |- RIGHT_ID APPEND[]
LEFT_ID_APPEND_NIL = |- LEFT_ID APPEND[]
MONOID_APPEND_NIL = |- MONOID APPEND[]
APPEND_LENGTH_EQ =
|- !l1 l1'.
(LENGTH l1 = LENGTH l1') ==>
(!l2 l2'.
(LENGTH l2 = LENGTH l2') ==>
((APPEND l1 l2 = APPEND l1' l2') = (l1 = l1') /\ (l2 = l2')))
FILTER_APPEND =
|- !f l1 l2. FILTER f(APPEND l1 l2) = APPEND(FILTER f l1)(FILTER f l2)
FLAT_SNOC = |- !x l. FLAT(SNOC x l) = APPEND(FLAT l)x
FLAT_FOLDR = |- !l. FLAT l = FOLDR APPEND[]l
FLAT_FOLDL = |- !l. FLAT l = FOLDL APPEND[]l
LENGTH_FLAT = |- !l. LENGTH(FLAT l) = SUM(MAP LENGTH l)
REVERSE_FOLDR = |- !l. REVERSE l = FOLDR SNOC[]l
REVERSE_FOLDL = |- !l. REVERSE l = FOLDL(\l' x. CONS x l')[]l
LENGTH_REVERSE = |- !l. LENGTH(REVERSE l) = LENGTH l
REVERSE_EQ_NIL = |- !l. (REVERSE l = []) = (l = [])
ALL_EL_SNOC = |- !P x l. ALL_EL P(SNOC x l) = ALL_EL P l /\ P x
ALL_EL_CONJ =
|- !P Q l. ALL_EL(\x. P x /\ Q x)l = ALL_EL P l /\ ALL_EL Q l
ALL_EL_MAP = |- !P f l. ALL_EL P(MAP f l) = ALL_EL(P o f)l
ALL_EL_APPEND =
|- !P l1 l2. ALL_EL P(APPEND l1 l2) = ALL_EL P l1 /\ ALL_EL P l2
SOME_EL_SNOC = |- !P x l. SOME_EL P(SNOC x l) = P x \/ SOME_EL P l
NOT_ALL_EL_SOME_EL = |- !P l. ~ALL_EL P l = SOME_EL($~ o P)l
NOT_SOME_EL_ALL_EL = |- !P l. ~SOME_EL P l = ALL_EL($~ o P)l
IS_EL =
|- (!x. IS_EL x[] = F) /\
(!y x l. IS_EL y(CONS x l) = (y = x) \/ IS_EL y l)
IS_EL_SNOC = |- !y x l. IS_EL y(SNOC x l) = (y = x) \/ IS_EL y l
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
SUM_SNOC = |- !x l. SUM(SNOC x l) = (SUM l) + x
SUM_FOLDR = |- !l. SUM l = FOLDR $+ 0 l
SUM_FOLDL = |- !l. SUM l = FOLDL $+ 0 l
IS_PREFIX_APPEND = |- !l1 l2. IS_PREFIX l1 l2 = (?l. l1 = APPEND l2 l)
IS_SUFFIX_APPEND = |- !l1 l2. IS_SUFFIX l1 l2 = (?l. l1 = APPEND l l2)
IS_SUBLIST_APPEND =
|- !l1 l2. IS_SUBLIST l1 l2 = (?l l'. l1 = APPEND l(APPEND l2 l'))
IS_PREFIX_IS_SUBLIST = |- !l1 l2. IS_PREFIX l1 l2 ==> IS_SUBLIST l1 l2
IS_SUFFIX_IS_SUBLIST = |- !l1 l2. IS_SUFFIX l1 l2 ==> IS_SUBLIST l1 l2
IS_PREFIX_REVERSE =
|- !l1 l2. IS_PREFIX(REVERSE l1)(REVERSE l2) = IS_SUFFIX l1 l2
IS_SUFFIX_REVERSE =
|- !l1 l2. IS_SUFFIX(REVERSE l1)(REVERSE l2) = IS_PREFIX l1 l2
IS_SUBLIST_REVERSE =
|- !l1 l2. IS_SUBLIST(REVERSE l1)(REVERSE l2) = IS_SUBLIST l1 l2
PREFIX_FOLDR =
|- !P l. PREFIX P l = FOLDR(\x l'. (P x => CONS x l' | []))[]l
PREFIX =
|- (!P. PREFIX P[] = []) /\
(!P x l. PREFIX P(CONS x l) = (P x => CONS x(PREFIX P l) | []))
IS_PREFIX_PREFIX = |- !P l. IS_PREFIX l(PREFIX P l)
LENGTH_SCANL = |- !f e l. LENGTH(SCANL f e l) = SUC(LENGTH l)
LENGTH_SCANR = |- !f e l. LENGTH(SCANR f e l) = SUC(LENGTH l)
COMM_MONOID_FOLDL =
|- !f.
COMM f ==>
(!e'. MONOID f e' ==> (!e l. FOLDL f e l = f e(FOLDL f e' l)))
COMM_MONOID_FOLDR =
|- !f.
COMM f ==>
(!e'. MONOID f e' ==> (!e l. FOLDR f e l = f e(FOLDR f e' l)))
FCOMM_FOLDR_APPEND =
|- !g f.
FCOMM g f ==>
(!e.
LEFT_ID g e ==>
(!l1 l2. FOLDR f e(APPEND l1 l2) = g(FOLDR f e l1)(FOLDR f e l2)))
FCOMM_FOLDL_APPEND =
|- !f g.
FCOMM f g ==>
(!e.
RIGHT_ID g e ==>
(!l1 l2. FOLDL f e(APPEND l1 l2) = g(FOLDL f e l1)(FOLDL f e l2)))
MONOID_FOLDR_APPEND_FOLDR =
|- !f e.
MONOID f e ==>
(!l1 l2. FOLDR f e(APPEND l1 l2) = f(FOLDR f e l1)(FOLDR f e l2))
MONOID_FOLDL_APPEND_FOLDL =
|- !f e.
MONOID f e ==>
(!l1 l2. FOLDL f e(APPEND l1 l2) = f(FOLDL f e l1)(FOLDL f e l2))
FOLDL_SINGLE = |- !f e x. FOLDL f e[x] = f e x
FOLDR_SINGLE = |- !f e x. FOLDR f e[x] = f x e
FOLDR_CONS_NIL = |- !l. FOLDR CONS[]l = l
FOLDL_SNOC_NIL = |- !l. FOLDL(\xs x. SNOC x xs)[]l = l
FOLDR_FOLDL_REVERSE =
|- !f e l. FOLDR f e l = FOLDL(\x y. f y x)e(REVERSE l)
FOLDL_FOLDR_REVERSE =
|- !f e l. FOLDL f e l = FOLDR(\x y. f y x)e(REVERSE l)
FOLDR_REVERSE = |- !f e l. FOLDR f e(REVERSE l) = FOLDL(\x y. f y x)e l
FOLDL_REVERSE = |- !f e l. FOLDL f e(REVERSE l) = FOLDR(\x y. f y x)e l
FOLDR_MAP = |- !f e g l. FOLDR f e(MAP g l) = FOLDR(\x y. f(g x)y)e l
FOLDL_MAP = |- !f e g l. FOLDL f e(MAP g l) = FOLDL(\x y. f x(g y))e l
ALL_EL_FOLDR = |- !P l. ALL_EL P l = FOLDR(\x l'. P x /\ l')T l
ALL_EL_FOLDL = |- !P l. ALL_EL P l = FOLDL(\l' x. l' /\ P x)T l
SOME_EL_FOLDR = |- !P l. SOME_EL P l = FOLDR(\x l'. P x \/ l')F l
SOME_EL_FOLDL = |- !P l. SOME_EL P l = FOLDL(\l' x. l' \/ P x)F l
ALL_EL_FOLDR_MAP = |- !P l. ALL_EL P l = FOLDR $/\ T(MAP P l)
ALL_EL_FOLDL_MAP = |- !P l. ALL_EL P l = FOLDL $/\ T(MAP P l)
SOME_EL_FOLDR_MAP = |- !P l. SOME_EL P l = FOLDR $\/ F(MAP P l)
SOME_EL_FOLDL_MAP = |- !P l. SOME_EL P l = FOLDL $\/ F(MAP P l)
FOLDR_FILTER =
|- !f e P l. FOLDR f e(FILTER P l) = FOLDR(\x y. (P x => f x y | y))e l
FOLDL_FILTER =
|- !f e P l. FOLDL f e(FILTER P l) = FOLDL(\x y. (P y => f x y | x))e l
ASSOC_FOLDR_FLAT =
|- !f.
ASSOC f ==>
(!e.
LEFT_ID f e ==>
(!l. FOLDR f e(FLAT l) = FOLDR f e(MAP(FOLDR f e)l)))
ASSOC_FOLDL_FLAT =
|- !f.
ASSOC f ==>
(!e.
RIGHT_ID f e ==>
(!l. FOLDL f e(FLAT l) = FOLDL f e(MAP(FOLDL f e)l)))
MAP_FLAT = |- !f l. MAP f(FLAT l) = FLAT(MAP(MAP f)l)
FILTER_FLAT = |- !P l. FILTER P(FLAT l) = FLAT(MAP(FILTER P)l)
SOME_EL_MAP = |- !P f l. SOME_EL P(MAP f l) = SOME_EL(P o f)l
SOME_EL_APPEND =
|- !P l1 l2. SOME_EL P(APPEND l1 l2) = SOME_EL P l1 \/ SOME_EL P l2
SOME_EL_DISJ =
|- !P Q l. SOME_EL(\x. P x \/ Q x)l = SOME_EL P l \/ SOME_EL Q l
IS_EL_APPEND =
|- !l1 l2 x. IS_EL x(APPEND l1 l2) = IS_EL x l1 \/ IS_EL x l2
IS_EL_FOLDR = |- !y l. IS_EL y l = FOLDR(\x l'. (y = x) \/ l')F l
IS_EL_FOLDL = |- !y l. IS_EL y l = FOLDL(\l' x. l' \/ (y = x))F l
NULL_FOLDR = |- !l. NULL l = FOLDR(\x l'. F)T l
NULL_FOLDL = |- !l. NULL l = FOLDL(\x l'. F)T l
MAP_REVERSE = |- !f l. MAP f(REVERSE l) = REVERSE(MAP f l)
FILTER_REVERSE = |- !P l. FILTER P(REVERSE l) = REVERSE(FILTER P l)
Theorem PRE autoloading from theory `prim_rec` ...
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
LAST = |- !x l. LAST(SNOC x l) = x
BUTLAST = |- !x l. BUTLAST(SNOC x l) = l
SEG_LENGTH_ID = |- !l. SEG(LENGTH l)0 l = l
SEG_SUC_CONS = |- !m n l x. SEG m(SUC n)(CONS x l) = SEG m n l
SEG_0_SNOC =
|- !m l x. m <= (LENGTH l) ==> (SEG m 0(SNOC x l) = SEG m 0 l)
Theorem SUB_LESS_EQ autoloading from theory `arithmetic` ...
SUB_LESS_EQ = |- !n m. (n - m) <= n
Theorem SUB_MONO_EQ autoloading from theory `arithmetic` ...
SUB_MONO_EQ = |- !n m. (SUC n) - (SUC m) = n - m
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
BUTLASTN_SEG =
|- !n l. n <= (LENGTH l) ==> (BUTLASTN n l = SEG((LENGTH l) - n)0 l)
LASTN_CONS =
|- !n l. n <= (LENGTH l) ==> (!x. LASTN n(CONS x l) = LASTN n l)
LENGTH_LASTN = |- !n l. n <= (LENGTH l) ==> (LENGTH(LASTN n l) = n)
LASTN_LENGTH_ID = |- !l. LASTN(LENGTH l)l = l
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
LASTN_LASTN =
|- !l n m.
m <= (LENGTH l) ==> n <= m ==> (LASTN n(LASTN m l) = LASTN n l)
Theorem NOT_SUC_LESS_EQ_0 autoloading from theory `arithmetic` ...
NOT_SUC_LESS_EQ_0 = |- !n. ~(SUC n) <= 0
NOT_SUC_LESS_EQ_0 = |- !n. ~(SUC n) <= 0
FIRSTN_LENGTH_ID = |- !l. FIRSTN(LENGTH l)l = l
FIRSTN_SNOC =
|- !n l. n <= (LENGTH l) ==> (!x. FIRSTN n(SNOC x l) = FIRSTN n l)
BUTLASTN_LENGTH_NIL = |- !l. BUTLASTN(LENGTH l)l = []
BUTLASTN_SUC_BUTLAST =
|- !n l. n < (LENGTH l) ==> (BUTLASTN(SUC n)l = BUTLASTN n(BUTLAST l))
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
BUTLASTN_BUTLAST =
|- !n l.
n < (LENGTH l) ==> (BUTLASTN n(BUTLAST l) = BUTLAST(BUTLASTN n l))
LENGTH_BUTLASTN =
|- !n l. n <= (LENGTH l) ==> (LENGTH(BUTLASTN n l) = (LENGTH l) - n)
ADD_SUC_lem = |- !m n. m + (SUC n) = (SUC m) + n
BUTLASTN_BUTLASTN =
|- !m n l.
(n + m) <= (LENGTH l) ==>
(BUTLASTN n(BUTLASTN m l) = BUTLASTN(n + m)l)
APPEND_BUTLASTN_LASTN =
|- !n l. n <= (LENGTH l) ==> (APPEND(BUTLASTN n l)(LASTN n l) = l)
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
APPEND_FIRSTN_LASTN =
|- !m n l. (m + n = LENGTH l) ==> (APPEND(FIRSTN n l)(LASTN m l) = l)
BUTLASTN_APPEND2 =
|- !n l1 l2.
n <= (LENGTH l2) ==>
(BUTLASTN n(APPEND l1 l2) = APPEND l1(BUTLASTN n l2))
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
BUTLASTN_LENGTH_APPEND =
|- !l2 l1. BUTLASTN(LENGTH l2)(APPEND l1 l2) = l1
LASTN_LENGTH_APPEND = |- !l1 l2. LASTN(LENGTH l2)(APPEND l1 l2) = l2
BUTLASTN_CONS =
|- !n l.
n <= (LENGTH l) ==>
(!x. BUTLASTN n(CONS x l) = CONS x(BUTLASTN n l))
BUTLASTN_LENGTH_CONS = |- !l x. BUTLASTN(LENGTH l)(CONS x l) = [x]
LAST_LASTN_LAST =
|- !n l. n <= (LENGTH l) ==> 0 < n ==> (LAST(LASTN n l) = LAST l)
BUTLASTN_LASTN_NIL =
|- !n l. n <= (LENGTH l) ==> (BUTLASTN n(LASTN n l) = [])
LASTN_BUTLASTN =
|- !n m l.
(n + m) <= (LENGTH l) ==>
(LASTN n(BUTLASTN m l) = BUTLASTN m(LASTN(n + m)l))
BUTLASTN_LASTN =
|- !m n l.
m <= n /\ n <= (LENGTH l) ==>
(BUTLASTN m(LASTN n l) = LASTN(n - m)(BUTLASTN m l))
LASTN_1 = |- !l. ~(l = []) ==> (LASTN 1 l = [LAST l])
BUTLASTN_1 = |- !l. ~(l = []) ==> (BUTLASTN 1 l = BUTLAST l)
BUTLASTN_APPEND1 =
|- !l2 n.
(LENGTH l2) <= n ==>
(!l1. BUTLASTN n(APPEND l1 l2) = BUTLASTN(n - (LENGTH l2))l1)
LASTN_APPEND2 =
|- !n l2. n <= (LENGTH l2) ==> (!l1. LASTN n(APPEND l1 l2) = LASTN n l2)
LASTN_APPEND1 =
|- !l2 n.
(LENGTH l2) <= n ==>
(!l1. LASTN n(APPEND l1 l2) = APPEND(LASTN(n - (LENGTH l2))l1)l2)
LASTN_MAP =
|- !n l. n <= (LENGTH l) ==> (!f. LASTN n(MAP f l) = MAP f(LASTN n l))
BUTLASTN_MAP =
|- !n l.
n <= (LENGTH l) ==> (!f. BUTLASTN n(MAP f l) = MAP f(BUTLASTN n l))
ALL_EL_LASTN =
|- !P l. ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(LASTN m l))
ALL_EL_BUTLASTN =
|- !P l. ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(BUTLASTN m l))
LENGTH_FIRSTN = |- !n l. n <= (LENGTH l) ==> (LENGTH(FIRSTN n l) = n)
FIRSTN_FIRSTN =
|- !m l.
m <= (LENGTH l) ==>
(!n. n <= m ==> (FIRSTN n(FIRSTN m l) = FIRSTN n l))
LENGTH_BUTFIRSTN =
|- !n l. n <= (LENGTH l) ==> (LENGTH(BUTFIRSTN n l) = (LENGTH l) - n)
BUTFIRSTN_LENGTH_NIL = |- !l. BUTFIRSTN(LENGTH l)l = []
BUTFIRSTN_APPEND1 =
|- !n l1.
n <= (LENGTH l1) ==>
(!l2. BUTFIRSTN n(APPEND l1 l2) = APPEND(BUTFIRSTN n l1)l2)
BUTFIRSTN_APPEND2 =
|- !l1 n.
(LENGTH l1) <= n ==>
(!l2. BUTFIRSTN n(APPEND l1 l2) = BUTFIRSTN(n - (LENGTH l1))l2)
BUTFIRSTN_BUTFIRSTN =
|- !n m l.
(n + m) <= (LENGTH l) ==>
(BUTFIRSTN n(BUTFIRSTN m l) = BUTFIRSTN(n + m)l)
APPEND_FIRSTN_BUTFIRSTN =
|- !n l. n <= (LENGTH l) ==> (APPEND(FIRSTN n l)(BUTFIRSTN n l) = l)
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c - c = 0
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
Definition SUB autoloading from theory `arithmetic` ...
SUB =
|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
Theorem LESS_SUC_NOT autoloading from theory `arithmetic` ...
LESS_SUC_NOT = |- !m n. m < n ==> ~n < (SUC m)
LASTN_SEG =
|- !n l. n <= (LENGTH l) ==> (LASTN n l = SEG n((LENGTH l) - n)l)
FIRSTN_SEG = |- !n l. n <= (LENGTH l) ==> (FIRSTN n l = SEG n 0 l)
BUTFIRSTN_SEG =
|- !n l. n <= (LENGTH l) ==> (BUTFIRSTN n l = SEG((LENGTH l) - n)n l)
APPEND_BUTLAST_LAST =
|- !l. ~(l = []) ==> (APPEND(BUTLAST l)[LAST l] = l)
BUTFIRSTN_SNOC =
|- !n l.
n <= (LENGTH l) ==>
(!x. BUTFIRSTN n(SNOC x l) = SNOC x(BUTFIRSTN n l))
APPEND_BUTLASTN_BUTFIRSTN =
|- !m n l.
(m + n = LENGTH l) ==> (APPEND(BUTLASTN m l)(BUTFIRSTN n l) = l)
SEG_SEG =
|- !n1 m1 n2 m2 l.
(n1 + m1) <= (LENGTH l) /\ (n2 + m2) <= n1 ==>
(SEG n2 m2(SEG n1 m1 l) = SEG n2(m1 + m2)l)
SEG_APPEND1 =
|- !n m l1.
(n + m) <= (LENGTH l1) ==> (!l2. SEG n m(APPEND l1 l2) = SEG n m l1)
SEG_APPEND2 =
|- !l1 m n l2.
(LENGTH l1) <= m /\ n <= (LENGTH l2) ==>
(SEG n m(APPEND l1 l2) = SEG n(m - (LENGTH l1))l2)
SEG_FIRSTN_BUTFIRSTN =
|- !n m l.
(n + m) <= (LENGTH l) ==> (SEG n m l = FIRSTN n(BUTFIRSTN m l))
Theorem ADD_SUB autoloading from theory `arithmetic` ...
ADD_SUB = |- !a c. (a + c) - c = a
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem LESS_0_CASES autoloading from theory `arithmetic` ...
LESS_0_CASES = |- !m. (0 = m) \/ 0 < m
Theorem LESS_EQUAL_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQUAL_ANTISYM = |- !n m. n <= m /\ m <= n ==> (n = m)
SEG_APPEND =
|- !m l1 n l2.
m < (LENGTH l1) /\
(LENGTH l1) <= (n + m) /\
(n + m) <= ((LENGTH l1) + (LENGTH l2)) ==>
(SEG n m(APPEND l1 l2) =
APPEND(SEG((LENGTH l1) - m)m l1)(SEG((n + m) - (LENGTH l1))0 l2))
SEG_LENGTH_SNOC = |- !l x. SEG 1(LENGTH l)(SNOC x l) = [x]
SEG_SNOC =
|- !n m l. (n + m) <= (LENGTH l) ==> (!x. SEG n m(SNOC x l) = SEG n m l)
Theorem SUB_LESS_0 autoloading from theory `arithmetic` ...
SUB_LESS_0 = |- !n m. m < n = 0 < (n - m)
Theorem PRE_SUC_EQ autoloading from theory `arithmetic` ...
PRE_SUC_EQ = |- !m n. 0 < n ==> ((m = PRE n) = (SUC m = n))
ELL_SEG =
|- !n l. n < (LENGTH l) ==> (ELL n l = HD(SEG 1(PRE((LENGTH l) - n))l))
REWRITE1_TAC = - : thm_tactic
SNOC_FOLDR = |- !x l. SNOC x l = FOLDR CONS[x]l
IS_EL_FOLDR_MAP = |- !x l. IS_EL x l = FOLDR $\/ F(MAP($= x)l)
IS_EL_FOLDL_MAP = |- !x l. IS_EL x l = FOLDL $\/ F(MAP($= x)l)
FILTER_FILTER =
|- !P Q l. FILTER P(FILTER Q l) = FILTER(\x. P x /\ Q x)l
FCOMM_FOLDR_FLAT =
|- !g f.
FCOMM g f ==>
(!e.
LEFT_ID g e ==>
(!l. FOLDR f e(FLAT l) = FOLDR g e(MAP(FOLDR f e)l)))
FCOMM_FOLDL_FLAT =
|- !f g.
FCOMM f g ==>
(!e.
RIGHT_ID g e ==>
(!l. FOLDL f e(FLAT l) = FOLDL g e(MAP(FOLDL f e)l)))
FOLDR1 =
|- !f.
(!a b c. f a(f b c) = f b(f a c)) ==>
(!e l. FOLDR f(f h e)l = f h(FOLDR f e l))
FOLDL1 =
|- !f.
(!a b c. f(f a b)c = f(f a c)b) ==>
(!e l. FOLDL f(f e h)l = f(FOLDL f e l)h)
FOLDR_REVERSE2 =
|- !f.
(!a b c. f a(f b c) = f b(f a c)) ==>
(!e l. FOLDR f e(REVERSE l) = FOLDR f e l)
FOLDR_MAP_REVERSE =
|- !f.
(!a b c. f a(f b c) = f b(f a c)) ==>
(!e g l. FOLDR f e(MAP g(REVERSE l)) = FOLDR f e(MAP g l))
FOLDR_FILTER_REVERSE =
|- !f.
(!a b c. f a(f b c) = f b(f a c)) ==>
(!e P l. FOLDR f e(FILTER P(REVERSE l)) = FOLDR f e(FILTER P l))
FOLDL_REVERSE2 =
|- !f.
(!a b c. f(f a b)c = f(f a c)b) ==>
(!e l. FOLDL f e(REVERSE l) = FOLDL f e l)
COMM_ASSOC_LEM1 =
|- !f. COMM f ==> ASSOC f ==> (!a b c. f a(f b c) = f b(f a c))
COMM_ASSOC_LEM2 =
|- !f. COMM f ==> ASSOC f ==> (!a b c. f(f a b)c = f(f a c)b)
COMM_ASSOC_FOLDR_REVERSE =
|- !f. COMM f ==> ASSOC f ==> (!e l. FOLDR f e(REVERSE l) = FOLDR f e l)
COMM_ASSOC_FOLDL_REVERSE =
|- !f. COMM f ==> ASSOC f ==> (!e l. FOLDL f e(REVERSE l) = FOLDL f e l)
ELL_LAST = |- !l. ~NULL l ==> (ELL 0 l = LAST l)
ELL_0_SNOC = |- !l x. ELL 0(SNOC x l) = x
ELL_SNOC = |- !n. 0 < n ==> (!x l. ELL n(SNOC x l) = ELL(PRE n)l)
ELL_SUC_SNOC = |- !n x l. ELL(SUC n)(SNOC x l) = ELL n l
ELL_CONS = |- !n l. n < (LENGTH l) ==> (!x. ELL n(CONS x l) = ELL n l)
ELL_LENGTH_CONS = |- !l x. ELL(LENGTH l)(CONS x l) = x
ELL_LENGTH_SNOC =
|- !l x. ELL(LENGTH l)(SNOC x l) = (NULL l => x | HD l)
ELL_APPEND2 =
|- !n l2. n < (LENGTH l2) ==> (!l1. ELL n(APPEND l1 l2) = ELL n l2)
ELL_APPEND1 =
|- !l2 n.
(LENGTH l2) <= n ==>
(!l1. ELL n(APPEND l1 l2) = ELL(n - (LENGTH l2))l1)
ELL_PRE_LENGTH = |- !l. ~(l = []) ==> (ELL(PRE(LENGTH l))l = HD l)
EL_LENGTH_SNOC = |- !l x. EL(LENGTH l)(SNOC x l) = x
EL_PRE_LENGTH = |- !l. ~(l = []) ==> (EL(PRE(LENGTH l))l = LAST l)
EL_SNOC = |- !n l. n < (LENGTH l) ==> (!x. EL n(SNOC x l) = EL n l)
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
LESS_PRE_SUB_LESS = |- !n m. m < n ==> (PRE(n - m)) < n
EL_ELL =
|- !n l. n < (LENGTH l) ==> (EL n l = ELL(PRE((LENGTH l) - n))l)
EL_LENGTH_APPEND =
|- !l2 l1. ~NULL l2 ==> (EL(LENGTH l1)(APPEND l1 l2) = HD l2)
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
ELL_EL =
|- !n l. n < (LENGTH l) ==> (ELL n l = EL(PRE((LENGTH l) - n))l)
ELL_MAP = |- !n l f. n < (LENGTH l) ==> (ELL n(MAP f l) = f(ELL n l))
LENGTH_BUTLAST =
|- !l. ~(l = []) ==> (LENGTH(BUTLAST l) = PRE(LENGTH l))
BUTFIRSTN_LENGTH_APPEND =
|- !l1 l2. BUTFIRSTN(LENGTH l1)(APPEND l1 l2) = l2
FIRSTN_APPEND1 =
|- !n l1.
n <= (LENGTH l1) ==> (!l2. FIRSTN n(APPEND l1 l2) = FIRSTN n l1)
FIRSTN_APPEND2 =
|- !l1 n.
(LENGTH l1) <= n ==>
(!l2. FIRSTN n(APPEND l1 l2) = APPEND l1(FIRSTN(n - (LENGTH l1))l2))
FIRSTN_LENGTH_APPEND = |- !l1 l2. FIRSTN(LENGTH l1)(APPEND l1 l2) = l1
REVERSE_FLAT = |- !l. REVERSE(FLAT l) = FLAT(REVERSE(MAP REVERSE l))
MAP_COND =
|- !f c l1 l2. MAP f(c => l1 | l2) = (c => MAP f l1 | MAP f l2)
MAP_FILTER =
|- !f P l.
(!x. P(f x) = P x) ==> (MAP f(FILTER P l) = FILTER P(MAP f l))
FLAT_APPEND = |- !l1 l2. FLAT(APPEND l1 l2) = APPEND(FLAT l1)(FLAT l2)
FLAT_REVERSE = |- !l. FLAT(REVERSE l) = REVERSE(FLAT(MAP REVERSE l))
FLAT_FLAT = |- !l. FLAT(FLAT l) = FLAT(MAP FLAT l)
ALL_EL_REVERSE = |- !P l. ALL_EL P(REVERSE l) = ALL_EL P l
SOME_EL_REVERSE = |- !P l. SOME_EL P(REVERSE l) = SOME_EL P l
ALL_EL_SEG =
|- !P l.
ALL_EL P l ==> (!m k. (m + k) <= (LENGTH l) ==> ALL_EL P(SEG m k l))
ALL_EL_FIRSTN =
|- !P l. ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(FIRSTN m l))
Theorem SUB_ADD autoloading from theory `arithmetic` ...
SUB_ADD = |- !m n. n <= m ==> ((m - n) + n = m)
ALL_EL_BUTFIRSTN =
|- !P l.
ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(BUTFIRSTN m l))
SOME_EL_SEG =
|- !m k l.
(m + k) <= (LENGTH l) ==> (!P. SOME_EL P(SEG m k l) ==> SOME_EL P l)
SOME_EL_FIRSTN =
|- !m l. m <= (LENGTH l) ==> (!P. SOME_EL P(FIRSTN m l) ==> SOME_EL P l)
SOME_EL_BUTFIRSTN =
|- !m l.
m <= (LENGTH l) ==> (!P. SOME_EL P(BUTFIRSTN m l) ==> SOME_EL P l)
SOME_EL_LASTN =
|- !m l. m <= (LENGTH l) ==> (!P. SOME_EL P(LASTN m l) ==> SOME_EL P l)
SOME_EL_BUTLASTN =
|- !m l.
m <= (LENGTH l) ==> (!P. SOME_EL P(BUTLASTN m l) ==> SOME_EL P l)
IS_EL_REVERSE = |- !x l. IS_EL x(REVERSE l) = IS_EL x l
IS_EL_FILTER = |- !P x. P x ==> (!l. IS_EL x(FILTER P l) = IS_EL x l)
IS_EL_SEG =
|- !n m l.
(n + m) <= (LENGTH l) ==> (!x. IS_EL x(SEG n m l) ==> IS_EL x l)
IS_EL_SOME_EL = |- !x l. IS_EL x l = SOME_EL($= x)l
IS_EL_FIRSTN =
|- !m l. m <= (LENGTH l) ==> (!x. IS_EL x(FIRSTN m l) ==> IS_EL x l)
IS_EL_BUTFIRSTN =
|- !m l. m <= (LENGTH l) ==> (!x. IS_EL x(BUTFIRSTN m l) ==> IS_EL x l)
IS_EL_BUTLASTN =
|- !m l. m <= (LENGTH l) ==> (!x. IS_EL x(BUTLASTN m l) ==> IS_EL x l)
IS_EL_LASTN =
|- !m l. m <= (LENGTH l) ==> (!x. IS_EL x(LASTN m l) ==> IS_EL x l)
ZIP_SNOC =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(!x1 x2. ZIP(SNOC x1 l1,SNOC x2 l2) = SNOC(x1,x2)(ZIP(l1,l2)))
UNZIP_SNOC =
|- !x l.
UNZIP(SNOC x l) =
SNOC(FST x)(FST(UNZIP l)),SNOC(SND x)(SND(UNZIP l))
LENGTH_ZIP =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(LENGTH(ZIP(l1,l2)) = LENGTH l1) /\ (LENGTH(ZIP(l1,l2)) = LENGTH l2)
LENGTH_UNZIP_FST = |- !l. LENGTH(UNZIP_FST l) = LENGTH l
LENGTH_UNZIP_SND = |- !l. LENGTH(UNZIP_SND l) = LENGTH l
ZIP_UNZIP = |- !l. ZIP(UNZIP l) = l
UNZIP_ZIP =
|- !l1 l2. (LENGTH l1 = LENGTH l2) ==> (UNZIP(ZIP(l1,l2)) = l1,l2)
SUM_APPEND = |- !l1 l2. SUM(APPEND l1 l2) = (SUM l1) + (SUM l2)
SUM_REVERSE = |- !l. SUM(REVERSE l) = SUM l
SUM_FLAT = |- !l. SUM(FLAT l) = SUM(MAP SUM l)
EL_APPEND1 =
|- !n l1 l2. n < (LENGTH l1) ==> (EL n(APPEND l1 l2) = EL n l1)
EL_APPEND2 =
|- !l1 n.
(LENGTH l1) <= n ==>
(!l2. EL n(APPEND l1 l2) = EL(n - (LENGTH l1))l2)
EL_MAP = |- !n l. n < (LENGTH l) ==> (!f. EL n(MAP f l) = f(EL n l))
EL_CONS = |- !n. 0 < n ==> (!x l. EL n(CONS x l) = EL(PRE n)l)
EL_SEG = |- !n l. n < (LENGTH l) ==> (EL n l = HD(SEG 1 n l))
EL_IS_EL = |- !n l. n < (LENGTH l) ==> IS_EL(EL n l)l
TL_SNOC = |- !x l. TL(SNOC x l) = (NULL l => [] | SNOC x(TL l))
SUB_SUC_LESS = |- !m n. n < m ==> (m - (SUC n)) < m
Theorem SUB_PLUS autoloading from theory `arithmetic` ...
SUB_PLUS = |- !a b c. a - (b + c) = (a - b) - c
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
EL_REVERSE =
|- !n l. n < (LENGTH l) ==> (EL n(REVERSE l) = EL(PRE((LENGTH l) - n))l)
EL_REVERSE_ELL = |- !n l. n < (LENGTH l) ==> (EL n(REVERSE l) = ELL n l)
ELL_LENGTH_APPEND =
|- !l1 l2. ~NULL l1 ==> (ELL(LENGTH l2)(APPEND l1 l2) = LAST l1)
ELL_IS_EL = |- !n l. n < (LENGTH l) ==> IS_EL(EL n l)l
ELL_REVERSE =
|- !n l.
n < (LENGTH l) ==> (ELL n(REVERSE l) = ELL(PRE((LENGTH l) - n))l)
ELL_REVERSE_EL = |- !n l. n < (LENGTH l) ==> (ELL n(REVERSE l) = EL n l)
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
LESS_EQ_SPLIT = |- !m n p. (m + n) <= p ==> n <= p /\ m <= p
Theorem LESS_EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
SUB_GREATER_EQ_ADD = |- !p n m. p >= n ==> ((p - n) >= m = p >= (m + n))
Theorem SUB_LESS_EQ_ADD autoloading from theory `arithmetic` ...
SUB_LESS_EQ_ADD = |- !m p. m <= p ==> (!n. (p - m) <= n = p <= (m + n))
SUB_LESS_EQ_ADD = |- !p n m. n <= p ==> (m <= (p - n) = (m + n) <= p)
FIRSTN_BUTLASTN =
|- !n l. n <= (LENGTH l) ==> (FIRSTN n l = BUTLASTN((LENGTH l) - n)l)
BUTLASTN_FIRSTN =
|- !n l. n <= (LENGTH l) ==> (BUTLASTN n l = FIRSTN((LENGTH l) - n)l)
LASTN_BUTFIRSTN =
|- !n l. n <= (LENGTH l) ==> (LASTN n l = BUTFIRSTN((LENGTH l) - n)l)
BUTFIRSTN_LASTN =
|- !n l. n <= (LENGTH l) ==> (BUTFIRSTN n l = LASTN((LENGTH l) - n)l)
SUB_ADD_lem = |- !l n m. (n + m) <= l ==> ((l - (n + m)) + n = l - m)
SEG_LASTN_BUTLASTN =
|- !n m l.
(n + m) <= (LENGTH l) ==>
(SEG n m l = LASTN n(BUTLASTN((LENGTH l) - (n + m))l))
BUTFIRSTN_REVERSE =
|- !n l.
n <= (LENGTH l) ==> (BUTFIRSTN n(REVERSE l) = REVERSE(BUTLASTN n l))
BUTLASTN_REVERSE =
|- !n l.
n <= (LENGTH l) ==> (BUTLASTN n(REVERSE l) = REVERSE(BUTFIRSTN n l))
LASTN_REVERSE =
|- !n l. n <= (LENGTH l) ==> (LASTN n(REVERSE l) = REVERSE(FIRSTN n l))
FIRSTN_REVERSE =
|- !n l. n <= (LENGTH l) ==> (FIRSTN n(REVERSE l) = REVERSE(LASTN n l))
Theorem SUB_SUB autoloading from theory `arithmetic` ...
SUB_SUB = |- !b c. c <= b ==> (!a. a - (b - c) = (a + c) - b)
SEG_REVERSE =
|- !n m l.
(n + m) <= (LENGTH l) ==>
(SEG n m(REVERSE l) = REVERSE(SEG n((LENGTH l) - (n + m))l))
LENGTH_GENLIST = |- !f n. LENGTH(GENLIST f n) = n
LENGTH_REPLICATE = |- !n x. LENGTH(REPLICATE n x) = n
IS_EL_REPLICATE = |- !n. 0 < n ==> (!x. IS_EL x(REPLICATE n x))
ALL_EL_REPLICATE = |- !x n. ALL_EL($= x)(REPLICATE n x)
AND_EL_FOLDL = |- !l. AND_EL l = FOLDL $/\ T l
AND_EL_FOLDR = |- !l. AND_EL l = FOLDR $/\ T l
OR_EL_FOLDL = |- !l. OR_EL l = FOLDL $\/ F l
OR_EL_FOLDR = |- !l. OR_EL l = FOLDR $\/ F l
MAP2_ZIP =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(!f. MAP2 f l1 l2 = MAP(UNCURRY f)(ZIP(l1,l2)))
File mk_list_thm2 loaded
() : void
##=======> theory list built
cd /<<PKGBUILDDIR>>/theories; rm -f tree.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_tree.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
#############################() : void
###Theory list loaded
() : void
#########list_Axiom =
|- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
list_INDUCT =
|- !P. P[] /\ (!t. P t ==> (!h. P(CONS h t))) ==> (!l. P l)
CONS_11 = |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
NULL = |- NULL[] /\ (!h t. ~NULL(CONS h t))
NOT_CONS_NIL = |- !h t. ~(CONS h t = [])
NOT_NIL_CONS = |- !h t. ~([] = CONS h t)
ALL_EL_CONJ =
|- !P Q l. ALL_EL(\x. P x /\ Q x)l = ALL_EL P l /\ ALL_EL Q l
######ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
HD = |- !h t. HD(CONS h t) = h
TL = |- !h t. TL(CONS h t) = t
####LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
###EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
####################LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
ADD_SYM = |- !m n. m + n = n + m
EXP_ADD = |- !p q n. n EXP (p + q) = (n EXP p) * (n EXP q)
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
MULT_EXP_MONO =
|- !p q n m. (n * ((SUC q) EXP p) = m * ((SUC q) EXP p)) = (n = m)
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
NOT_ODD_EQ_EVEN = |- !n m. ~(SUC(n + n) = m + m)
LESS_CASES = |- !m n. m < n \/ n <= m
WOP = |- !P. (?n. P n) ==> (?n. P n /\ (!m. m < n ==> ~P m))
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
NOT_LESS = |- !m n. ~m < n = n <= m
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
LESS_EQ_ADD = |- !m n. m <= (m + n)
LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
LESS_EQ_ANTISYM = |- !m n. ~(m < n /\ n <= m)
LESS_EQ = |- !m n. m < n = (SUC m) <= n
###########INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
PRIM_REC_THM =
|- !x f.
(PRIM_REC x f 0 = x) /\
(!m. PRIM_REC x f(SUC m) = f(PRIM_REC x f m)m)
LESS_0 = |- !n. 0 < (SUC n)
LESS_SUC_REFL = |- !n. n < (SUC n)
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
NOT_LESS_0 = |- !n. ~n < 0
LESS_REFL = |- !n. ~n < n
####NOT_SUC = |- !n. ~(SUC n = 0)
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
#######
num_CONV = - : conv
File /<<PKGBUILDDIR>>/ml/numconv.ml loaded
() : void
#######
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
#######
Section prove_rec_fn_exists begun
derive_existence_thm = - : (thm -> conv)
mk_fn =
-
: ((term # term # term list # term # goal) -> (term # term list # thm))
instantiate_existence_thm = - : (thm -> conv)
closeup = - : (term -> term)
prove_rec_fn_exists = - : (thm -> conv)
- : (thm -> conv)
Section prove_rec_fn_exists ended
prove_rec_fn_exists = - : (thm -> conv)
new_recursive_definition = - : (bool -> thm -> string -> conv)
File /<<PKGBUILDDIR>>/ml/prim_rec.ml loaded
() : void
###INDUCT_TAC = - : tactic
###LIST_INDUCT_TAC = - : tactic
#####################arith_lemma =
|- !p q n m.
p < q ==> ~((SUC(n + n)) * (2 EXP p) = (SUC(m + m)) * (2 EXP q))
#############fun_11_1 =
|- !p q n m.
((SUC(n + n)) * (2 EXP p) = (SUC(m + m)) * (2 EXP q)) ==> (p = q)
##############fun_11_2 =
|- !p q n m.
((SUC(n + n)) * (2 EXP p) = (SUC(m + m)) * (2 EXP q)) ==> (n = m)
#######ty = ":num" : type
#########node_REP =
|- (node_REP[] = 0) /\
(!h t. node_REP(CONS h t) = (SUC(h + h)) * (2 EXP (node_REP t)))
########################node_REP_one_one = |- !l1 l2. (node_REP l1 = node_REP l2) = (l1 = l2)
#############Is_tree_REP =
|- Is_tree_REP = (\t. !P. (!tl. ALL_EL P tl ==> P(node_REP tl)) ==> P t)
#############ALL_EL_Is_tree_REP =
|- !trl.
ALL_EL Is_tree_REP trl =
(!P. ALL_EL(\t. (!tl. ALL_EL P tl ==> P(node_REP tl)) ==> P t)trl)
##########Is_tree_lemma1 =
|- !trl. ALL_EL Is_tree_REP trl ==> Is_tree_REP(node_REP trl)
#####taut1 = |- !a b. ~(a ==> b) = a /\ ~b
###########################Is_tree_lemma2 =
|- !t.
Is_tree_REP t ==>
(?trl. ALL_EL Is_tree_REP trl /\ (t = node_REP trl))
#######Is_tree_lemma3 =
|- !tl. Is_tree_REP(node_REP tl) ==> ALL_EL Is_tree_REP tl
#########Is_tree_lemma4 =
|- !tl. Is_tree_REP(node_REP tl) = ALL_EL Is_tree_REP tl
#########Exists_tree_REP = |- ?t. Is_tree_REP t
############tree_TY_DEF = |- ?rep. TYPE_DEFINITION Is_tree_REP rep
##########tree_ISO_DEF =
|- (!a. ABS_tree(REP_tree a) = a) /\
(!r. Is_tree_REP r = (REP_tree(ABS_tree r) = r))
#######R_11 = |- !a a'. (REP_tree a = REP_tree a') = (a = a')
R_ONTO = |- !r. Is_tree_REP r = (?a. r = REP_tree a)
A_11 =
|- !r r'.
Is_tree_REP r ==>
Is_tree_REP r' ==>
((ABS_tree r = ABS_tree r') = (r = r'))
A_ONTO = |- !a. ?r. (a = ABS_tree r) /\ Is_tree_REP r
A_R = |- !a. ABS_tree(REP_tree a) = a
R_A = |- !r. Is_tree_REP r = (REP_tree(ABS_tree r) = r)
######node = |- !tl. node tl = ABS_tree(node_REP(MAP REP_tree tl))
#####dest_node = |- !t. dest_node t = (@p. t = node p)
##########IS_REP_lemma = |- !tl. ALL_EL Is_tree_REP(MAP REP_tree tl)
############REP_ABS_lemma = |- !tl. REP_tree(node tl) = node_REP(MAP REP_tree tl)
######ABS_REP = |- !tl. Is_tree_REP(node_REP(MAP REP_tree tl))
#####ABS_11_lemma =
|- (ABS_tree(node_REP(MAP REP_tree tl1)) =
ABS_tree(node_REP(MAP REP_tree tl2))) =
(node_REP(MAP REP_tree tl1) = node_REP(MAP REP_tree tl2))
###################node_11 = |- !tl1 tl2. (node tl1 = node tl2) = (tl1 = tl2)
########A_R_list = |- !tl. tl = MAP ABS_tree(MAP REP_tree tl)
######R_A_R = |- REP_tree(ABS_tree(REP_tree t)) = REP_tree t
#####Is_R = |- Is_tree_REP(REP_tree t)
######R_A_R_list =
|- !tl. MAP REP_tree(MAP ABS_tree(MAP REP_tree tl)) = MAP REP_tree tl
###########A_ONTO_list =
|- !tl. ?trl. (tl = MAP ABS_tree trl) /\ ALL_EL Is_tree_REP trl
############R_ONTO_list =
|- !trl. ALL_EL Is_tree_REP trl ==> (?tl. trl = MAP REP_tree tl)
########R_A_list =
|- !trl.
ALL_EL Is_tree_REP trl ==> (MAP REP_tree(MAP ABS_tree trl) = trl)
############################induct_lemma1 =
|- (!tl. ALL_EL P tl ==> P(node tl)) =
(!trl.
ALL_EL Is_tree_REP trl ==>
ALL_EL(\x. P(ABS_tree x))trl ==>
(\x. P(ABS_tree x))(node_REP trl))
#################induct_lemma2 =
|- (!t. P t) =
(!rep.
Is_tree_REP rep ==> (\r. Is_tree_REP r /\ (\x. P(ABS_tree x))r)rep)
#############tree_Induct = |- !P. (!tl. ALL_EL P tl ==> P(node tl)) ==> (!t. P t)
#######################tree_INDUCT = - : (thm -> thm)
####################tree_INDUCT_TAC = - : tactic
##############bht =
|- bht =
PRIM_REC
(\tr. tr = node[])
(\res n tr. ?trl. (tr = node trl) /\ ALL_EL res trl)
#########bht_thm =
|- (bht 0 tr = (tr = node[])) /\
(bht(SUC n)tr = (?trl. (tr = node trl) /\ ALL_EL(bht n)trl))
##################bht_lemma1 = |- !n tr. bht n tr ==> bht(SUC n)tr
#########bht_lemma2 = |- !n tr. bht n tr ==> (!m. bht(n + m)tr)
######################bht_lemma3 =
|- !trl. ALL_EL(\tr. ?n. bht n tr)trl ==> (?n. ALL_EL(bht n)trl)
##########exists_bht = |- !t. ?n. bht n t
##########min_bht = |- !t. ?n. bht n t /\ (!m. m < n ==> ~bht m t)
######HT = |- !t. HT t = (@n. bht n t /\ (!m. m < n ==> ~bht m t))
###########HT_thm1 = |- !tr. bht(HT tr)tr
######HT_thm2 = |- !tr m. m < (HT tr) ==> ~bht m tr
##################HT_leaf = |- !trl. (HT(node trl) = 0) = (trl = [])
############HT_thm3 = |- !m tr. ~bht m tr ==> m < (HT tr)
#####HT_thm4 = |- !tr m. m < (HT tr) = ~bht m tr
###################HT_thm5 = |- !n tl h. ~bht n(node tl) ==> ~bht n(node(CONS h tl))
###########HT_thm6 =
|- !trl tl t.
ALL_EL(\t'. ~bht(HT t')(node tl))trl ==>
ALL_EL(\t'. ~bht(HT t')(node(CONS h tl)))trl
##########################HT_node = |- !tl. ALL_EL(\t. (HT t) < (HT(node tl)))tl
########Less_lemma = |- !n m. n < (SUC m) = n <= m
#############less_HT =
|- !trl m n.
m <= n ==> ALL_EL(\t. (HT t) < m)trl ==> ALL_EL(\t. (HT t) <= n)trl
###################less_HT2 = |- !trl n. (HT(node trl)) < n ==> ALL_EL(\t. (HT t) < n)trl
##########less_HT3 = |- !trl. (HT(node trl)) <= (HT(node[node trl]))
################less_HT4 =
|- !trl m n.
m <= n ==> ALL_EL(\t. (HT t) < m)trl ==> ALL_EL(\t. (HT t) < n)trl
######less_HT5 = |- !h. (HT h) < (HT(node[h]))
########less_HT6 = |- !h trl. (HT h) < (HT(node[node(CONS h trl)]))
#####less_HT7 = |- ALL_EL(\t. (HT t) < (HT(node[node tl])))tl
#####less_HT8 = |- ALL_EL(\t. (HT t) < (HT(node[node(CONS h trl)])))trl
##########dest_node_thm = |- !tl. dest_node(node tl) = tl
########################################approx_lemma =
|- !f n.
?fn. !trl. (HT(node trl)) <= n ==> (fn(node trl) = f(MAP fn trl))
#########trf =
|- !n f.
trf n f =
(@fn. !trl. (HT(node trl)) <= n ==> (fn(node trl) = f(MAP fn trl)))
#########trf_thm =
|- !f n trl.
(HT(node trl)) <= n ==> (trf n f(node trl) = f(MAP(trf n f)trl))
#######################trf_EQ_thm =
|- !t n m f. (HT t) < n /\ (HT t) < m ==> (trf n f t = trf m f t)
#############trf_EQ_thm2 =
|- !trl n m f.
ALL_EL(\t. (HT t) < n)trl /\ ALL_EL(\t. (HT t) < m)trl ==>
(MAP(trf n f)trl = MAP(trf m f)trl)
##############################FN_EXISTS = |- !f. ?fn. !trl. fn(node trl) = f(MAP fn trl)
##########FN_thm = |- ?FN. !f trl. FN f(node trl) = f(MAP(FN f)trl)
######AP =
|- ?AP.
(!l. AP[]l = []) /\
(!h t l. AP(CONS h t)l = CONS(h(HD l))(AP t(TL l)))
###AP =
|- ?AP.
(!l. AP[]l = []) /\
(!h t l. AP(CONS h t)l = CONS(h(HD l))(AP t(TL l)))
#AP_DEF =
["!l. AP[]l = []"; "!h t l. AP(CONS h t)l = CONS(h(HD l))(AP t(TL l))"]
: term list
#########AP_MAP = .. |- !l. AP(MAP f l)l = MAP(\x. f x x)l
#################EXISTS_THM = |- !f. ?fn. !tl. fn(node tl) = f(MAP fn tl)tl
#########lemma = |- !l. ALL_EL(\x. f x = g x)l ==> (MAP f l = MAP g l)
###############tree_Axiom = |- !f. ?! fn. !tl. fn(node tl) = f(MAP fn tl)tl
###() : void
##=======> theory tree built
cd /<<PKGBUILDDIR>>/theories; rm -f ltree.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_ltree.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
############################() : void
###Theory tree loaded
() : void
###Theory combin loaded
() : void
#####node_11 = |- !tl1 tl2. (node tl1 = node tl2) = (tl1 = tl2)
tree_Induct = |- !P. (!tl. ALL_EL P tl ==> P(node tl)) ==> (!t. P t)
tree_Axiom = |- !f. ?! fn. !tl. fn(node tl) = f(MAP fn tl)tl
##########SUM = |- (SUM[] = 0) /\ (!h t. SUM(CONS h t) = h + (SUM t))
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
FLAT = |- (FLAT[] = []) /\ (!h t. FLAT(CONS h t) = APPEND h(FLAT t))
APPEND =
|- (!l. APPEND[]l = l) /\
(!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
HD = |- !h t. HD(CONS h t) = h
TL = |- !h t. TL(CONS h t) = t
ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
#######list_Axiom =
|- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
list_INDUCT =
|- !P. P[] /\ (!t. P t ==> (!h. P(CONS h t))) ==> (!l. P l)
LENGTH_APPEND =
|- !l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)
LENGTH_NIL = |- !l. (LENGTH l = 0) = (l = [])
LENGTH_CONS =
|- !l n.
(LENGTH l = SUC n) = (?h l'. (LENGTH l' = n) /\ (l = CONS h l'))
####o_THM = |- !f g x. (f o g)x = f(g x)
####ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
ADD_EQ_0 = |- !m n. (m + n = 0) = (m = 0) /\ (n = 0)
#####num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
###INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
###########
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
#######
Section prove_rec_fn_exists begun
derive_existence_thm = - : (thm -> conv)
mk_fn =
-
: ((term # term # term list # term # goal) -> (term # term list # thm))
instantiate_existence_thm = - : (thm -> conv)
closeup = - : (term -> term)
prove_rec_fn_exists = - : (thm -> conv)
- : (thm -> conv)
Section prove_rec_fn_exists ended
prove_rec_fn_exists = - : (thm -> conv)
new_recursive_definition = - : (bool -> thm -> string -> conv)
File /<<PKGBUILDDIR>>/ml/prim_rec.ml loaded
() : void
#######################tree_INDUCT = - : (thm -> thm)
####################tree_INDUCT_TAC = - : tactic
###LIST_INDUCT_TAC = - : tactic
###INDUCT_TAC = - : tactic
########Size = |- Size = (@fn. !tl. fn(node tl) = SUC(SUM(MAP fn tl)))
###########Size_thm = |- !tl. Size(node tl) = SUC(SUM(MAP Size tl))
#########Is_ltree = |- !t l. Is_ltree(t,l) = (Size t = LENGTH l)
###ty = ":tree # (*)list" : type
######Exists_ltree_REP = |- ?t. Is_ltree t
#######ltree_TY_DEF = |- ?rep. TYPE_DEFINITION Is_ltree rep
##########ltree_ISO_DEF =
|- (!a. ABS_ltree(REP_ltree a) = a) /\
(!r. Is_ltree r = (REP_ltree(ABS_ltree r) = r))
#######R_11 = |- !a a'. (REP_ltree a = REP_ltree a') = (a = a')
R_ONTO = |- !r. Is_ltree r = (?a. r = REP_ltree a)
A_11 =
|- !r r'.
Is_ltree r ==>
Is_ltree r' ==>
((ABS_ltree r = ABS_ltree r') = (r = r'))
A_ONTO = |- !a. ?r. (a = ABS_ltree r) /\ Is_ltree r
A_R = |- !a. ABS_ltree(REP_ltree a) = a
R_A = |- !r. Is_ltree r = (REP_ltree(ABS_ltree r) = r)
########Node =
|- !v tl.
Node v tl =
ABS_ltree
(node(MAP(FST o REP_ltree)tl),CONS v(FLAT(MAP(SND o REP_ltree)tl)))
######################REP_Node =
|- !tl.
REP_ltree(Node v tl) =
node(MAP(FST o REP_ltree)tl),CONS v(FLAT(MAP(SND o REP_ltree)tl))
###########Size_LENGTH_lemma =
|- !t. Size(FST(REP_ltree t)) = LENGTH(SND(REP_ltree t))
#########MAP_Size_LENGTH =
|- !tl.
MAP Size(MAP(FST o REP_ltree)tl) =
MAP LENGTH(MAP(SND o REP_ltree)tl)
##############AP =
|- (!l. AP[]l = []) /\
(!h t l. AP(CONS h t)l = CONS(h(HD l))(AP t(TL l)))
######SPLIT =
|- (!l. SPLIT 0 l = [],l) /\
(!n l.
SPLIT(SUC n)l = CONS(HD l)(FST(SPLIT n(TL l))),SND(SPLIT n(TL l)))
######PART =
|- (!l. PART[]l = []) /\
(!n t l.
PART(CONS n t)l = CONS(FST(SPLIT n l))(PART t(SND(SPLIT n l))))
##########SPLIT_APPEND = |- !l l'. SPLIT(LENGTH l)(APPEND l l') = l,l'
######PART_FLAT = |- !l. PART(MAP LENGTH l)(FLAT l) = l
###############LENGTH_SND_SPLIT =
|- !l n m. (LENGTH l = n + m) ==> (LENGTH(SND(SPLIT n l)) = m)
###############LENGTH_FST_SPLIT =
|- !l n m. (LENGTH l = n + m) ==> (LENGTH(FST(SPLIT n l)) = n)
#################APPEND_SPLIT =
|- !l n m.
(LENGTH l = n + m) ==> (APPEND(FST(SPLIT n l))(SND(SPLIT n l)) = l)
##################################REP_REC_lemma =
|- !f.
?! fn.
!tl l.
fn(node tl,l) =
f
(AP(MAP(\t e. fn(t,e))tl)(PART(MAP Size tl)(TL l)))
(HD l)
(MAP ABS_ltree(AP(MAP $, tl)(PART(MAP Size tl)(TL l))))
############lemma1 =
|- !tl.
MAP
ABS_ltree
(AP
(MAP $,(MAP(FST o REP_ltree)tl))
(PART
(MAP Size(MAP(FST o REP_ltree)tl))
(FLAT(MAP(SND o REP_ltree)tl)))) =
tl
##############lemma2 =
|- !tl.
AP
(MAP(\t e. fn(t,e))(MAP(FST o REP_ltree)tl))
(PART
(MAP Size(MAP(FST o REP_ltree)tl))
(FLAT(MAP(SND o REP_ltree)tl))) =
MAP(fn o REP_ltree)tl
#######################lemma3 =
|- !trl l.
(LENGTH l = SUM(MAP Size trl)) ==>
(FLAT
(MAP
(SND o REP_ltree)
(MAP ABS_ltree(AP(MAP $, trl)(PART(MAP Size trl)l)))) =
l)
#########################lemma4 =
|- !trl l.
(LENGTH l = SUM(MAP Size trl)) ==>
(node
(MAP
(FST o REP_ltree)
(MAP ABS_ltree(AP(MAP $, trl)(PART(MAP Size trl)l)))) =
node trl)
####################lemma5 =
|- !trl l.
(Size(node trl) = LENGTH l) ==>
(ABS_ltree(node trl,l) =
Node(HD l)(MAP ABS_ltree(AP(MAP $, trl)(PART(MAP Size trl)(TL l)))))
#######################lemma6 =
|- !trl l.
(Size(node trl) = LENGTH l) ==>
ALL_EL
(\p. Size(FST p) = LENGTH(SND p))
(AP(MAP $, trl)(PART(MAP Size trl)(TL l)))
##################lemma7 =
|- !trl.
ALL_EL
(\t.
!l.
(Size t = LENGTH l) ==> (x(ABS_ltree(t,l)) = y(ABS_ltree(t,l))))
trl ==>
(!l.
ALL_EL(\p. Size(FST p) = LENGTH(SND p))(AP(MAP $, trl)l) ==>
(MAP x(MAP ABS_ltree(AP(MAP $, trl)l)) =
MAP y(MAP ABS_ltree(AP(MAP $, trl)l))))
###########################ltree_Axiom = |- !f. ?! fn. !v tl. fn(Node v tl) = f(MAP fn tl)v tl
####unique_lemma =
|- !f fn fn'.
(!v tl. fn(Node v tl) = f(MAP fn tl)v tl) /\
(!v tl. fn'(Node v tl) = f(MAP fn' tl)v tl) ==>
(fn = fn')
##############################ltree_Induct =
|- !P. (!t. ALL_EL P t ==> (!h. P(Node h t))) ==> (!l. P l)
###exists_lemma = |- !f. ?fn. !v tl. fn(Node v tl) = f(MAP fn tl)v tl
################Node_11 =
|- !v1 v2 trl1 trl2.
(Node v1 trl1 = Node v2 trl2) = (v1 = v2) /\ (trl1 = trl2)
#######################ltree_INDUCT = - : (thm -> thm)
#######################ltree_INDUCT_TAC = - : tactic
########Node_onto = |- !l. ?v trl. l = Node v trl
##() : void
##=======> theory ltree built
cd /<<PKGBUILDDIR>>/theories; rm -f tydefs.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_tydefs.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
############################() : void
###Theory ltree loaded
[()] : void list
###o_THM = |- !f g x. (f o g)x = f(g x)
###list_INDUCT =
|- !P. P[] /\ (!t. P t ==> (!h. P(CONS h t))) ==> (!l. P l)
#MAP_o = |- !f g. MAP(f o g) = (MAP f) o (MAP g)
####ltree_Axiom = |- !f. ?! fn. !v tl. fn(Node v tl) = f(MAP fn tl)v tl
ltree_Induct =
|- !P. (!t. ALL_EL P t ==> (!h. P(Node h t))) ==> (!l. P l)
####ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
###########
Section INDUCT_THEN begun
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
Section INDUCT_THEN ended
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
File /<<PKGBUILDDIR>>/ml/ind.ml loaded
() : void
###LIST_INDUCT_TAC = - : tactic
########################ltree_INDUCT = - : (thm -> thm)
#######################ltree_INDUCT_TAC = - : tactic
#######Node_onto = |- !l. ?v trl. l = Node v trl
#########ALL_EL_MAP_lemma = |- !l. ALL_EL(\x. x)(MAP P l) = ALL_EL P l
####exists_lemma = |- !f. ?fn. !v tl. fn(Node v tl) = f(MAP fn tl)v tl
###############TRP_thm = |- !P. ?TRP. !v tl. TRP(Node v tl) = P v tl /\ ALL_EL TRP tl
##########lemma1 =
|- !l x y.
ALL_EL P l /\ ALL_EL(\e. P e ==> (x e = y e))l ==>
(MAP x l = MAP y l)
######################TRP_EU =
|- !TRP P.
(!v tl. TRP(Node v tl) = P v tl /\ ALL_EL TRP tl) ==>
(!f.
(?fn.
!v tl. TRP(Node v tl) ==> (fn(Node v tl) = f(MAP fn tl)v tl)) /\
(!x y.
(!v tl. TRP(Node v tl) ==> (x(Node v tl) = f(MAP x tl)v tl)) ==>
(!v tl. TRP(Node v tl) ==> (y(Node v tl) = f(MAP y tl)v tl)) ==>
(!l. TRP l ==> (x l = y l))))
######TRP_DEF =
|- !P. TRP P = (@trp. !v tl. trp(Node v tl) = P v tl /\ ALL_EL trp tl)
########TRP = |- !P v tl. TRP P(Node v tl) = P v tl /\ ALL_EL(TRP P)tl
##############TRP_EU_thm =
|- !P f.
(?fn.
!v tl. TRP P(Node v tl) ==> (fn(Node v tl) = f(MAP fn tl)v tl)) /\
(!x y.
(!v tl. TRP P(Node v tl) ==> (x(Node v tl) = f(MAP x tl)v tl)) ==>
(!v tl. TRP P(Node v tl) ==> (y(Node v tl) = f(MAP y tl)v tl)) ==>
(!l. TRP P l ==> (x l = y l)))
########AR_lemma1 =
|- (!a. ABS(REP a) = a) ==>
(!r. TRP P r = (REP(ABS r) = r)) ==>
(!tl. ALL_EL(TRP P)(MAP REP tl))
############AR_lemma2 =
|- (!a. ABS(REP a) = a) ==>
(!r. TRP P r = (REP(ABS r) = r)) ==>
(!tl v.
P v(MAP REP tl) ==>
(REP(ABS(Node v(MAP REP tl))) = Node v(MAP REP tl)))
############AR_lemma3 =
|- (!a. ABS(REP a) = a) ==>
(!r. TRP P r = (REP(ABS r) = r)) ==>
(!trl. ALL_EL(TRP P)trl ==> (?tl. trl = MAP REP tl))
#######AR_lemma4 = |- (!a. ABS(REP a) = a) ==> (!al. MAP ABS(MAP REP al) = al)
#####AR_lemma5 = .. |- !a. ?r. (a = ABS r) /\ TRP P r
###############################################################TY_DEF_THM =
|- !REP ABS P.
(!a. ABS(REP a) = a) /\ (!r. TRP P r = (REP(ABS r) = r)) ==>
(!f.
?! fn.
!v tl.
P v(MAP REP tl) ==>
(fn(ABS(Node v(MAP REP tl))) = f(MAP fn tl)v tl))
########exists_TRP = |- !P. (?v. P v[]) ==> (?t. TRP P t)
##() : void
##=======> theory tydefs built
cd /<<PKGBUILDDIR>>/theories; rm -f sum.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_sum.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
############################################() : void
###Theory combin loaded
() : void
###o_DEF = |- !f g. f o g = (\x. f(g x))
#o_THM = |- !f g x. (f o g)x = f(g x)
###################IS_SUM_REP =
|- !f.
IS_SUM_REP f =
(?v1 v2.
(f = (\b x y. (x = v1) /\ b)) \/ (f = (\b x y. (y = v2) /\ ~b)))
###########EXISTS_SUM_REP = |- ?f. IS_SUM_REP f
#########sum_TY_DEF = |- ?rep. TYPE_DEFINITION IS_SUM_REP rep
##########sum_ISO_DEF =
|- (!a. ABS_sum(REP_sum a) = a) /\
(!r. IS_SUM_REP r = (REP_sum(ABS_sum r) = r))
######R_A = |- !r. (REP_sum(ABS_sum r) = r) = IS_SUM_REP r
R_11 = |- (a = a') = (REP_sum a = REP_sum a')
A_ONTO =
|- !a.
?r.
(a = ABS_sum r) /\
(?v1 v2.
(r = (\b x y. (x = v1) /\ b)) \/ (r = (\b x y. (y = v2) /\ ~b)))
##########INL_DEF = |- !e. INL e = ABS_sum(\b x y. (x = e) /\ b)
######INR_DEF = |- !e. INR e = ABS_sum(\b x y. (y = e) /\ ~b)
#######SIMP = - : (thm -> thm)
#REWRITE1_TAC = - : thm_tactic
#######REP_INL = |- REP_sum(INL v) = (\b x y. (x = v) /\ b)
#######REP_INR = |- REP_sum(INR v) = (\b x y. (y = v) /\ ~b)
#########INL_11 = |- (INL x = INL y) = (x = y)
#########INR_11 = |- (INR x = INR y) = (x = y)
########INR_neq_INL = |- !v1 v2. ~(INR v2 = INL v1)
######EPS_lemma = |- (@x. y = x) = y
#############################sum_axiom = |- !f g. ?! h. (h o INL = f) /\ (h o INR = g)
##############sum_Axiom = |- !f g. ?! h. (!x. h(INL x) = f x) /\ (!x. h(INR x) = g x)
################ISL_DEF = |- ?ISL. (!x. ISL(INL x)) /\ (!y. ~ISL(INR y))
###ISL = |- (!x. ISL(INL x)) /\ (!y. ~ISL(INR y))
##########ISR_DEF = |- ?ISR. (!x. ISR(INR x)) /\ (!y. ~ISR(INL y))
###ISR = |- (!x. ISR(INR x)) /\ (!y. ~ISR(INL y))
##########OUTL_DEF = |- ?OUTL. !x. OUTL(INL x) = x
###OUTL = |- !x. OUTL(INL x) = x
##########OUTR_DEF = |- ?OUTR. !x. OUTR(INR x) = x
###OUTR = |- !x. OUTR(INR x) = x
###() : void
###########################sum_EXISTS = |- !f g. ?h. (!x. h(INL x) = f x) /\ (!x. h(INR x) = g x)
sum_UNIQUE =
|- !f g h h'.
((!x. h(INL x) = f x) /\ (!x. h(INR x) = g x)) /\
(!x. h'(INL x) = f x) /\
(!x. h'(INR x) = g x) ==>
(!s. h s = h' s)
########################sum_lemma = |- !v. (?x. v = INL x) \/ (?x. v = INR x)
########ISL_OR_ISR = |- !x. ISL x \/ ISR x
########INL = |- !x. ISL x ==> (INL(OUTL x) = x)
########INR = |- !x. ISR x ==> (INR(OUTR x) = x)
##=======> theory sum built
cd /<<PKGBUILDDIR>>/theories; rm -f one.th;\
/<<PKGBUILDDIR>>/basic-hol < /<<PKGBUILDDIR>>/theories/mk_one.ml;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
##################################() : void
################EXISTS_ONE_REP = |- ?b. (\b. b)b
#######one_TY_DEF =
|- ?rep.
(!x' x''. (rep x' = rep x'') ==> (x' = x'')) /\
(!x'''. (\b. b)x''' = (?x'. x''' = rep x'))
###one_DEF = |- one = (@x. T)
###() : void
###################one_axiom = |- !f g. f = g
##########one = |- !v. v = one
###########one_Axiom = |- !e. ?! fn. fn one = e
##=======> theory one built
cd /<<PKGBUILDDIR>>/theories; rm -f HOL.th;\
echo 'new_theory `HOL`;;'\
'map new_parent [`one`;`sum`;`tydefs`];;'\
'close_theory();;'\
'quit();;'\
| /<<PKGBUILDDIR>>/basic-hol;\
cd /<<PKGBUILDDIR>>
BASIC-HOL version 2.02 (GCL) created 19/1/23
#() : void
Theory one loaded
Theory sum loaded
Theory tydefs loaded
[(); (); ()] : void list
() : void
=======> theory HOL built
echo 'load_theory `num`;;'\
'compilet `ml/numconv`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#Theory num loaded
() : void
num_CONV = - : conv
Calling Lisp compiler
File ml/numconv compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `HOL`;;'\
'compilet `ml/tydefs`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#() : void
Theory HOL loaded
() : void
ignore = - : (string -> bool)
is_sing = - : (string -> bool)
getid = - : (string -> string list -> (string # string list))
gettyvid = - : (string -> string list -> (string # string list))
gnt =
-
: (string list -> ((string + string + string + void) # string list))
isid = - : ((* + **) -> bool)
istyvar = - : ((* + ** + ***) -> bool)
is = - : ((* + ** + *** + ****) -> *** -> bool)
end = - : ((* + ** + *** + ****) -> bool)
istyop = - : ((string + *) -> bool)
ckrb = - : ((* + ** + string + ***) -> (* + ** + string + ***))
mk_ty = - : ((string # type list) -> type)
parse_types =
-
: (string -> string list -> ((type + void) list # string list))
parse_clause =
-
: (string ->
string ->
string list ->
string list ->
(string # (type + void) list # string list))
parse_clauses =
-
: (string ->
string list ->
string list ->
(string # (type + void) list) list)
parse_input =
-
: (string -> (string # (string # (type + void) list) list))
pargs = - : ((* + **) list -> (* list # term))
mk_tuple_ty = - : (type list -> type)
mk_tuple = - : (term list -> term)
mk_sum_ty = - : (type list -> type)
inject = - : (type -> term list -> term list)
mkvars = - : (type list -> term list)
mk_subset_pred = - : ((type + *) list list -> term)
splitf = - : ((* -> bool) -> * list -> (* list # * # * list))
prove_existence_thm = - : conv
variant_tyvar = - : (type list -> string list -> type)
OR_IMP_CONV = - : conv
FORALL_IN_CONV = - : conv
CONJS_CONV = - : (conv -> conv)
EQN_ELIM_CONV = - : conv
LENGTH_MAP_CONV = - : (thm -> conv)
LENGTH_ELIM_CONV = - : conv
MAP_CONV = - : conv
ELIM_MAP_CONV = - : conv
TRANSFORM = - : (term -> thm -> (term # thm))
part = - : (int -> * list -> (* list # * list))
define_const = - : ((string # (* + **) list # term) -> thm)
DEFINE_CONSTRUCTORS =
-
: (string list -> (* + **) list list -> thm -> thm)
mk_tests = - : (* list -> type -> (term # term list))
mk_proj = - : (term -> * list -> type -> term list)
extract_list = - : (type -> term -> term -> term list)
strip_inj = - : (term -> term)
extract_tuple = - : (type -> term -> term -> term list)
gen_names = - : ((bool # bool) -> * list list -> string list)
mk_fun_ty = - : (term -> type -> type)
make_rhs =
-
: (type ->
term ->
term ->
(bool # term # string # term list) ->
(term # term))
make_conditional = - : (term list -> term list -> term)
make_function = - : ((* + **) list list -> thm -> goal)
PROJ_CONV = - : conv
TEST_SIMP_CONV = - : conv
LIST_ELS = - : (term -> thm list)
GEN_PROJ_CONV = - : conv
TUPLE_COMPS = - : (thm -> thm list)
SIMP_CONV = - : conv
SIMPLIFY = - : (thm -> thm)
define_type = - : (string -> string -> thm)
- : (string -> string -> thm)
define_type = - : (string -> string -> thm)
Calling Lisp compiler
File ml/tydefs compiled
() : void
#echo 'compilet `ml/ind`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#
BETAS = - : (term -> term -> conv)
GTAC = - : (term -> tactic)
TACF = - : (term -> term -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> tactic list)
GOALS =
-
: (* -> ((* # term) -> (** # ***)) list -> term -> (** list # *** list))
GALPH = - : conv
GALPHA = - : conv
mapshape = - : (int list -> (* list -> **) list -> * list -> ** list)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> tactic)
INDUCT_THEN = - : (thm -> thm_tactic -> tactic)
Calling Lisp compiler
File ml/ind compiled
() : void
#echo 'compilet `ml/prim_rec`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#
derive_existence_thm = - : (thm -> conv)
mk_fn =
-
: ((term # term # term list # term # goal) -> (term # term list # thm))
instantiate_existence_thm = - : (thm -> conv)
closeup = - : (term -> term)
prove_rec_fn_exists = - : (thm -> conv)
- : (thm -> conv)
prove_rec_fn_exists = - : (thm -> conv)
new_recursive_definition = - : (bool -> thm -> string -> conv)
Calling Lisp compiler
File ml/prim_rec compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `HOL`;;'\
'compilet `ml/tyfns`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#() : void
Theory HOL loaded
() : void
() : void
UNIQUENESS = - : (thm -> thm)
DEPTH_FORALL_CONV = - : (conv -> conv)
CONJS_CONV = - : (conv -> conv)
CONJS_SIMP = - : (conv -> conv)
T_AND_CONV = - : conv
GENL_T = - : (term list -> thm)
SIMP_CONV = - : conv
HYP_SIMP = - : conv
ANTE_ALL_CONV = - : conv
CONCL_SIMP = - : conv
prove_induction_thm = - : (thm -> thm)
- : (thm -> thm)
prove_induction_thm = - : (thm -> thm)
NOT_ALL_THENC = - : (conv -> conv)
BASE_CONV = - : conv
STEP_CONV = - : conv
NOT_IN_CONV = - : conv
STEP_SIMP = - : conv
DISJS_CHAIN = - : (conv -> thm -> thm)
prove_cases_thm = - : (thm -> thm)
- : (thm -> thm)
prove_cases_thm = - : (thm -> thm)
PAIR_EQ_CONV = - : conv
list_variant = - : (term list -> term list -> term list)
prove_const_one_one = - : (thm -> conv)
prove_constructors_one_one = - : (thm -> thm)
- : (thm -> thm)
prove_constructors_one_one = - : (thm -> thm)
prove_constructors_distinct = - : (thm -> thm)
Calling Lisp compiler
File ml/tyfns compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `HOL`;;'\
'compilet `ml/num`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#() : void
Theory HOL loaded
() : void
() : void
INDUCT = - : ((thm # thm) -> thm)
INDUCT_TAC = - : tactic
new_prim_rec_definition = - : ((string # term) -> thm)
new_infix_prim_rec_definition = - : ((string # term) -> thm)
ADD_CONV = - : conv
num_EQ_CONV = - : conv
EXISTS_LEAST_CONV = - : conv
EXISTS_GREATEST_CONV = - : conv
term_of_int = - : (int -> term)
int_of_term = - : (term -> int)
Calling Lisp compiler
File ml/num compiled
() : void
#echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `HOL`;;'\
'compilet `ml/list`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#() : void
Theory HOL loaded
() : void
() : void
LIST_INDUCT = - : ((thm # thm) -> thm)
LIST_INDUCT_TAC = - : tactic
SNOC_INDUCT_TAC = - : tactic
EQ_LENGTH_INDUCT_TAC = - : tactic
EQ_LENGTH_SNOC_INDUCT_TAC = - : tactic
new_list_rec_definition = - : ((string # term) -> thm)
new_infix_list_rec_definition = - : ((string # term) -> thm)
LENGTH_CONV = - : conv
list_EQ_CONV = - : (conv -> conv)
check_const = - : (string -> term -> bool)
int_of_term = - : (term -> int)
term_of_int = - : (int -> term)
APPEND_CONV = - : conv
MAP_CONV = - : (conv -> conv)
FOLDR_CONV = - : (conv -> conv)
FOLDL_CONV = - : (conv -> conv)
list_FOLD_CONV = - : (thm -> conv -> conv)
SUM_CONV = - : conv
FILTER_CONV = - : (conv -> conv)
SNOC_CONV = - : conv
REVERSE_CONV = - : conv
FLAT_CONV = - : conv
EL_CONV = - : conv
ELL_CONV = - : conv
MAP2_CONV = - : (conv -> conv)
ALL_EL_CONV = - : (conv -> conv)
SOME_EL_CONV = - : (conv -> conv)
IS_EL_CONV = - : (conv -> conv)
LAST_CONV = - : conv
BUTLAST_CONV = - : conv
SUC_CONV = - : conv
SEG_CONV = - : conv
LASTN_CONV = - : conv
BUTLASTN_CONV = - : conv
BUTFIRSTN_CONV = - : conv
FIRSTN_CONV = - : conv
SCANL_CONV = - : (conv -> conv)
SCANR_CONV = - : (conv -> conv)
REPLICATE_CONV = - : conv
GENLIST_CONV = - : (conv -> conv)
((-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
-)
: (conv #
(conv -> conv) #
(conv -> conv) #
(conv -> conv) #
(thm -> conv -> conv) #
conv #
(conv -> conv) #
conv #
conv #
conv #
conv #
conv #
(conv -> conv) #
(conv -> conv) #
(conv -> conv) #
(conv -> conv) #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
(conv -> conv) #
(conv -> conv) #
conv #
(conv -> conv))
APPEND_CONV = - : conv
MAP_CONV = - : (conv -> conv)
FOLDR_CONV = - : (conv -> conv)
FOLDL_CONV = - : (conv -> conv)
list_FOLD_CONV = - : (thm -> conv -> conv)
SUM_CONV = - : conv
FILTER_CONV = - : (conv -> conv)
SNOC_CONV = - : conv
REVERSE_CONV = - : conv
FLAT_CONV = - : conv
EL_CONV = - : conv
ELL_CONV = - : conv
MAP2_CONV = - : (conv -> conv)
ALL_EL_CONV = - : (conv -> conv)
SOME_EL_CONV = - : (conv -> conv)
IS_EL_CONV = - : (conv -> conv)
LAST_CONV = - : conv
BUTLAST_CONV = - : conv
SEG_CONV = - : conv
LASTN_CONV = - : conv
BUTLASTN_CONV = - : conv
BUTFIRSTN_CONV = - : conv
FIRSTN_CONV = - : conv
SCANL_CONV = - : (conv -> conv)
SCANR_CONV = - : (conv -> conv)
REPLICATE_CONV = - : conv
GENLIST_CONV = - : (conv -> conv)
Calling Lisp compiler
File ml/list compiled
() : void
#echo 'compilet `ml/lib_loader`;;'\
'quit();;'\
| basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#
define_load_lib_function = - : (string list -> void -> void)
library_loader =
-
: ((string #
string list #
string list #
string list #
string #
string #
string list) ->
void)
Calling Lisp compiler
File ml/lib_loader compiled
() : void
#if [ cl = cl ]; then\
echo '#+allegro (progn () (set-case-mode :case-insensitive-upper) (setq *cltl1-in-package-compatibility-p* t) (setq comp:*cltl1-compile-file-toplevel-compatibility-p* t) (setq *enable-package-locked-errors* nil))'\
'(load "lisp/f-cl") (compile-file "lisp/banner.l") (quit)'\
| gcl; else\
lisp/banner; fi
GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>;; Loading "lisp/f-cl"
start address -T 0x77b480 ;; Finished loading "lisp/f-cl"
16585
>
Compiling lisp/banner.l.
End of Pass 1.
End of Pass 2.
OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
Finished compiling /<<PKGBUILDDIR>>/lisp/banner.o.
#p"/<<PKGBUILDDIR>>/lisp/banner.o"
NIL
NIL
>echo 'set_search_path[``; `/<<PKGBUILDDIR>>/theories/`];;'\
'load_theory `HOL`;;'\
'loadf `ml/load_thms`;;'\
'loadf `ml/lib_loader`;;'\
'loadf `ml/numconv`;;'\
'loadf `ml/tydefs`;;'\
'loadf `ml/ind`;;'\
'loadf `ml/prim_rec`;;'\
'loadf `ml/tyfns`;;'\
'loadf `ml/num`;;'\
'loadf `ml/list`;;'\
'map delete_cache [`arithmetic`;`sum`;`list`];;'\
'map delete_cache [`tree`;`ltree`;`prim_rec`];;'\
'lisp `(load "lisp/banner")`;;'\
'lisp `(setq %system-name "HOL")`;;'\
'lisp `(setq %hol-dir "/<<PKGBUILDDIR>>")`;;'\
'lisp `(setq %lib-dir "/<<PKGBUILDDIR>>/Library")`;;'\
'lisp `(setq %liszt "")`;;'\
'lisp `(setq %version "2.02 (GCL)")`;;'\
'set_flag(`abort_when_fail`,false);;'\
'set_search_path[``; `~/`; `/<<PKGBUILDDIR>>/theories/`];;'\
'set_help_search_path (words `/<<PKGBUILDDIR>>/help/ENTRIES/`);;'\
'set_library_search_path [`/<<PKGBUILDDIR>>/Library/`];;'\
'lisp `(setup)`;;' >foo2
echo 'lisp `(throw (quote eof) t)`;; #+native-reloc(progn (with-open-file (s "foo2") (let ((*standard-input* s)) (tml)))(ml-save "hol")) #-native-reloc(let ((si::*collect-binary-modules* t)(si::*binary-modules* (with-open-file (s "bm.l") (read s)))) (with-open-file (s "foo2") (let ((*standard-input* s)) (tml)))(compiler::link (remove-duplicates si::*binary-modules* :test (function equal)) "hol" "(progn (load \"debian/gcl_patch.l\")(load \"foo\")(with-open-file (s \"foo1\") (let ((*standard-input* s)) (tml)))(with-open-file (s \"foo2\") (let ((*standard-input* s)) (tml)))(ml-save \"hol\")(quit))" "" nil)(quit))`;;' | basic-hol
BASIC-HOL version 2.02 (GCL) created 19/1/23
#GCL (GNU Common Lisp) 2.6.14 Fri Jan 13 10:47:56 AM EST 2023 CLtL1 git: Version_2_6_14
Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl)
Binary License: GPL due to GPL'ed components: (XGCL UNEXEC)
Modifications of this banner must retain notice of a compatible license
Dedicated to the memory of W. Schelter
Use (help) to get some basic information on how to use GCL.
Temporary directory for compiler files:
/tmp/
>
BASIC-HOL version 2.02 (GCL) created 19/1/23
#() : void
Theory HOL loaded
() : void
.........() : void
#..() : void
.() : void
.......................................................() : void
...........() : void
........() : void
..............................() : void
...........() : void
...........................................() : void
[(); (); ()] : void list
[(); (); ()] : void list
() : void
() : void
() : void
() : void
() : void
() : void
true : bool
() : void
() : void
() : void
() : void
#make permissions
make[3]: Entering directory '/<<PKGBUILDDIR>>'
find $(ls -1 | grep -v debian) \
\( -type d -exec chmod 775 {} \; \) -o\
\( -type f -exec chmod 664 {} \; \)
for f in hol hol-lcf basic-hol Manual/LaTeX/makeindex Manual/LaTeX/makeindex.bin/*/makeindex Manual/Reference/bin/mktex Manual/Reference/bin/typecheck ; do\
( if [ -f $f ] ; then\
find $f -exec chmod 775 {} \; ;fi) ; \
done
make[3]: Leaving directory '/<<PKGBUILDDIR>>'
=======> hol88 version 2.02 (GCL) made
make[2]: Leaving directory '/<<PKGBUILDDIR>>'
date
Thu Jan 19 17:57:16 UTC 2023
/usr/bin/make library
make[2]: Entering directory '/<<PKGBUILDDIR>>'
date
Thu Jan 19 17:57:16 UTC 2023
(cd /<<PKGBUILDDIR>>/Library; /usr/bin/make LispType=cl\
Obj=o\
Lisp=gcl\
Liszt=\
LispDir=/<<PKGBUILDDIR>>/lisp\
Hol=/<<PKGBUILDDIR>>/hol library; cd ..)
make[3]: Entering directory '/<<PKGBUILDDIR>>/Library'
for lib in unwind taut sets reduce arith pred_sets string finite_sets res_quan wellorder abs_theory reals window pair word record_proof parser prettyp trs latex-hol more_arithmetic numeral ind_defs ; \
do (cd $lib; /usr/bin/make LispType=cl\
Obj=o\
Lisp=gcl\
Liszt=\
LispDir=/<<PKGBUILDDIR>>/lisp\
Hol=/<<PKGBUILDDIR>>/hol all; cd ..) ; \
done
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/unwind'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `unwinding`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
DEPTH_FORALL_CONV = - : (conv -> conv)
DEPTH_EXISTS_CONV = - : (conv -> conv)
FLATTEN_CONJ_CONV = - : conv
CONJ_FORALL_ONCE_CONV = - : conv
FORALL_CONJ_ONCE_CONV = - : conv
CONJ_FORALL_CONV = - : conv
FORALL_CONJ_CONV = - : conv
CONJ_FORALL_RIGHT_RULE = - : (thm -> thm)
FORALL_CONJ_RIGHT_RULE = - : (thm -> thm)
UNFOLD_CONV = - : (thm list -> conv)
UNFOLD_RIGHT_RULE = - : (thm list -> thm -> thm)
line_var = - : (term -> term)
line_name = - : (term -> string)
UNWIND_ONCE_CONV = - : ((term -> bool) -> conv)
UNWIND_CONV = - : ((term -> bool) -> conv)
UNWIND_ALL_BUT_CONV = - : (string list -> conv)
UNWIND_AUTO_CONV = - : conv
UNWIND_ALL_BUT_RIGHT_RULE = - : (string list -> thm -> thm)
UNWIND_AUTO_RIGHT_RULE = - : (thm -> thm)
EXISTS_DEL1_CONV = - : conv
EXISTS_DEL_CONV = - : conv
EXISTS_EQN_CONV = - : conv
PRUNE_ONCE_CONV = - : conv
PRUNE_ONE_CONV = - : (string -> conv)
PRUNE_SOME_CONV = - : (string list -> conv)
PRUNE_CONV = - : conv
PRUNE_SOME_RIGHT_RULE = - : (string list -> thm -> thm)
PRUNE_RIGHT_RULE = - : (thm -> thm)
EXPAND_ALL_BUT_CONV = - : (string list -> thm list -> conv)
EXPAND_AUTO_CONV = - : (thm list -> conv)
EXPAND_ALL_BUT_RIGHT_RULE = - : (string list -> thm list -> thm -> thm)
EXPAND_AUTO_RIGHT_RULE = - : (thm list -> thm -> thm)
Calling Lisp compiler
File unwinding compiled
() : void
#===> library unwind rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/unwind'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/taut'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `taut_check`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
is_T = - : (term -> bool)
is_F = - : (term -> bool)
BOOL_CASES_T_F = |- !f. (f T = F) ==> ((!x. f x) = F)
BOOL_CASES_F_F = |- !f. (f F = F) ==> ((!x. f x) = F)
BOOL_CASES_BOTH_T_RULE = - : ((thm # thm) -> conv)
BOOL_CASES_T_F_RULE = - : (thm -> conv)
BOOL_CASES_F_F_RULE = - : (thm -> conv)
qconv = `QCONV` : string
QCONV = - : (conv -> conv)
ALL_QCONV = - : conv
THENQC = - : (conv -> conv -> conv)
ORELSEQC = - : (conv -> conv -> conv)
TRY_QCONV = - : (conv -> conv)
RAND_QCONV = - : (conv -> conv)
RATOR_QCONV = - : (conv -> conv)
ABS_QCONV = - : (conv -> conv)
T_REFL = |- T = T
F_REFL = |- F = F
NOT_CONV = - : conv
EQ_CONV = - : conv
EQ_THEN_NOT_CONV = - : conv
AND_CONV = - : conv
OR_CONV = - : conv
IMP_CONV = - : conv
IMP_THEN_NOT_CONV = - : conv
IF_CONV = - : conv
SIMP_PROP_QCONV = - : conv
DEPTH_FORALL_QCONV = - : (conv -> conv)
FORALL_T = - : (term list -> thm)
FORALL_F = - : (term list -> thm)
TAUT_CHECK_CONV = - : conv
PTAUT_CONV = - : conv
PTAUT_TAC = - : tactic
PTAUT_PROVE = - : conv
non_prop_terms = - : (term -> term list)
TAUT_CONV = - : conv
TAUT_TAC = - : tactic
TAUT_PROVE = - : conv
((-), (-), (-), (-), (-), -)
: (conv # tactic # conv # conv # tactic # conv)
PTAUT_CONV = - : conv
PTAUT_TAC = - : tactic
PTAUT_PROVE = - : conv
TAUT_CONV = - : conv
TAUT_TAC = - : tactic
TAUT_PROVE = - : conv
Calling Lisp compiler
File taut_check compiled
() : void
#===> library taut rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/taut'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/sets'
rm -f sets.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_sets`;;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
EXISTENCE_THM = |- ?s. (\p. T)s
set_TY_DEF = |- ?rep. TYPE_DEFINITION(\p. T)rep
set_ISO_DEF =
|- (!a. SPEC(CHF a) = a) /\ (!r. (\p. T)r = (CHF(SPEC r) = r))
CHF_11 = |- !a a'. (CHF a = CHF a') = (a = a')
set_ISO_DEF = |- (!a. SPEC(CHF a) = a) /\ (!r. CHF(SPEC r) = r)
IN_DEF = |- !x s. x IN s = CHF s x
SPECIFICATION = |- !P x. x IN (SPEC P) = P x
EXTENSION = |- !s t. (s = t) = (!x. x IN s = x IN t)
NOT_EQUAL_SETS = |- !s t. ~(s = t) = (?x. x IN t = ~x IN s)
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem WOP autoloading from theory `arithmetic` ...
WOP = |- !P. (?n. P n) ==> (?n. P n /\ (!m. m < n ==> ~P m))
NUM_SET_WOP =
|- !s. (?n. n IN s) = (?n. n IN s /\ (!m. m IN s ==> n <= m))
GSPEC_DEF = |- !f. GSPEC f = SPEC(\y. ?x. y,T = f x)
GSPECIFICATION = |- !f v. v IN (GSPEC f) = (?x. v,T = f x)
Section SET_SPEC_CONV begun
dest_tuple = - : (term -> term list)
MK_PAIR = - : (* list -> conv)
EXISTS_TUPLE_CONV = - : (term list -> conv)
PAIR_EQ_CONV = - : conv
ELIM_EXISTS_CONV = - : conv
PROVE_EXISTS = - : conv
list_variant = - : (term list -> term list -> term list)
SET_SPEC_CONV = - : conv
- : conv
Section SET_SPEC_CONV ended
SET_SPEC_CONV = - : conv
File gspec.ml loaded
() : void
() : void
true : bool
lemma = |- !s x. x IN s ==> (!f. (f x) IN {f x | x IN s})
SET_MINIMUM =
|- !s M. (?x. x IN s) = (?x. x IN s /\ (!y. y IN s ==> (M x) <= (M y)))
EMPTY_DEF = |- EMPTY = SPEC(\x. F)
NOT_IN_EMPTY = |- !x. ~x IN EMPTY
MEMBER_NOT_EMPTY = |- !s. (?x. x IN s) = ~(s = EMPTY)
UNIV_DEF = |- UNIV = SPEC(\x. T)
IN_UNIV = |- !x. x IN UNIV
UNIV_NOT_EMPTY = |- ~(UNIV = EMPTY)
EMPTY_NOT_UNIV = |- ~(EMPTY = UNIV)
EQ_UNIV = |- (!x. x IN s) = (s = UNIV)
SUBSET_DEF = |- !s t. s SUBSET t = (!x. x IN s ==> x IN t)
SUBSET_TRANS = |- !s t u. s SUBSET t /\ t SUBSET u ==> s SUBSET u
SUBSET_REFL = |- !s. s SUBSET s
SUBSET_ANTISYM = |- !s t. s SUBSET t /\ t SUBSET s ==> (s = t)
EMPTY_SUBSET = |- !s. EMPTY SUBSET s
SUBSET_EMPTY = |- !s. s SUBSET EMPTY = (s = EMPTY)
SUBSET_UNIV = |- !s. s SUBSET UNIV
UNIV_SUBSET = |- !s. UNIV SUBSET s = (s = UNIV)
PSUBSET_DEF = |- !s t. s PSUBSET t = s SUBSET t /\ ~(s = t)
PSUBSET_TRANS = |- !s t u. s PSUBSET t /\ t PSUBSET u ==> s PSUBSET u
PSUBSET_IRREFL = |- !s. ~s PSUBSET s
NOT_PSUBSET_EMPTY = |- !s. ~s PSUBSET EMPTY
NOT_UNIV_PSUBSET = |- !s. ~UNIV PSUBSET s
PSUBSET_UNIV = |- !s. s PSUBSET UNIV = (?x. ~x IN s)
UNION_DEF = |- !s t. s UNION t = {x | x IN s \/ x IN t}
IN_UNION = |- !s t x. x IN (s UNION t) = x IN s \/ x IN t
UNION_ASSOC = |- !s t u. (s UNION t) UNION u = s UNION (t UNION u)
UNION_IDEMPOT = |- !s. s UNION s = s
UNION_COMM = |- !s t. s UNION t = t UNION s
SUBSET_UNION =
|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
SUBSET_UNION_ABSORPTION = |- !s t. s SUBSET t = (s UNION t = t)
UNION_EMPTY = |- (!s. EMPTY UNION s = s) /\ (!s. s UNION EMPTY = s)
UNION_UNIV = |- (!s. UNIV UNION s = UNIV) /\ (!s. s UNION UNIV = UNIV)
EMPTY_UNION = |- !s t. (s UNION t = EMPTY) = (s = EMPTY) /\ (t = EMPTY)
INTER_DEF = |- !s t. s INTER t = {x | x IN s /\ x IN t}
IN_INTER = |- !s t x. x IN (s INTER t) = x IN s /\ x IN t
INTER_ASSOC = |- !s t u. (s INTER t) INTER u = s INTER (t INTER u)
INTER_IDEMPOT = |- !s. s INTER s = s
INTER_COMM = |- !s t. s INTER t = t INTER s
INTER_SUBSET =
|- (!s t. (s INTER t) SUBSET s) /\ (!s t. (t INTER s) SUBSET s)
SUBSET_INTER_ABSORPTION = |- !s t. s SUBSET t = (s INTER t = s)
INTER_EMPTY =
|- (!s. EMPTY INTER s = EMPTY) /\ (!s. s INTER EMPTY = EMPTY)
INTER_UNIV = |- (!s. UNIV INTER s = s) /\ (!s. s INTER UNIV = s)
UNION_OVER_INTER =
|- !s t u. s INTER (t UNION u) = (s INTER t) UNION (s INTER u)
INTER_OVER_UNION =
|- !s t u. s UNION (t INTER u) = (s UNION t) INTER (s UNION u)
DISJOINT_DEF = |- !s t. DISJOINT s t = (s INTER t = EMPTY)
IN_DISJOINT = |- !s t. DISJOINT s t = ~(?x. x IN s /\ x IN t)
DISJOINT_SYM = |- !s t. DISJOINT s t = DISJOINT t s
DISJOINT_EMPTY = |- !s. DISJOINT EMPTY s /\ DISJOINT s EMPTY
DISJOINT_EMPTY_REFL = |- !s. (s = EMPTY) = DISJOINT s s
DISJOINT_UNION =
|- !s t u. DISJOINT(s UNION t)u = DISJOINT s u /\ DISJOINT t u
DIFF_DEF = |- !s t. s DIFF t = {x | x IN s /\ ~x IN t}
IN_DIFF = |- !s t x. x IN (s DIFF t) = x IN s /\ ~x IN t
DIFF_EMPTY = |- !s. s DIFF EMPTY = s
EMPTY_DIFF = |- !s. EMPTY DIFF s = EMPTY
DIFF_UNIV = |- !s. s DIFF UNIV = EMPTY
DIFF_DIFF = |- !s t. (s DIFF t) DIFF t = s DIFF t
DIFF_EQ_EMPTY = |- !s. s DIFF s = EMPTY
INSERT_DEF = |- !x s. x INSERT s = {y | (y = x) \/ y IN s}
() : void
IN_INSERT = |- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
COMPONENT = |- !x s. x IN (x INSERT s)
SET_CASES = |- !s. (s = {}) \/ (?x t. (s = x INSERT t) /\ ~x IN t)
DECOMPOSITION = |- !s x. x IN s = (?t. (s = x INSERT t) /\ ~x IN t)
ABSORPTION = |- !x s. x IN s = (x INSERT s = s)
INSERT_INSERT = |- !x s. x INSERT (x INSERT s) = x INSERT s
INSERT_COMM = |- !x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)
INSERT_UNIV = |- !x. x INSERT UNIV = UNIV
NOT_INSERT_EMPTY = |- !x s. ~(x INSERT s = {})
NOT_EMPTY_INSERT = |- !x s. ~({} = x INSERT s)
INSERT_UNION =
|- !x s t.
(x INSERT s) UNION t = (x IN t => s UNION t | x INSERT (s UNION t))
INSERT_UNION_EQ = |- !x s t. (x INSERT s) UNION t = x INSERT (s UNION t)
INSERT_INTER =
|- !x s t.
(x INSERT s) INTER t = (x IN t => x INSERT (s INTER t) | s INTER t)
DISJOINT_INSERT =
|- !x s t. DISJOINT(x INSERT s)t = DISJOINT s t /\ ~x IN t
INSERT_SUBSET = |- !x s t. (x INSERT s) SUBSET t = x IN t /\ s SUBSET t
SUBSET_INSERT =
|- !x s. ~x IN s ==> (!t. s SUBSET (x INSERT t) = s SUBSET t)
INSERT_DIFF =
|- !s t x.
(x INSERT s) DIFF t = (x IN t => s DIFF t | x INSERT (s DIFF t))
DELETE_DEF = |- !s x. s DELETE x = s DIFF {x}
IN_DELETE = |- !s x y. x IN (s DELETE y) = x IN s /\ ~(x = y)
DELETE_NON_ELEMENT = |- !x s. ~x IN s = (s DELETE x = s)
IN_DELETE_EQ =
|- !s x x'.
(x IN s = x' IN s) = (x IN (s DELETE x') = x' IN (s DELETE x))
EMPTY_DELETE = |- !x. {} DELETE x = {}
DELETE_DELETE = |- !x s. (s DELETE x) DELETE x = s DELETE x
DELETE_COMM = |- !x y s. (s DELETE x) DELETE y = (s DELETE y) DELETE x
DELETE_SUBSET = |- !x s. (s DELETE x) SUBSET s
SUBSET_DELETE = |- !x s t. s SUBSET (t DELETE x) = ~x IN s /\ s SUBSET t
SUBSET_INSERT_DELETE =
|- !x s t. s SUBSET (x INSERT t) = (s DELETE x) SUBSET t
DIFF_INSERT = |- !s t x. s DIFF (x INSERT t) = (s DELETE x) DIFF t
PSUBSET_INSERT_SUBSET =
|- !s t. s PSUBSET t = (?x. ~x IN s /\ (x INSERT s) SUBSET t)
lemma = |- ~(a = b) = (b = ~a)
PSUBSET_MEMBER =
|- !s t. s PSUBSET t = s SUBSET t /\ (?y. y IN t /\ ~y IN s)
DELETE_INSERT =
|- !x y s.
(x INSERT s) DELETE y =
((x = y) => s DELETE y | x INSERT (s DELETE y))
INSERT_DELETE = |- !x s. x IN s ==> (x INSERT (s DELETE x) = s)
DELETE_INTER = |- !s t x. (s DELETE x) INTER t = (s INTER t) DELETE x
DISJOINT_DELETE_SYM =
|- !s t x. DISJOINT(s DELETE x)t = DISJOINT(t DELETE x)s
CHOICE_EXISTS = |- ?CHOICE. !s. ~(s = {}) ==> (CHOICE s) IN s
CHOICE_DEF = |- !s. ~(s = {}) ==> (CHOICE s) IN s
REST_DEF = |- !s. REST s = s DELETE (CHOICE s)
CHOICE_NOT_IN_REST = |- !s. ~(CHOICE s) IN (REST s)
CHOICE_INSERT_REST =
|- !s. ~(s = {}) ==> ((CHOICE s) INSERT (REST s) = s)
REST_SUBSET = |- !s. (REST s) SUBSET s
lemma = |- (P /\ Q = P) = P ==> Q
REST_PSUBSET = |- !s. ~(s = {}) ==> (REST s) PSUBSET s
SING_DEF = |- !s. SING s = (?x. s = {x})
SING = |- !x. SING{x}
IN_SING = |- !x y. x IN {y} = (x = y)
NOT_SING_EMPTY = |- !x. ~({x} = {})
NOT_EMPTY_SING = |- !x. ~({} = {x})
EQUAL_SING = |- !x y. ({x} = {y}) = (x = y)
DISJOINT_SING_EMPTY = |- !x. DISJOINT{x}{}
INSERT_SING_UNION = |- !s x. x INSERT s = {x} UNION s
SING_DELETE = |- !x. {x} DELETE x = {}
DELETE_EQ_SING = |- !s x. x IN s ==> ((s DELETE x = {}) = (s = {x}))
CHOICE_SING = |- !x. CHOICE{x} = x
REST_SING = |- !x. REST{x} = {}
SING_IFF_EMPTY_REST = |- !s. SING s = ~(s = {}) /\ (REST s = {})
IMAGE_DEF = |- !f s. IMAGE f s = {f x | x IN s}
IN_IMAGE = |- !y s f. y IN (IMAGE f s) = (?x. (y = f x) /\ x IN s)
IMAGE_IN = |- !x s. x IN s ==> (!f. (f x) IN (IMAGE f s))
IMAGE_EMPTY = |- !f. IMAGE f{} = {}
IMAGE_ID = |- !s. IMAGE(\x. x)s = s
Theorem o_THM autoloading from theory `combin` ...
o_THM = |- !f g x. (f o g)x = f(g x)
IMAGE_COMPOSE = |- !f g s. IMAGE(f o g)s = IMAGE f(IMAGE g s)
IMAGE_INSERT = |- !f x s. IMAGE f(x INSERT s) = (f x) INSERT (IMAGE f s)
IMAGE_EQ_EMPTY = |- !s f. (IMAGE f s = {}) = (s = {})
IMAGE_DELETE = |- !f x s. ~x IN s ==> (IMAGE f(s DELETE x) = IMAGE f s)
IMAGE_UNION =
|- !f s t. IMAGE f(s UNION t) = (IMAGE f s) UNION (IMAGE f t)
IMAGE_SUBSET =
|- !s t. s SUBSET t ==> (!f. (IMAGE f s) SUBSET (IMAGE f t))
IMAGE_INTER =
|- !f s t. (IMAGE f(s INTER t)) SUBSET ((IMAGE f s) INTER (IMAGE f t))
INJ_DEF =
|- !f s t.
INJ f s t =
(!x. x IN s ==> (f x) IN t) /\
(!x y. x IN s /\ y IN s ==> (f x = f y) ==> (x = y))
INJ_ID = |- !s. INJ(\x. x)s s
INJ_COMPOSE = |- !f g s t u. INJ f s t /\ INJ g t u ==> INJ(g o f)s u
INJ_EMPTY = |- !f. (!s. INJ f{}s) /\ (!s. INJ f s{} = (s = {}))
SURJ_DEF =
|- !f s t.
SURJ f s t =
(!x. x IN s ==> (f x) IN t) /\
(!x. x IN t ==> (?y. y IN s /\ (f y = x)))
SURJ_ID = |- !s. SURJ(\x. x)s s
SURJ_COMPOSE =
|- !f g s t u. SURJ f s t /\ SURJ g t u ==> SURJ(g o f)s u
SURJ_EMPTY =
|- !f. (!s. SURJ f{}s = (s = {})) /\ (!s. SURJ f s{} = (s = {}))
IMAGE_SURJ = |- !f s t. SURJ f s t = (IMAGE f s = t)
BIJ_DEF = |- !f s t. BIJ f s t = INJ f s t /\ SURJ f s t
BIJ_ID = |- !s. BIJ(\x. x)s s
BIJ_EMPTY =
|- !f. (!s. BIJ f{}s = (s = {})) /\ (!s. BIJ f s{} = (s = {}))
BIJ_COMPOSE = |- !f g s t u. BIJ f s t /\ BIJ g t u ==> BIJ(g o f)s u
lemma1 =
|- !f s.
(!x y. x IN s /\ y IN s ==> (f x = f y) ==> (x = y)) =
(!y. y IN s ==> (!x. x IN s /\ (f x = f y) = y IN s /\ (x = y)))
lemma2 = |- !f s. ?g. !t. INJ f s t ==> (!x. x IN s ==> (g(f x) = x))
LINV_DEF = |- !f s t. INJ f s t ==> (!x. x IN s ==> (LINV f s(f x) = x))
lemma3 = |- !f s. ?g. !t. SURJ f s t ==> (!x. x IN t ==> (f(g x) = x))
RINV_DEF =
|- !f s t. SURJ f s t ==> (!x. x IN t ==> (f(RINV f s x) = x))
FINITE_DEF =
|- !s.
FINITE s = (!P. P{} /\ (!s'. P s' ==> (!e. P(e INSERT s'))) ==> P s)
FINITE_EMPTY = |- FINITE{}
FINITE_INSERT = |- !s. FINITE s ==> (!x. FINITE(x INSERT s))
SIMPLE_FINITE_INDUCT =
|- !P.
P{} /\ (!s. P s ==> (!e. P(e INSERT s))) ==> (!s. FINITE s ==> P s)
lemma =
|- P{} /\
(!s. FINITE s /\ P s ==> (!e. FINITE(e INSERT s) /\ P(e INSERT s))) ==>
(!s. FINITE s ==> P s)
FINITE_INDUCT =
|- !P.
P{} /\ (!s. FINITE s /\ P s ==> (!e. ~e IN s ==> P(e INSERT s))) ==>
(!s. FINITE s ==> P s)
SET_INDUCT_TAC = - : tactic
File set_ind loaded
() : void
FINITE_DELETE = |- !s. FINITE s ==> (!x. FINITE(s DELETE x))
INSERT_FINITE = |- !x s. FINITE(x INSERT s) ==> FINITE s
FINITE_INSERT = |- !x s. FINITE(x INSERT s) = FINITE s
DELETE_FINITE = |- !x s. FINITE(s DELETE x) ==> FINITE s
FINITE_DELETE = |- !x s. FINITE(s DELETE x) = FINITE s
UNION_FINITE = |- !s. FINITE s ==> (!t. FINITE t ==> FINITE(s UNION t))
FINITE_UNION_LEMMA =
|- !s. FINITE s ==> (!t. FINITE(s UNION t) ==> FINITE t)
FINITE_UNION = |- !s t. FINITE(s UNION t) ==> FINITE s /\ FINITE t
FINITE_UNION = |- !s t. FINITE(s UNION t) = FINITE s /\ FINITE t
INTER_FINITE = |- !s. FINITE s ==> (!t. FINITE(s INTER t))
SUBSET_FINITE = |- !s. FINITE s ==> (!t. t SUBSET s ==> FINITE t)
PSUBSET_FINITE = |- !s. FINITE s ==> (!t. t PSUBSET s ==> FINITE t)
FINITE_DIFF = |- !s. FINITE s ==> (!t. FINITE(s DIFF t))
FINITE_SING = |- !x. FINITE{x}
SING_FINITE = |- !s. SING s ==> FINITE s
IMAGE_FINITE = |- !s. FINITE s ==> (!f. FINITE(IMAGE f s))
card_rel_def =
"(!s. R s 0 = (s = {})) /\
(!s n. R s(SUC n) = (?x. x IN s /\ R(s DELETE x)n))"
: term
Theorem num_Axiom autoloading from theory `prim_rec` ...
num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
CARD_REL_EXISTS =
|- ?R.
(!s. R s 0 = (s = {})) /\
(!s n. R s(SUC n) = (?x. x IN s /\ R(s DELETE x)n))
CARD_REL_DEL_LEMMA =
.. |- !n s x.
x IN s ==> R(s DELETE x)n ==> (!y. y IN s ==> R(s DELETE y)n)
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
CARD_REL_UNIQUE = .. |- !n s. R s n ==> (!m. R s m ==> (n = m))
CARD_REL_EXISTS_LEMMA = .. |- !s. FINITE s ==> (?n. R s n)
CARD_REL_THM = .. |- !m s. FINITE s ==> (((@n. R s n) = m) = R s m)
CARD_EXISTS =
|- ?CARD.
(CARD{} = 0) /\
(!s.
FINITE s ==>
(!x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s))))
CARD_DEF =
|- (CARD{} = 0) /\
(!s.
FINITE s ==>
(!x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s))))
CARD_EMPTY = |- CARD{} = 0
CARD_INSERT =
|- !s.
FINITE s ==>
(!x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s)))
CARD_EQ_0 = |- !s. FINITE s ==> ((CARD s = 0) = (s = {}))
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
CARD_DELETE =
|- !s.
FINITE s ==>
(!x. CARD(s DELETE x) = (x IN s => (CARD s) - 1 | CARD s))
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
lemma1 = |- !n m. (SUC n) <= (SUC m) = n <= m
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
lemma2 = |- !n m. n <= (SUC m) = n <= m \/ (n = SUC m)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
CARD_INTER_LESS_EQ =
|- !s. FINITE s ==> (!t. (CARD(s INTER t)) <= (CARD s))
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
CARD_UNION =
|- !s.
FINITE s ==>
(!t.
FINITE t ==>
((CARD(s UNION t)) + (CARD(s INTER t)) = (CARD s) + (CARD t)))
lemma = |- !n m. n <= (SUC m) = n <= m \/ (n = SUC m)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
CARD_SUBSET =
|- !s. FINITE s ==> (!t. t SUBSET s ==> (CARD t) <= (CARD s))
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
CARD_PSUBSET =
|- !s. FINITE s ==> (!t. t PSUBSET s ==> (CARD t) < (CARD s))
CARD_SING = |- !x. CARD{x} = 1
SING_IFF_CARD1 = |- !s. SING s = (CARD s = 1) /\ FINITE s
Theorem SUB_PLUS autoloading from theory `arithmetic` ...
SUB_PLUS = |- !a b c. a - (b + c) = (a - b) - c
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
CARD_DIFF =
|- !t.
FINITE t ==>
(!s. FINITE s ==> (CARD(s DIFF t) = (CARD s) - (CARD(s INTER t))))
Theorem SUB_LESS_0 autoloading from theory `arithmetic` ...
SUB_LESS_0 = |- !n m. m < n = 0 < (n - m)
LESS_CARD_DIFF =
|- !t.
FINITE t ==>
(!s. FINITE s ==> (CARD t) < (CARD s) ==> 0 < (CARD(s DIFF t)))
INFINITE_DEF = |- !s. INFINITE s = ~FINITE s
NOT_IN_FINITE = |- INFINITE UNIV = (!s. FINITE s ==> (?x. ~x IN s))
INVERSE_LEMMA =
|- !f.
(!x y. (f x = f y) ==> (x = y)) ==>
((\x. @y. x = f y) o f = (\x. x))
IMAGE_11_INFINITE =
|- !f.
(!x y. (f x = f y) ==> (x = y)) ==>
(!s. INFINITE s ==> INFINITE(IMAGE f s))
INFINITE_SUBSET = |- !s. INFINITE s ==> (!t. s SUBSET t ==> INFINITE t)
IN_INFINITE_NOT_FINITE =
|- !s t. INFINITE s /\ FINITE t ==> (?x. x IN s /\ ~x IN t)
gdef =
["g 0 = {}"; "!n. g(SUC n) = (@x. ~x IN (g n)) INSERT (g n)"]
: term list
g_finite = .. |- !n. FINITE(g n)
g_subset = . |- !n x. x IN (g n) ==> (!i. x IN (g(n + i)))
lemma = |- (A \/ B) /\ ~B = A /\ ~B
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
g_cases =
.. |- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(!x. (?n. x IN (g n)) ==> (?m. x IN (g(SUC m)) /\ ~x IN (g m)))
z_in_g1 = .. |- (@x. ~x IN {}) IN (g(SUC 0))
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
z_in_gn = .. |- !n. (@x. ~x IN {}) IN (g(SUC n))
in_lemma = . |- !n. (@x. ~x IN (g n)) IN (g(SUC n))
not_in_lemma =
.. |- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(!i n. ~(@x. ~x IN (g(n + i))) IN (g n))
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
less_lemma = |- !m n. ~(m = n) = m < n \/ n < m
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
gn_unique =
.. |- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(!n m. ((@x. ~x IN (g n)) = (@x. ~x IN (g m))) = (n = m))
x_unique =
.. |- !n x y.
~x IN (g n) /\ ~y IN (g n) ==>
x IN (g(SUC n)) ==>
y IN (g(SUC n)) ==>
(x = y)
fdef =
"\x.
((?n. x IN (g n)) =>
(@y. ~y IN (g(SUC(@n. x IN (g(SUC n)) /\ ~x IN (g n))))) |
x)"
: term
cases = |- !x. (?n. x IN (g n)) \/ (!n. ~x IN (g n))
INF_IMP_INFINITY =
|- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y)))
prth =
|- ?fn. (!f x. fn f x 0 = x) /\ (!f x n. fn f x(SUC n) = f(fn f x n))
prmth = |- !x f. ?fn. (fn 0 = x) /\ (!n. fn(SUC n) = f(fn n))
num_fn_thm =
|- (?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y))) ==>
(?fn. !n m. (fn n = fn m) ==> (n = m))
Theorem LESS_IMP_LESS_ADD autoloading from theory `arithmetic` ...
LESS_IMP_LESS_ADD = |- !n m. n < m ==> (!p. n < (m + p))
Theorem LESS_ADD_SUC autoloading from theory `arithmetic` ...
LESS_ADD_SUC = |- !m n. m < (m + (SUC n))
finite_N_bounded = |- !s. FINITE s ==> (?m. !n. n IN s ==> n < m)
N_lemma = |- INFINITE UNIV
main_lemma =
|- !s.
FINITE s ==>
(!f. (!n m. (f n = f m) ==> (n = m)) ==> (?n. ~(f n) IN s))
INFINITY_IMP_INF =
|- (?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y))) ==>
(!s. FINITE s ==> (?x. ~x IN s))
INFINITE_UNIV =
|- INFINITE UNIV =
(?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y)))
FINITE_PSUBSET_INFINITE =
|- !s. INFINITE s = (!t. FINITE t ==> t SUBSET s ==> t PSUBSET s)
FINITE_PSUBSET_UNIV =
|- INFINITE UNIV = (!s. FINITE s ==> s PSUBSET UNIV)
INFINITE_DIFF_FINITE =
|- !s t. INFINITE s /\ FINITE t ==> ~(s DIFF t = {})
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
FINITE_ISO_NUM =
|- !s.
FINITE s ==>
(?f.
(!n m. n < (CARD s) /\ m < (CARD s) ==> (f n = f m) ==> (n = m)) /\
(s = {f n | n < (CARD s)}))
echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `sets`;;'\
'compilet `set_ind`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory sets loaded
() : void
SET_INDUCT_TAC = - : tactic
Calling Lisp compiler
File set_ind compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `sets`;;'\
'compilet `gspec`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory sets loaded
() : void
dest_tuple = - : (term -> term list)
MK_PAIR = - : (* list -> conv)
EXISTS_TUPLE_CONV = - : (term list -> conv)
PAIR_EQ_CONV = - : conv
ELIM_EXISTS_CONV = - : conv
PROVE_EXISTS = - : conv
list_variant = - : (term list -> term list -> term list)
SET_SPEC_CONV = - : conv
- : conv
SET_SPEC_CONV = - : conv
Calling Lisp compiler
File gspec compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `sets`;;'\
'compilet `fset_conv`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory sets loaded
() : void
FINITE_CONV = - : conv
IN_CONV = - : (conv -> conv)
DELETE_CONV = - : (conv -> conv)
UNION_CONV = - : (conv -> conv)
INSERT_CONV = - : (conv -> conv)
IMAGE_CONV = - : (conv -> conv -> conv)
Calling Lisp compiler
File fset_conv compiled
() : void
#===> library sets rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/reduce'
\
echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `arithconv`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
dest_op = - : (term -> term -> term list)
term_of_int = - : (int -> term)
int_of_term = - : (term -> int)
provelt = - : (int -> int -> thm)
NEQ_CONV = - : conv
LT_CONV = - : conv
GT_CONV = - : conv
LE_CONV = - : conv
GE_CONV = - : conv
SUC_CONV = - : conv
PRE_CONV = - : conv
SBC_CONV = - : conv
ADD_CONV = - : conv
MUL_CONV = - : conv
EXP_CONV = - : conv
DIV_CONV = - : conv
MOD_CONV = - : conv
Calling Lisp compiler
File arithconv compiled
() : void
#\
echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `boolconv`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
dest_op = - : (term -> term -> term list)
NOT_CONV = - : conv
AND_CONV = - : conv
OR_CONV = - : conv
IMP_CONV = - : conv
BEQ_CONV = - : conv
COND_CONV = - : conv
Calling Lisp compiler
File boolconv compiled
() : void
#\
echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `reduce`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Extending help search path() : void
Loading boolean conversions() : void
Loading arithmetic conversions() : void
Loading general conversions, rule and tactic() : void
RED_CONV = - : conv
REDUCE_CONV = - : conv
REDUCE_RULE = - : (thm -> thm)
REDUCE_TAC = - : tactic
Calling Lisp compiler
File reduce compiled
() : void
#make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/reduce'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/arith'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `int_extra`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
abs = - : (int -> int)
() : void
mod = - : (int -> int -> int)
gcd = - : ((int # int) -> int)
lcm = - : ((int # int) -> int)
Calling Lisp compiler
File int_extra compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'compilet `arith_cons`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
mk_arith_op = - : (string -> string -> (term # term) -> term)
mk_plus = - : ((term # term) -> term)
mk_minus = - : ((term # term) -> term)
mk_mult = - : ((term # term) -> term)
dest_arith_op = - : (string -> string -> term -> (term # term))
dest_plus = - : (term -> (term # term))
dest_minus = - : (term -> (term # term))
dest_mult = - : (term -> (term # term))
is_plus = - : (term -> bool)
is_minus = - : (term -> bool)
is_mult = - : (term -> bool)
is_arith_op = - : (term -> bool)
mk_num_reln = - : (string -> string -> (term # term) -> term)
mk_less = - : ((term # term) -> term)
mk_leq = - : ((term # term) -> term)
mk_great = - : ((term # term) -> term)
mk_geq = - : ((term # term) -> term)
dest_num_reln = - : (string -> string -> term -> (term # term))
dest_less = - : (term -> (term # term))
dest_leq = - : (term -> (term # term))
dest_great = - : (term -> (term # term))
dest_geq = - : (term -> (term # term))
is_less = - : (term -> bool)
is_leq = - : (term -> bool)
is_great = - : (term -> bool)
is_geq = - : (term -> bool)
is_num_reln = - : (term -> bool)
mk_suc = - : (term -> term)
dest_suc = - : (term -> term)
is_suc = - : (term -> bool)
is_num_const = - : (term -> bool)
is_zero = - : (term -> bool)
int_of_term = - : (term -> int)
term_of_int = - : (int -> term)
mk_num_var = - : (string -> term)
arg1 = - : (term -> term)
arg2 = - : (term -> term)
Calling Lisp compiler
File arith_cons compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `string_extra`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
string_less = - : (string -> string -> bool)
Calling Lisp compiler
File string_extra compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'compilet `term_coeffs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
.....................() : void
.() : void
negate_coeffs = - : ((int # (* # int) list) -> (int # (* # int) list))
merge_coeffs =
-
: ((int # (string # int) list) ->
(int # (string # int) list) ->
(int # (string # int) list))
lhs_coeffs = - : ((int # (* # int) list) -> (int # (* # int) list))
rhs_coeffs = - : ((int # (* # int) list) -> (int # (* # int) list))
diff_of_coeffs =
-
: (((int # (string # int) list) # int # (string # int) list) ->
((int # (string # int) list) # int # (string # int) list))
vars_of_coeffs = - : ((* # (** # ***) list) list -> ** list)
var_of_prod = - : (term -> string)
coeffs_of_arith = - : (term -> (int # (string # int) list))
coeffs_of_leq = - : (term -> (int # (string # int) list))
coeffs_of_leq_set = - : (term -> (int # (string # int) list) list)
build_arith = - : ((int # (string # int) list) -> term)
build_leq = - : ((int # (string # int) list) -> term)
Calling Lisp compiler
File term_coeffs compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `qconv`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
qconv = `QCONV` : string
qfailwith = - : (string -> string -> *)
QCONV = - : (conv -> conv)
ALL_QCONV = - : conv
() : void
THENQC = - : (conv -> conv -> conv)
() : void
ORELSEQC = - : (conv -> conv -> conv)
REPEATQC = - : (conv -> conv)
CHANGED_QCONV = - : (conv -> conv)
TRY_QCONV = - : (conv -> conv)
QCONV_RULE = - : (conv -> thm -> thm)
RAND_QCONV = - : (conv -> conv)
RATOR_QCONV = - : (conv -> conv)
ABS_QCONV = - : (conv -> conv)
ARGS_QCONV = - : (conv -> conv)
Calling Lisp compiler
File qconv compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `decls`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
ONE_PLUS = |- T
ZERO_PLUS = |- T
PLUS_ZERO = |- T
SUC_ADD1 = |- T
SUC_ADD2 = |- T
ZERO_MULT = |- T
ONE_MULT = |- T
MULT_ZERO = |- T
MULT_ONE = |- T
MULT_SUC = |- T
MULT_COMM = |- T
SUC_ADD_LESS_EQ_F = |- T
MULT_LEQ_SUC = |- T
ZERO_LESS_EQ_T = |- T
SUC_LESS_EQ_ZERO_F = |- T
ZERO_LESS_EQ_ONE_TIMES = |- T
LESS_EQ_PLUS = |- T
LESS_EQ_TRANSIT = |- T
NOT_T_F = |- T
NOT_F_T = |- T
CONJ_ASSOC_NORM_CONV = - : conv
DISJ_ASSOC_NORM_CONV = - : conv
EQ_EXPAND_CONV = - : conv
IMP_EXPAND_CONV = - : conv
IMP_F_EQ_F_CONV = - : conv
IMP_IMP_CONJ_IMP_CONV = - : conv
LEFT_DIST_NORM_CONV = - : conv
NOT_CONJ_NORM_CONV = - : conv
NOT_DISJ_NORM_CONV = - : conv
NOT_NOT_NORM_CONV = - : conv
OR_F_CONV = - : conv
RIGHT_DIST_NORM_CONV = - : conv
ADD_ASSOC_CONV = - : conv
ADD_SYM_CONV = - : conv
GATHER_BOTH_CONV = - : conv
GATHER_LEFT_CONV = - : conv
GATHER_NEITHER_CONV = - : conv
GATHER_RIGHT_CONV = - : conv
GEQ_NORM_CONV = - : conv
GREAT_NORM_CONV = - : conv
LEFT_ADD_DISTRIB_CONV = - : conv
LESS_NORM_CONV = - : conv
MULT_ASSOC_CONV = - : conv
MULT_COMM_CONV = - : conv
NOT_GEQ_NORM_CONV = - : conv
NOT_GREAT_NORM_CONV = - : conv
NOT_LEQ_NORM_CONV = - : conv
NOT_LESS_NORM_CONV = - : conv
NOT_NUM_EQ_NORM_CONV = - : conv
NUM_EQ_NORM_CONV = - : conv
PLUS_ZERO_CONV = - : conv
SYM_ADD_ASSOC_CONV = - : conv
SYM_ONE_MULT_CONV = - : conv
ZERO_MULT_CONV = - : conv
ZERO_MULT_PLUS_CONV = - : conv
ZERO_PLUS_CONV = - : conv
LEQ_PLUS_CONV = - : conv
FORALL_SIMP_CONV = - : conv
NUM_COND_RATOR_CONV = - : conv
NUM_COND_RAND_CONV = - : conv
SUB_NORM_CONV = - : conv
COND_RATOR_CONV = - : conv
COND_RAND_CONV = - : conv
COND_EXPAND_CONV = - : conv
Calling Lisp compiler
File decls compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'compilet `norm_bool`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
EQ_IMP_ELIM_QCONV = - : ((term -> bool) -> conv)
MOVE_NOT_DOWN_QCONV = - : ((term -> bool) -> conv -> conv)
DISJ_LINEAR_QCONV = - : conv
DISJ_NORM_FORM_QCONV = - : conv
Calling Lisp compiler
File norm_bool compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'loadf `norm_bool`;;'\
'compilet `norm_arith`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
....() : void
COLLECT_NUM_CONSTS_CONV = - : conv
NUM_RELN_NORM_QCONV = - : (conv -> conv -> conv)
MULT_CONV = - : conv
mult_lookup = - : (((int # int) # thm) list -> (int # int) -> thm)
multiplication_theorems = [] : ((int # int) # thm) list
FAST_MULT_CONV = - : conv
reset_multiplication_theorems = - : (void -> ((int # int) # thm) list)
multiplication_theorems = - : (void -> ((int # int) # thm) list)
SUM_OF_PRODUCTS_SUC_CONV = - : conv
SUM_OF_PRODUCTS_MULT_QCONV = - : conv
SUM_OF_PRODUCTS_QCONV = - : conv
LINEAR_SUM_QCONV = - : conv
GATHER_QCONV = - : conv
IN_LINE_SUM_QCONV = - : (conv -> conv)
ONE_PASS_SORT_QCONV = - : conv
SORT_AND_GATHER_QCONV = - : conv
SYM_ONE_MULT_VAR_CONV = - : conv
NORM_ZERO_AND_ONE_QCONV = - : conv
Calling Lisp compiler
File norm_arith compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'loadf `norm_bool`;;'\
'loadf `norm_arith`;;'\
'compilet `norm_ineqs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
....() : void
..................() : void
ADD_TERM_TO_LEQ_CONV = - : (term -> conv)
ADD_COEFFS_TO_LEQ_QCONV = - : ((int # (string # int) list) -> conv)
LESS_OR_EQ_GATHER_QCONV = - : conv
ARITH_FORM_NORM_QCONV = - : conv
Calling Lisp compiler
File norm_ineqs compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'loadf `norm_bool`;;'\
'loadf `norm_arith`;;'\
'loadf `norm_ineqs`;;'\
'compilet `solve_ineqs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
....() : void
..................() : void
....() : void
CONST_TIMES_ARITH_QCONV = - : conv
MULT_LEQ_BY_CONST_QCONV = - : (term -> conv)
LEQ_CONV = - : conv
WEIGHTED_SUM =
-
: (string ->
((int # (string # int) list) # int # (string # int) list) ->
((int # (string # int) list) # (void -> thm)))
var_to_elim = - : ((* # (string # int) list) list -> string)
VAR_ELIM =
-
: ((int # (string # int) list) list -> (int list # (void -> thm)))
Calling Lisp compiler
File solve_ineqs compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'loadf `norm_bool`;;'\
'loadf `norm_arith`;;'\
'loadf `norm_ineqs`;;'\
'loadf `solve_ineqs`;;'\
'compilet `solve`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
....() : void
..................() : void
....() : void
......() : void
INEQS_FALSE_CONV = - : conv
DISJ_INEQS_FALSE_QCONV = - : conv
NOT_NOT_INTRO_CONV = - : conv
is_T = - : (term -> bool)
is_F = - : (term -> bool)
NEGATE_CONV = - : (conv -> conv)
DEPTH_FORALL_QCONV = - : (conv -> conv)
FORALL_ARITH_CONV = - : conv
Calling Lisp compiler
File solve compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'compilet `rationals`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
Rat = - : ((int # int) -> rat)
Numerator = - : (rat -> int)
Denominator = - : (rat -> int)
rat_inv = - : (rat -> rat)
rat_plus = - : (rat -> rat -> rat)
rat_minus = - : (rat -> rat -> rat)
rat_mult = - : (rat -> rat -> rat)
rat_div = - : (rat -> rat -> rat)
print_rat = - : (rat -> void)
- : (rat -> void)
rat_of_int = - : (int -> rat)
lower_int_of_rat = - : (rat -> int)
upper_int_of_rat = - : (rat -> int)
rat_zero = 0 : rat
rat_one = 1 : rat
rat_less = - : (rat -> rat -> bool)
Calling Lisp compiler
File rationals compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `rationals`;;'\
'loadf `string_extra`;;'\
'compilet `sup-inf`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
........() : void
.() : void
New constructors declared:
Bound : ((rat # (string # rat) list) -> bound)
Max_bound : (bound list -> bound)
Min_bound : (bound list -> bound)
Pos_inf : bound
Neg_inf : bound
New constructors declared:
Ibound : (bound -> internal_bound)
Mult_ibound : ((rat # internal_bound) -> internal_bound)
Plus_ibound : ((internal_bound # internal_bound) -> internal_bound)
Max_ibound : (internal_bound list -> internal_bound)
Min_ibound : (internal_bound list -> internal_bound)
solve_ineqs =
-
: ((int # (* # int) list) list ->
* ->
((rat # (* # rat) list) list # (rat # (* # rat) list) list))
UPPER = - : ((int # (string # int) list) list -> string -> bound)
LOWER = - : ((int # (string # int) list) list -> string -> bound)
SIMP_mult = - : (rat -> bound -> bound)
sum_bindings =
-
: ((string # rat) list -> (string # rat) list -> (string # rat) list)
SIMP_plus = - : (bound -> bound -> bound)
SIMP = - : (internal_bound -> bound)
SUPP = - : ((string # bound) -> bound)
INFF = - : ((string # bound) -> bound)
occurs_in_bound = - : (string -> bound -> bool)
occurs_in_ibound = - : (string -> internal_bound -> bool)
SUP =
-
: ((int # (string # int) list) list ->
(bound # string list) ->
internal_bound)
INF =
-
: ((int # (string # int) list) list ->
(bound # string list) ->
internal_bound)
eval_max_bound = - : (bound list -> bound)
eval_min_bound = - : (bound list -> bound)
eval_bound = - : (bound -> bound)
SUP_INF =
-
: ((int # (string # int) list) list -> (string # bound # bound) list)
Calling Lisp compiler
File sup-inf compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `streams`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
New constructors declared:
Stream : ((* # (void -> * stream)) -> * stream)
stream_map = - : ((* -> **) -> (void -> * stream) -> void -> ** stream)
stream_append =
-
: ((void -> * stream) -> (void -> * stream) -> void -> * stream)
stream_flat =
-
: ((void -> (void -> * stream) stream) -> void -> * stream)
permutations = - : (* list -> void -> * list stream)
Calling Lisp compiler
File streams compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `int_extra`;;'\
'loadf `rationals`;;'\
'loadf `string_extra`;;'\
'loadf `sup-inf`;;'\
'loadf `streams`;;'\
'compilet `sol_ranges`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
.....() : void
........() : void
.() : void
..................() : void
.....() : void
less_bound = - : (bound -> bound -> bool)
is_neg_bound = - : (bound -> bool)
is_finite_bound = - : (bound -> bool)
rat_of_bound = - : (bound -> rat)
is_int_range = - : (rat -> rat -> bool)
non_neg_int_between = - : (bound -> bound -> int)
inst_var_in_coeffs =
-
: ((string # int) ->
(int # (string # int) list) list ->
(int # (string # int) list) list)
Shostak = - : ((int # (string # int) list) list -> (string # int) list)
Calling Lisp compiler
File sol_ranges compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_library `reduce`;;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'loadf `norm_bool`;;'\
'loadf `norm_arith`;;'\
'loadf `norm_ineqs`;;'\
'loadf `rationals`;;'\
'loadf `sup-inf`;;'\
'loadf `streams`;;'\
'loadf `sol_ranges`;;'\
'compilet `exists_arith`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
() : void
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
....() : void
..................() : void
....() : void
........() : void
..................() : void
.....() : void
........() : void
NUM_REDUCE_QCONV = - : conv
INEQ_REDUCE_QCONV = - : conv
BOOL_REDUCE_QCONV = - : conv
WITNESS = - : ((string # int) list -> conv)
witness = - : (term list -> (string # int) list)
EXISTS_ARITH_CONV = - : conv
Calling Lisp compiler
File exists_arith compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `decls`;;'\
'compilet `sub_and_cond`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
................................................................() : void
COND_ABS_CONV = - : conv
SUB_AND_COND_ELIM_CONV = - : conv
COND_ELIM_CONV = - : conv
Calling Lisp compiler
File sub_and_cond compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `decls`;;'\
'compilet `prenex`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
................................................................() : void
QUANT_EQ_IMP_CONV = - : conv
is_prenex = - : (term -> bool)
PRENEX_CONV = - : conv
Calling Lisp compiler
File prenex compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `instance`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
INSTANCE_T_CONV = - : ((term -> term list) -> conv -> conv)
Calling Lisp compiler
File instance compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_library `reduce`;;'\
'loadf `int_extra`;;'\
'loadf `arith_cons`;;'\
'loadf `string_extra`;;'\
'loadf `term_coeffs`;;'\
'loadf `qconv`;;'\
'loadf `decls`;;'\
'loadf `norm_bool`;;'\
'loadf `norm_arith`;;'\
'loadf `norm_ineqs`;;'\
'loadf `solve_ineqs`;;'\
'loadf `solve`;;'\
'loadf `rationals`;;'\
'loadf `sup-inf`;;'\
'loadf `streams`;;'\
'loadf `sol_ranges`;;'\
'loadf `exists_arith`;;'\
'loadf `sub_and_cond`;;'\
'loadf `prenex`;;'\
'loadf `instance`;;'\
'compilet `gen_arith`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
() : void
.....() : void
.....................() : void
.() : void
............() : void
................() : void
................................................................() : void
....() : void
..................() : void
....() : void
......() : void
.......() : void
........() : void
..................() : void
.....() : void
........() : void
......() : void
...() : void
...() : void
.() : void
contains_var = - : (term -> bool)
is_linear_mult = - : (term -> bool)
non_presburger_subterms = - : (term -> term list)
is_presburger = - : (term -> bool)
ARITH_CONV = - : conv
Calling Lisp compiler
File gen_arith compiled
() : void
#===> library arith rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/arith'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/pred_sets'
rm -f pred_sets.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_pred_sets`;;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
SPECIFICATION = |- !P x. x IN P = P x
EXTENSION = |- !s t. (s = t) = (!x. x IN s = x IN t)
NOT_EQUAL_SETS = |- !s t. ~(s = t) = (?x. x IN t = ~x IN s)
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem WOP autoloading from theory `arithmetic` ...
WOP = |- !P. (?n. P n) ==> (?n. P n /\ (!m. m < n ==> ~P m))
NUM_SET_WOP =
|- !s. (?n. n IN s) = (?n. n IN s /\ (!m. m IN s ==> n <= m))
GSPEC_DEF_LEMMA = |- ?g. !f v. v IN (g f) = (?x. v,T = f x)
GSPECIFICATION = |- !f v. v IN (GSPEC f) = (?x. v,T = f x)
Section SET_SPEC_CONV begun
dest_tuple = - : (term -> term list)
MK_PAIR = - : (* list -> conv)
EXISTS_TUPLE_CONV = - : (term list -> conv)
PAIR_EQ_CONV = - : conv
ELIM_EXISTS_CONV = - : conv
PROVE_EXISTS = - : conv
list_variant = - : (term list -> term list -> term list)
SET_SPEC_CONV = - : conv
- : conv
Section SET_SPEC_CONV ended
SET_SPEC_CONV = - : conv
File gspec.ml loaded
() : void
() : void
true : bool
lemma = |- !s x. x IN s ==> (!f. (f x) IN {f x | x IN s})
SET_MINIMUM =
|- !s M. (?x. x IN s) = (?x. x IN s /\ (!y. y IN s ==> (M x) <= (M y)))
EMPTY_DEF = |- EMPTY = (\x. F)
NOT_IN_EMPTY = |- !x. ~x IN EMPTY
MEMBER_NOT_EMPTY = |- !s. (?x. x IN s) = ~(s = EMPTY)
UNIV_DEF = |- UNIV = (\x. T)
IN_UNIV = |- !x. x IN UNIV
UNIV_NOT_EMPTY = |- ~(UNIV = EMPTY)
EMPTY_NOT_UNIV = |- ~(EMPTY = UNIV)
EQ_UNIV = |- (!x. x IN s) = (s = UNIV)
SUBSET_DEF = |- !s t. s SUBSET t = (!x. x IN s ==> x IN t)
SUBSET_TRANS = |- !s t u. s SUBSET t /\ t SUBSET u ==> s SUBSET u
SUBSET_REFL = |- !s. s SUBSET s
SUBSET_ANTISYM = |- !s t. s SUBSET t /\ t SUBSET s ==> (s = t)
EMPTY_SUBSET = |- !s. EMPTY SUBSET s
SUBSET_EMPTY = |- !s. s SUBSET EMPTY = (s = EMPTY)
SUBSET_UNIV = |- !s. s SUBSET UNIV
UNIV_SUBSET = |- !s. UNIV SUBSET s = (s = UNIV)
PSUBSET_DEF = |- !s t. s PSUBSET t = s SUBSET t /\ ~(s = t)
PSUBSET_TRANS = |- !s t u. s PSUBSET t /\ t PSUBSET u ==> s PSUBSET u
PSUBSET_IRREFL = |- !s. ~s PSUBSET s
NOT_PSUBSET_EMPTY = |- !s. ~s PSUBSET EMPTY
NOT_UNIV_PSUBSET = |- !s. ~UNIV PSUBSET s
PSUBSET_UNIV = |- !s. s PSUBSET UNIV = (?x. ~x IN s)
UNION_DEF = |- !s t. s UNION t = {x | x IN s \/ x IN t}
IN_UNION = |- !s t x. x IN (s UNION t) = x IN s \/ x IN t
UNION_ASSOC = |- !s t u. (s UNION t) UNION u = s UNION (t UNION u)
UNION_IDEMPOT = |- !s. s UNION s = s
UNION_COMM = |- !s t. s UNION t = t UNION s
SUBSET_UNION =
|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
SUBSET_UNION_ABSORPTION = |- !s t. s SUBSET t = (s UNION t = t)
UNION_EMPTY = |- (!s. EMPTY UNION s = s) /\ (!s. s UNION EMPTY = s)
UNION_UNIV = |- (!s. UNIV UNION s = UNIV) /\ (!s. s UNION UNIV = UNIV)
EMPTY_UNION = |- !s t. (s UNION t = EMPTY) = (s = EMPTY) /\ (t = EMPTY)
INTER_DEF = |- !s t. s INTER t = {x | x IN s /\ x IN t}
IN_INTER = |- !s t x. x IN (s INTER t) = x IN s /\ x IN t
INTER_ASSOC = |- !s t u. (s INTER t) INTER u = s INTER (t INTER u)
INTER_IDEMPOT = |- !s. s INTER s = s
INTER_COMM = |- !s t. s INTER t = t INTER s
INTER_SUBSET =
|- (!s t. (s INTER t) SUBSET s) /\ (!s t. (t INTER s) SUBSET s)
SUBSET_INTER_ABSORPTION = |- !s t. s SUBSET t = (s INTER t = s)
INTER_EMPTY =
|- (!s. EMPTY INTER s = EMPTY) /\ (!s. s INTER EMPTY = EMPTY)
INTER_UNIV = |- (!s. UNIV INTER s = s) /\ (!s. s INTER UNIV = s)
UNION_OVER_INTER =
|- !s t u. s INTER (t UNION u) = (s INTER t) UNION (s INTER u)
INTER_OVER_UNION =
|- !s t u. s UNION (t INTER u) = (s UNION t) INTER (s UNION u)
DISJOINT_DEF = |- !s t. DISJOINT s t = (s INTER t = EMPTY)
IN_DISJOINT = |- !s t. DISJOINT s t = ~(?x. x IN s /\ x IN t)
DISJOINT_SYM = |- !s t. DISJOINT s t = DISJOINT t s
DISJOINT_EMPTY = |- !s. DISJOINT EMPTY s /\ DISJOINT s EMPTY
DISJOINT_EMPTY_REFL = |- !s. (s = EMPTY) = DISJOINT s s
DISJOINT_UNION =
|- !s t u. DISJOINT(s UNION t)u = DISJOINT s u /\ DISJOINT t u
DIFF_DEF = |- !s t. s DIFF t = {x | x IN s /\ ~x IN t}
IN_DIFF = |- !s t x. x IN (s DIFF t) = x IN s /\ ~x IN t
DIFF_EMPTY = |- !s. s DIFF EMPTY = s
EMPTY_DIFF = |- !s. EMPTY DIFF s = EMPTY
DIFF_UNIV = |- !s. s DIFF UNIV = EMPTY
DIFF_DIFF = |- !s t. (s DIFF t) DIFF t = s DIFF t
DIFF_EQ_EMPTY = |- !s. s DIFF s = EMPTY
INSERT_DEF = |- !x s. x INSERT s = {y | (y = x) \/ y IN s}
() : void
IN_INSERT = |- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
COMPONENT = |- !x s. x IN (x INSERT s)
SET_CASES = |- !s. (s = {}) \/ (?x t. (s = x INSERT t) /\ ~x IN t)
DECOMPOSITION = |- !s x. x IN s = (?t. (s = x INSERT t) /\ ~x IN t)
ABSORPTION = |- !x s. x IN s = (x INSERT s = s)
INSERT_INSERT = |- !x s. x INSERT (x INSERT s) = x INSERT s
INSERT_COMM = |- !x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)
INSERT_UNIV = |- !x. x INSERT UNIV = UNIV
NOT_INSERT_EMPTY = |- !x s. ~(x INSERT s = {})
NOT_EMPTY_INSERT = |- !x s. ~({} = x INSERT s)
INSERT_UNION =
|- !x s t.
(x INSERT s) UNION t = (x IN t => s UNION t | x INSERT (s UNION t))
INSERT_UNION_EQ = |- !x s t. (x INSERT s) UNION t = x INSERT (s UNION t)
INSERT_INTER =
|- !x s t.
(x INSERT s) INTER t = (x IN t => x INSERT (s INTER t) | s INTER t)
DISJOINT_INSERT =
|- !x s t. DISJOINT(x INSERT s)t = DISJOINT s t /\ ~x IN t
INSERT_SUBSET = |- !x s t. (x INSERT s) SUBSET t = x IN t /\ s SUBSET t
SUBSET_INSERT =
|- !x s. ~x IN s ==> (!t. s SUBSET (x INSERT t) = s SUBSET t)
INSERT_DIFF =
|- !s t x.
(x INSERT s) DIFF t = (x IN t => s DIFF t | x INSERT (s DIFF t))
DELETE_DEF = |- !s x. s DELETE x = s DIFF {x}
IN_DELETE = |- !s x y. x IN (s DELETE y) = x IN s /\ ~(x = y)
DELETE_NON_ELEMENT = |- !x s. ~x IN s = (s DELETE x = s)
IN_DELETE_EQ =
|- !s x x'.
(x IN s = x' IN s) = (x IN (s DELETE x') = x' IN (s DELETE x))
EMPTY_DELETE = |- !x. {} DELETE x = {}
DELETE_DELETE = |- !x s. (s DELETE x) DELETE x = s DELETE x
DELETE_COMM = |- !x y s. (s DELETE x) DELETE y = (s DELETE y) DELETE x
DELETE_SUBSET = |- !x s. (s DELETE x) SUBSET s
SUBSET_DELETE = |- !x s t. s SUBSET (t DELETE x) = ~x IN s /\ s SUBSET t
SUBSET_INSERT_DELETE =
|- !x s t. s SUBSET (x INSERT t) = (s DELETE x) SUBSET t
DIFF_INSERT = |- !s t x. s DIFF (x INSERT t) = (s DELETE x) DIFF t
PSUBSET_INSERT_SUBSET =
|- !s t. s PSUBSET t = (?x. ~x IN s /\ (x INSERT s) SUBSET t)
lemma = |- ~(a = b) = (b = ~a)
PSUBSET_MEMBER =
|- !s t. s PSUBSET t = s SUBSET t /\ (?y. y IN t /\ ~y IN s)
DELETE_INSERT =
|- !x y s.
(x INSERT s) DELETE y =
((x = y) => s DELETE y | x INSERT (s DELETE y))
INSERT_DELETE = |- !x s. x IN s ==> (x INSERT (s DELETE x) = s)
DELETE_INTER = |- !s t x. (s DELETE x) INTER t = (s INTER t) DELETE x
DISJOINT_DELETE_SYM =
|- !s t x. DISJOINT(s DELETE x)t = DISJOINT(t DELETE x)s
CHOICE_EXISTS = |- ?CHOICE. !s. ~(s = {}) ==> (CHOICE s) IN s
CHOICE_DEF = |- !s. ~(s = {}) ==> (CHOICE s) IN s
REST_DEF = |- !s. REST s = s DELETE (CHOICE s)
CHOICE_NOT_IN_REST = |- !s. ~(CHOICE s) IN (REST s)
CHOICE_INSERT_REST =
|- !s. ~(s = {}) ==> ((CHOICE s) INSERT (REST s) = s)
REST_SUBSET = |- !s. (REST s) SUBSET s
lemma = |- (P /\ Q = P) = P ==> Q
REST_PSUBSET = |- !s. ~(s = {}) ==> (REST s) PSUBSET s
SING_DEF = |- !s. SING s = (?x. s = {x})
SING = |- !x. SING{x}
IN_SING = |- !x y. x IN {y} = (x = y)
NOT_SING_EMPTY = |- !x. ~({x} = {})
NOT_EMPTY_SING = |- !x. ~({} = {x})
EQUAL_SING = |- !x y. ({x} = {y}) = (x = y)
DISJOINT_SING_EMPTY = |- !x. DISJOINT{x}{}
INSERT_SING_UNION = |- !s x. x INSERT s = {x} UNION s
SING_DELETE = |- !x. {x} DELETE x = {}
DELETE_EQ_SING = |- !s x. x IN s ==> ((s DELETE x = {}) = (s = {x}))
CHOICE_SING = |- !x. CHOICE{x} = x
REST_SING = |- !x. REST{x} = {}
SING_IFF_EMPTY_REST = |- !s. SING s = ~(s = {}) /\ (REST s = {})
IMAGE_DEF = |- !f s. IMAGE f s = {f x | x IN s}
IN_IMAGE = |- !y s f. y IN (IMAGE f s) = (?x. (y = f x) /\ x IN s)
IMAGE_IN = |- !x s. x IN s ==> (!f. (f x) IN (IMAGE f s))
IMAGE_EMPTY = |- !f. IMAGE f{} = {}
IMAGE_ID = |- !s. IMAGE(\x. x)s = s
Theorem o_THM autoloading from theory `combin` ...
o_THM = |- !f g x. (f o g)x = f(g x)
IMAGE_COMPOSE = |- !f g s. IMAGE(f o g)s = IMAGE f(IMAGE g s)
IMAGE_INSERT = |- !f x s. IMAGE f(x INSERT s) = (f x) INSERT (IMAGE f s)
IMAGE_EQ_EMPTY = |- !s f. (IMAGE f s = {}) = (s = {})
IMAGE_DELETE = |- !f x s. ~x IN s ==> (IMAGE f(s DELETE x) = IMAGE f s)
IMAGE_UNION =
|- !f s t. IMAGE f(s UNION t) = (IMAGE f s) UNION (IMAGE f t)
IMAGE_SUBSET =
|- !s t. s SUBSET t ==> (!f. (IMAGE f s) SUBSET (IMAGE f t))
IMAGE_INTER =
|- !f s t. (IMAGE f(s INTER t)) SUBSET ((IMAGE f s) INTER (IMAGE f t))
INJ_DEF =
|- !f s t.
INJ f s t =
(!x. x IN s ==> (f x) IN t) /\
(!x y. x IN s /\ y IN s ==> (f x = f y) ==> (x = y))
INJ_ID = |- !s. INJ(\x. x)s s
INJ_COMPOSE = |- !f g s t u. INJ f s t /\ INJ g t u ==> INJ(g o f)s u
INJ_EMPTY = |- !f. (!s. INJ f{}s) /\ (!s. INJ f s{} = (s = {}))
SURJ_DEF =
|- !f s t.
SURJ f s t =
(!x. x IN s ==> (f x) IN t) /\
(!x. x IN t ==> (?y. y IN s /\ (f y = x)))
SURJ_ID = |- !s. SURJ(\x. x)s s
SURJ_COMPOSE =
|- !f g s t u. SURJ f s t /\ SURJ g t u ==> SURJ(g o f)s u
SURJ_EMPTY =
|- !f. (!s. SURJ f{}s = (s = {})) /\ (!s. SURJ f s{} = (s = {}))
IMAGE_SURJ = |- !f s t. SURJ f s t = (IMAGE f s = t)
BIJ_DEF = |- !f s t. BIJ f s t = INJ f s t /\ SURJ f s t
BIJ_ID = |- !s. BIJ(\x. x)s s
BIJ_EMPTY =
|- !f. (!s. BIJ f{}s = (s = {})) /\ (!s. BIJ f s{} = (s = {}))
BIJ_COMPOSE = |- !f g s t u. BIJ f s t /\ BIJ g t u ==> BIJ(g o f)s u
lemma1 =
|- !f s.
(!x y. x IN s /\ y IN s ==> (f x = f y) ==> (x = y)) =
(!y. y IN s ==> (!x. x IN s /\ (f x = f y) = y IN s /\ (x = y)))
lemma2 = |- !f s. ?g. !t. INJ f s t ==> (!x. x IN s ==> (g(f x) = x))
LINV_DEF = |- !f s t. INJ f s t ==> (!x. x IN s ==> (LINV f s(f x) = x))
lemma3 = |- !f s. ?g. !t. SURJ f s t ==> (!x. x IN t ==> (f(g x) = x))
RINV_DEF =
|- !f s t. SURJ f s t ==> (!x. x IN t ==> (f(RINV f s x) = x))
FINITE_DEF =
|- !s.
FINITE s = (!P. P{} /\ (!s'. P s' ==> (!e. P(e INSERT s'))) ==> P s)
FINITE_EMPTY = |- FINITE{}
FINITE_INSERT = |- !s. FINITE s ==> (!x. FINITE(x INSERT s))
SIMPLE_FINITE_INDUCT =
|- !P.
P{} /\ (!s. P s ==> (!e. P(e INSERT s))) ==> (!s. FINITE s ==> P s)
lemma =
|- P{} /\
(!s. FINITE s /\ P s ==> (!e. FINITE(e INSERT s) /\ P(e INSERT s))) ==>
(!s. FINITE s ==> P s)
FINITE_INDUCT =
|- !P.
P{} /\ (!s. FINITE s /\ P s ==> (!e. ~e IN s ==> P(e INSERT s))) ==>
(!s. FINITE s ==> P s)
SET_INDUCT_TAC = - : tactic
File set_ind loaded
() : void
FINITE_DELETE = |- !s. FINITE s ==> (!x. FINITE(s DELETE x))
INSERT_FINITE = |- !x s. FINITE(x INSERT s) ==> FINITE s
FINITE_INSERT = |- !x s. FINITE(x INSERT s) = FINITE s
DELETE_FINITE = |- !x s. FINITE(s DELETE x) ==> FINITE s
FINITE_DELETE = |- !x s. FINITE(s DELETE x) = FINITE s
UNION_FINITE = |- !s. FINITE s ==> (!t. FINITE t ==> FINITE(s UNION t))
FINITE_UNION_LEMMA =
|- !s. FINITE s ==> (!t. FINITE(s UNION t) ==> FINITE t)
FINITE_UNION = |- !s t. FINITE(s UNION t) ==> FINITE s /\ FINITE t
FINITE_UNION = |- !s t. FINITE(s UNION t) = FINITE s /\ FINITE t
INTER_FINITE = |- !s. FINITE s ==> (!t. FINITE(s INTER t))
SUBSET_FINITE = |- !s. FINITE s ==> (!t. t SUBSET s ==> FINITE t)
PSUBSET_FINITE = |- !s. FINITE s ==> (!t. t PSUBSET s ==> FINITE t)
FINITE_DIFF = |- !s. FINITE s ==> (!t. FINITE(s DIFF t))
FINITE_SING = |- !x. FINITE{x}
SING_FINITE = |- !s. SING s ==> FINITE s
IMAGE_FINITE = |- !s. FINITE s ==> (!f. FINITE(IMAGE f s))
card_rel_def =
"(!s. R s 0 = (s = {})) /\
(!s n. R s(SUC n) = (?x. x IN s /\ R(s DELETE x)n))"
: term
Theorem num_Axiom autoloading from theory `prim_rec` ...
num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
CARD_REL_EXISTS =
|- ?R.
(!s. R s 0 = (s = {})) /\
(!s n. R s(SUC n) = (?x. x IN s /\ R(s DELETE x)n))
CARD_REL_DEL_LEMMA =
.. |- !n s x.
x IN s ==> R(s DELETE x)n ==> (!y. y IN s ==> R(s DELETE y)n)
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
CARD_REL_UNIQUE = .. |- !n s. R s n ==> (!m. R s m ==> (n = m))
CARD_REL_EXISTS_LEMMA = .. |- !s. FINITE s ==> (?n. R s n)
CARD_REL_THM = .. |- !m s. FINITE s ==> (((@n. R s n) = m) = R s m)
CARD_EXISTS =
|- ?CARD.
(CARD{} = 0) /\
(!s.
FINITE s ==>
(!x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s))))
CARD_DEF =
|- (CARD{} = 0) /\
(!s.
FINITE s ==>
(!x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s))))
CARD_EMPTY = |- CARD{} = 0
CARD_INSERT =
|- !s.
FINITE s ==>
(!x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s)))
CARD_EQ_0 = |- !s. FINITE s ==> ((CARD s = 0) = (s = {}))
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
CARD_DELETE =
|- !s.
FINITE s ==>
(!x. CARD(s DELETE x) = (x IN s => (CARD s) - 1 | CARD s))
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
lemma1 = |- !n m. (SUC n) <= (SUC m) = n <= m
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
lemma2 = |- !n m. n <= (SUC m) = n <= m \/ (n = SUC m)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
CARD_INTER_LESS_EQ =
|- !s. FINITE s ==> (!t. (CARD(s INTER t)) <= (CARD s))
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
CARD_UNION =
|- !s.
FINITE s ==>
(!t.
FINITE t ==>
((CARD(s UNION t)) + (CARD(s INTER t)) = (CARD s) + (CARD t)))
lemma = |- !n m. n <= (SUC m) = n <= m \/ (n = SUC m)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
CARD_SUBSET =
|- !s. FINITE s ==> (!t. t SUBSET s ==> (CARD t) <= (CARD s))
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
CARD_PSUBSET =
|- !s. FINITE s ==> (!t. t PSUBSET s ==> (CARD t) < (CARD s))
CARD_SING = |- !x. CARD{x} = 1
SING_IFF_CARD1 = |- !s. SING s = (CARD s = 1) /\ FINITE s
Theorem SUB_PLUS autoloading from theory `arithmetic` ...
SUB_PLUS = |- !a b c. a - (b + c) = (a - b) - c
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
CARD_DIFF =
|- !t.
FINITE t ==>
(!s. FINITE s ==> (CARD(s DIFF t) = (CARD s) - (CARD(s INTER t))))
Theorem SUB_LESS_0 autoloading from theory `arithmetic` ...
SUB_LESS_0 = |- !n m. m < n = 0 < (n - m)
LESS_CARD_DIFF =
|- !t.
FINITE t ==>
(!s. FINITE s ==> (CARD t) < (CARD s) ==> 0 < (CARD(s DIFF t)))
INFINITE_DEF = |- !s. INFINITE s = ~FINITE s
NOT_IN_FINITE = |- INFINITE UNIV = (!s. FINITE s ==> (?x. ~x IN s))
INVERSE_LEMMA =
|- !f.
(!x y. (f x = f y) ==> (x = y)) ==>
((\x. @y. x = f y) o f = (\x. x))
IMAGE_11_INFINITE =
|- !f.
(!x y. (f x = f y) ==> (x = y)) ==>
(!s. INFINITE s ==> INFINITE(IMAGE f s))
INFINITE_SUBSET = |- !s. INFINITE s ==> (!t. s SUBSET t ==> INFINITE t)
IN_INFINITE_NOT_FINITE =
|- !s t. INFINITE s /\ FINITE t ==> (?x. x IN s /\ ~x IN t)
gdef =
["g 0 = {}"; "!n. g(SUC n) = (@x. ~x IN (g n)) INSERT (g n)"]
: term list
g_finite = .. |- !n. FINITE(g n)
g_subset = . |- !n x. x IN (g n) ==> (!i. x IN (g(n + i)))
lemma = |- (A \/ B) /\ ~B = A /\ ~B
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
g_cases =
.. |- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(!x. (?n. x IN (g n)) ==> (?m. x IN (g(SUC m)) /\ ~x IN (g m)))
z_in_g1 = .. |- (@x. ~x IN {}) IN (g(SUC 0))
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
z_in_gn = .. |- !n. (@x. ~x IN {}) IN (g(SUC n))
in_lemma = . |- !n. (@x. ~x IN (g n)) IN (g(SUC n))
not_in_lemma =
.. |- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(!i n. ~(@x. ~x IN (g(n + i))) IN (g n))
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
less_lemma = |- !m n. ~(m = n) = m < n \/ n < m
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
gn_unique =
.. |- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(!n m. ((@x. ~x IN (g n)) = (@x. ~x IN (g m))) = (n = m))
x_unique =
.. |- !n x y.
~x IN (g n) /\ ~y IN (g n) ==>
x IN (g(SUC n)) ==>
y IN (g(SUC n)) ==>
(x = y)
fdef =
"\x.
((?n. x IN (g n)) =>
(@y. ~y IN (g(SUC(@n. x IN (g(SUC n)) /\ ~x IN (g n))))) |
x)"
: term
cases = |- !x. (?n. x IN (g n)) \/ (!n. ~x IN (g n))
INF_IMP_INFINITY =
|- (!s. FINITE s ==> (?x. ~x IN s)) ==>
(?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y)))
prth =
|- ?fn. (!f x. fn f x 0 = x) /\ (!f x n. fn f x(SUC n) = f(fn f x n))
prmth = |- !x f. ?fn. (fn 0 = x) /\ (!n. fn(SUC n) = f(fn n))
num_fn_thm =
|- (?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y))) ==>
(?fn. !n m. (fn n = fn m) ==> (n = m))
Theorem LESS_IMP_LESS_ADD autoloading from theory `arithmetic` ...
LESS_IMP_LESS_ADD = |- !n m. n < m ==> (!p. n < (m + p))
Theorem LESS_ADD_SUC autoloading from theory `arithmetic` ...
LESS_ADD_SUC = |- !m n. m < (m + (SUC n))
finite_N_bounded = |- !s. FINITE s ==> (?m. !n. n IN s ==> n < m)
N_lemma = |- INFINITE UNIV
main_lemma =
|- !s.
FINITE s ==>
(!f. (!n m. (f n = f m) ==> (n = m)) ==> (?n. ~(f n) IN s))
INFINITY_IMP_INF =
|- (?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y))) ==>
(!s. FINITE s ==> (?x. ~x IN s))
INFINITE_UNIV =
|- INFINITE UNIV =
(?f. (!x y. (f x = f y) ==> (x = y)) /\ (?y. !x. ~(f x = y)))
FINITE_PSUBSET_INFINITE =
|- !s. INFINITE s = (!t. FINITE t ==> t SUBSET s ==> t PSUBSET s)
FINITE_PSUBSET_UNIV =
|- INFINITE UNIV = (!s. FINITE s ==> s PSUBSET UNIV)
INFINITE_DIFF_FINITE =
|- !s t. INFINITE s /\ FINITE t ==> ~(s DIFF t = {})
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
FINITE_ISO_NUM =
|- !s.
FINITE s ==>
(?f.
(!n m. n < (CARD s) /\ m < (CARD s) ==> (f n = f m) ==> (n = m)) /\
(s = {f n | n < (CARD s)}))
echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `pred_sets`;;'\
'compilet `set_ind`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory pred_sets loaded
() : void
SET_INDUCT_TAC = - : tactic
Calling Lisp compiler
File set_ind compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `pred_sets`;;'\
'compilet `gspec`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory pred_sets loaded
() : void
dest_tuple = - : (term -> term list)
MK_PAIR = - : (* list -> conv)
EXISTS_TUPLE_CONV = - : (term list -> conv)
PAIR_EQ_CONV = - : conv
ELIM_EXISTS_CONV = - : conv
PROVE_EXISTS = - : conv
list_variant = - : (term list -> term list -> term list)
SET_SPEC_CONV = - : conv
- : conv
SET_SPEC_CONV = - : conv
Calling Lisp compiler
File gspec compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `pred_sets`;;'\
'compilet `fset_conv`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory pred_sets loaded
() : void
FINITE_CONV = - : conv
IN_CONV = - : (conv -> conv)
DELETE_CONV = - : (conv -> conv)
UNION_CONV = - : (conv -> conv)
INSERT_CONV = - : (conv -> conv)
IMAGE_CONV = - : (conv -> conv -> conv)
Calling Lisp compiler
File fset_conv compiled
() : void
#===> library pred_sets rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/pred_sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/string'
rm -f ascii.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_ascii`;;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
ascii_Axiom =
|- !f.
?! fn.
!b0 b1 b2 b3 b4 b5 b6 b7.
fn(ASCII b0 b1 b2 b3 b4 b5 b6 b7) = f b0 b1 b2 b3 b4 b5 b6 b7
ascii_Induct =
|- !P.
(!b0 b1 b2 b3 b4 b5 b6 b7. P(ASCII b0 b1 b2 b3 b4 b5 b6 b7)) ==>
(!a. P a)
ascii_CASES =
|- !a. ?b0 b1 b2 b3 b4 b5 b6 b7. a = ASCII b0 b1 b2 b3 b4 b5 b6 b7
ASCII_11 =
|- !b0 b1 b2 b3 b4 b5 b6 b7 b0' b1' b2' b3' b4' b5' b6' b7'.
(ASCII b0 b1 b2 b3 b4 b5 b6 b7 =
ASCII b0' b1' b2' b3' b4' b5' b6' b7') =
(b0 = b0') /\
(b1 = b1') /\
(b2 = b2') /\
(b3 = b3') /\
(b4 = b4') /\
(b5 = b5') /\
(b6 = b6') /\
(b7 = b7')
rm -f string.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_string`;;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
Theory ascii loaded
() : void
() : void
() : void
() : void
() : void
string_Axiom = `string_Axiom` : string
spec = `string = `` | STRING ascii string` : string
tok = `tok` : string
string_Induct = `string_Induct` : string
string_CASES = `string_CASES` : string
STRING_11 = `STRING_11` : string
NOT_STRING_EMPTY = `NOT_STRING_EMPTY` : string
NOT_EMPTY_STRING = `NOT_EMPTY_STRING` : string
() : void
string_Axiom =
|- !e f. ?! fn. (fn `` = e) /\ (!a s. fn(STRING a s) = f(fn s)a s)
() : void
string_Induct =
|- !P. P `` /\ (!s. P s ==> (!a. P(STRING a s))) ==> (!s. P s)
string_CASES = |- !s. (s = ``) \/ (?s' a. s = STRING a s')
STRING_11 =
|- !a s a' s'. (STRING a s = STRING a' s') = (a = a') /\ (s = s')
NOT_STRING_EMPTY = |- !a s. ~(`` = STRING a s)
NOT_EMPTY_STRING = |- !a s. ~(STRING a s = ``)
() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `ascii`;;'\
'compilet `ascii`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory ascii loaded
() : void
ascii_EQ_CONV = - : conv
Calling Lisp compiler
File ascii compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `string`;;'\
'compilet `stringconv`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory string loaded
() : void
string_CONV = - : conv
Calling Lisp compiler
File stringconv compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `string`;;'\
'loadf `stringconv`;;'\
'loadf `ascii`;;'\
'compilet `string_rules`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory string loaded
() : void
.() : void
.() : void
string_EQ_CONV = - : conv
Calling Lisp compiler
File string_rules compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `string`;;'\
'compilet `string`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory string loaded
() : void
Updating search path
() : void
Updating help search path
() : void
Theory string loaded
() : void
() : void
() : void
Calling Lisp compiler
File string compiled
() : void
#===> library string rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/string'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/finite_sets'
rm -f finite_sets.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_finite_sets`;;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
IS_SET_REP =
"\s. !P. P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==> P s"
: term
IS_SET_REP_EMPTY =
|- (\s.
!P. P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==> P s)
(\x. F)
INSERTION_PRESERVES_IS_SET_REP =
|- !s.
(\s.
!P. P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==> P s)
s ==>
(!x.
(\s.
!P.
P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==> P s)
(\y. (y = x) \/ s y))
REP_INDUCT =
|- !P.
P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==>
(!s.
(\s.
!P.
P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==> P s)
s ==>
P s)
IS_SET_REP_EXISTS =
|- ?IS_SET_REP.
IS_SET_REP(\x. F) /\
(!s. IS_SET_REP s ==> (!x. IS_SET_REP(\y. (y = x) \/ s y))) /\
(!P.
P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==>
(!s. IS_SET_REP s ==> P s))
IS_SET_REP =
|- IS_SET_REP(\x. F) /\
(!s. IS_SET_REP s ==> (!x. IS_SET_REP(\y. (y = x) \/ s y))) /\
(!P.
P(\x. F) /\ (!t. P t ==> (!x. P(\y. (y = x) \/ t y))) ==>
(!s. IS_SET_REP s ==> P s))
STRONG_SET_REP_INDUCT =
|- !P.
P(\x. F) /\
(!t. IS_SET_REP t ==> P t ==> (!x. P(\y. (y = x) \/ t y))) ==>
(!s. IS_SET_REP s ==> P s)
EXISTENCE_THM = |- ?s. IS_SET_REP s
set_TY_DEF = |- ?rep. TYPE_DEFINITION IS_SET_REP rep
EXISTENCE_LEMMA =
|- ?EMPTY INSERT IN.
(!x. ~IN x EMPTY) /\
(!x y s. IN x(INSERT y s) = (x = y) \/ IN x s) /\
(!x s. INSERT x(INSERT x s) = INSERT x s) /\
(!x y s. INSERT x(INSERT y s) = INSERT y(INSERT x s)) /\
(!P. P EMPTY /\ (!s. P s ==> (!e. P(INSERT e s))) ==> (!s. P s))
FINITE_SET_DEF =
|- (!x. ~x IN EMPTY) /\
(!x y s. x IN (y INSERT s) = (x = y) \/ x IN s) /\
(!x s. x INSERT (x INSERT s) = x INSERT s) /\
(!x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)) /\
(!P. P EMPTY /\ (!s. P s ==> (!e. P(e INSERT s))) ==> (!s. P s))
() : void
NOT_IN_EMPTY = |- !x. ~x IN {}
IN_INSERT = |- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
INSERT_INSERT = |- !x s. x INSERT (x INSERT s) = x INSERT s
INSERT_COMM = |- !x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)
|- !x. ~x IN {}
|- !x y s. x IN (y INSERT s) = (x = y) \/ x IN s
|- !x s. x INSERT (x INSERT s) = x INSERT s
|- !x y s. x INSERT (y INSERT s) = y INSERT (x INSERT s)
COMPONENT = |- !x s. x IN (x INSERT s)
NOT_EMPTY_INSERT = |- !x s. ~({} = x INSERT s)
NOT_INSERT_EMPTY = |- !x s. ~(x INSERT s = {})
lemma = |- !x s. x IN s ==> (x INSERT s = s)
ABSORPTION = |- !x s. x IN s = (x INSERT s = s)
SET_INDUCT =
|- !P.
P{} /\ (!s. P s ==> (!e. ~e IN s ==> P(e INSERT s))) ==> (!s. P s)
SET_INDUCT_TAC = - : tactic
File set_ind.ml loaded
() : void
DECOMPOSITION = |- !s x. x IN s = (?t. (s = x INSERT t) /\ ~x IN t)
MEMBER_NOT_EMPTY = |- !s. (?x. x IN s) = ~(s = {})
lemma = |- !s t. (!x. x IN s = x IN t) ==> (s = t)
EXTENSION = |- !s t. (s = t) = (!x. x IN s = x IN t)
NOT_EQUAL_SETS = |- !s t. ~(s = t) = (?x. x IN t = ~x IN s)
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem WOP autoloading from theory `arithmetic` ...
WOP = |- !P. (?n. P n) ==> (?n. P n /\ (!m. m < n ==> ~P m))
NUM_SET_WOP =
|- !s. (?n. n IN s) = (?n. n IN s /\ (!m. m IN s ==> n <= m))
SET_CASES = |- !s. (s = {}) \/ (?x t. (s = x INSERT t) /\ ~x IN t)
SUBSET_DEF = |- !s t. s SUBSET t = (!x. x IN s ==> x IN t)
SUBSET_TRANS = |- !s t u. s SUBSET t /\ t SUBSET u ==> s SUBSET u
SUBSET_REFL = |- !s. s SUBSET s
SUBSET_ANTISYM = |- !s t. s SUBSET t /\ t SUBSET s ==> (s = t)
EMPTY_SUBSET = |- !s. {} SUBSET s
SUBSET_EMPTY = |- !s. s SUBSET {} = (s = {})
INSERT_SUBSET = |- !x s t. (x INSERT s) SUBSET t = x IN t /\ s SUBSET t
SUBSET_INSERT =
|- !x s. ~x IN s ==> (!t. s SUBSET (x INSERT t) = s SUBSET t)
PSUBSET_DEF = |- !s t. s PSUBSET t = s SUBSET t /\ ~(s = t)
PSUBSET_TRANS = |- !s t u. s PSUBSET t /\ t PSUBSET u ==> s PSUBSET u
PSUBSET_IRREFL = |- !s. ~s PSUBSET s
NOT_PSUBSET_EMPTY = |- !s. ~s PSUBSET {}
PSUBSET_INSERT_SUBSET =
|- !s t. s PSUBSET t = (?x. ~x IN s /\ (x INSERT s) SUBSET t)
lemma = |- ~(a = b) = (b = ~a)
PSUBSET_MEMBER =
|- !s t. s PSUBSET t = s SUBSET t /\ (?y. y IN t /\ ~y IN s)
UNION_EXISTS = |- !s t. ?u. !x. x IN u = x IN s \/ x IN t
IN_UNION = |- !s t x. x IN (s UNION t) = x IN s \/ x IN t
UNION_ASSOC = |- !s t u. (s UNION t) UNION u = s UNION (t UNION u)
UNION_IDEMPOT = |- !s. s UNION s = s
UNION_COMM = |- !s t. s UNION t = t UNION s
SUBSET_UNION =
|- (!s t. s SUBSET (s UNION t)) /\ (!s t. s SUBSET (t UNION s))
SUBSET_UNION_ABSORPTION = |- !s t. s SUBSET t = (s UNION t = t)
UNION_EMPTY = |- (!s. {} UNION s = s) /\ (!s. s UNION {} = s)
EMPTY_UNION = |- !s t. (s UNION t = {}) = (s = {}) /\ (t = {})
INSERT_UNION =
|- !x s t.
(x INSERT s) UNION t = (x IN t => s UNION t | x INSERT (s UNION t))
INSERT_UNION_EQ = |- !x s t. (x INSERT s) UNION t = x INSERT (s UNION t)
INTER_EXISTS = |- !s t. ?i. !x. x IN i = x IN s /\ x IN t
IN_INTER = |- !s t x. x IN (s INTER t) = x IN s /\ x IN t
INTER_ASSOC = |- !s t u. (s INTER t) INTER u = s INTER (t INTER u)
INTER_IDEMPOT = |- !s. s INTER s = s
INTER_COMM = |- !s t. s INTER t = t INTER s
INTER_SUBSET =
|- (!s t. (s INTER t) SUBSET s) /\ (!s t. (t INTER s) SUBSET s)
SUBSET_INTER_ABSORPTION = |- !s t. s SUBSET t = (s INTER t = s)
INTER_EMPTY = |- (!s. {} INTER s = {}) /\ (!s. s INTER {} = {})
INSERT_INTER =
|- !x s t.
(x INSERT s) INTER t = (x IN t => x INSERT (s INTER t) | s INTER t)
UNION_OVER_INTER =
|- !s t u. s INTER (t UNION u) = (s INTER t) UNION (s INTER u)
INTER_OVER_UNION =
|- !s t u. s UNION (t INTER u) = (s UNION t) INTER (s UNION u)
DISJOINT_DEF = |- !s t. DISJOINT s t = (s INTER t = {})
IN_DISJOINT = |- !s t. DISJOINT s t = ~(?x. x IN s /\ x IN t)
DISJOINT_SYM = |- !s t. DISJOINT s t = DISJOINT t s
DISJOINT_EMPTY = |- !s. DISJOINT{}s /\ DISJOINT s{}
DISJOINT_EMPTY_REFL = |- !s. (s = {}) = DISJOINT s s
DISJOINT_INSERT =
|- !x s t. DISJOINT(x INSERT s)t = DISJOINT s t /\ ~x IN t
DISJOINT_UNION =
|- !s t u. DISJOINT(s UNION t)u = DISJOINT s u /\ DISJOINT t u
DIFF_EXISTS = |- !s t. ?d. !x. x IN d = x IN s /\ ~x IN t
IN_DIFF = |- !s t x. x IN (s DIFF t) = x IN s /\ ~x IN t
DIFF_EMPTY = |- !s. s DIFF {} = s
EMPTY_DIFF = |- !s. {} DIFF s = {}
DIFF_DIFF = |- !s t. (s DIFF t) DIFF t = s DIFF t
DIFF_EQ_EMPTY = |- !s. s DIFF s = {}
DELETE_DEF = |- !s x. s DELETE x = s DIFF {x}
IN_DELETE = |- !s x y. x IN (s DELETE y) = x IN s /\ ~(x = y)
DELETE_NON_ELEMENT = |- !x s. ~x IN s = (s DELETE x = s)
IN_DELETE_EQ =
|- !s x x'.
(x IN s = x' IN s) = (x IN (s DELETE x') = x' IN (s DELETE x))
EMPTY_DELETE = |- !x. {} DELETE x = {}
DELETE_DELETE = |- !x s. (s DELETE x) DELETE x = s DELETE x
DELETE_COMM = |- !x y s. (s DELETE x) DELETE y = (s DELETE y) DELETE x
DELETE_SUBSET = |- !x s. (s DELETE x) SUBSET s
SUBSET_DELETE = |- !x s t. s SUBSET (t DELETE x) = ~x IN s /\ s SUBSET t
SUBSET_INSERT_DELETE =
|- !x s t. s SUBSET (x INSERT t) = (s DELETE x) SUBSET t
DIFF_INSERT = |- !s t x. s DIFF (x INSERT t) = (s DELETE x) DIFF t
DELETE_INSERT =
|- !x y s.
(x INSERT s) DELETE y =
((x = y) => s DELETE y | x INSERT (s DELETE y))
INSERT_DELETE = |- !x s. x IN s ==> (x INSERT (s DELETE x) = s)
DELETE_INTER = |- !s t x. (s DELETE x) INTER t = (s INTER t) DELETE x
DISJOINT_DELETE_SYM =
|- !s t x. DISJOINT(s DELETE x)t = DISJOINT(t DELETE x)s
CHOICE_EXISTS = |- ?CHOICE. !s. ~(s = {}) ==> (CHOICE s) IN s
CHOICE_DEF = |- !s. ~(s = {}) ==> (CHOICE s) IN s
REST_DEF = |- !s. REST s = s DELETE (CHOICE s)
CHOICE_NOT_IN_REST = |- !s. ~(CHOICE s) IN (REST s)
CHOICE_INSERT_REST =
|- !s. ~(s = {}) ==> ((CHOICE s) INSERT (REST s) = s)
REST_SUBSET = |- !s. (REST s) SUBSET s
lemma = |- (P /\ Q = P) = P ==> Q
REST_PSUBSET = |- !s. ~(s = {}) ==> (REST s) PSUBSET s
SING_DEF = |- !s. SING s = (?x. s = {x})
SING = |- !x. SING{x}
IN_SING = |- !x y. x IN {y} = (x = y)
NOT_SING_EMPTY = |- !x. ~({x} = {})
NOT_EMPTY_SING = |- !x. ~({} = {x})
EQUAL_SING = |- !x y. ({x} = {y}) = (x = y)
DISJOINT_SING_EMPTY = |- !x. DISJOINT{x}{}
INSERT_SING_UNION = |- !s x. x INSERT s = {x} UNION s
SING_DELETE = |- !x. {x} DELETE x = {}
DELETE_EQ_SING = |- !s x. x IN s ==> ((s DELETE x = {}) = (s = {x}))
CHOICE_SING = |- !x. CHOICE{x} = x
REST_SING = |- !x. REST{x} = {}
SING_IFF_EMPTY_REST = |- !s. SING s = ~(s = {}) /\ (REST s = {})
IMAGE_EXISTS = |- !f s. ?t. !y. y IN t = (?x. (y = f x) /\ x IN s)
IN_IMAGE = |- !f s y. y IN (IMAGE f s) = (?x. (y = f x) /\ x IN s)
IMAGE_IN = |- !x s. x IN s ==> (!f. (f x) IN (IMAGE f s))
IMAGE_EMPTY = |- !f. IMAGE f{} = {}
IMAGE_ID = |- !s. IMAGE(\x. x)s = s
Theorem o_THM autoloading from theory `combin` ...
o_THM = |- !f g x. (f o g)x = f(g x)
IMAGE_COMPOSE = |- !f g s. IMAGE(f o g)s = IMAGE f(IMAGE g s)
IMAGE_INSERT = |- !f x s. IMAGE f(x INSERT s) = (f x) INSERT (IMAGE f s)
IMAGE_EQ_EMPTY = |- !s f. (IMAGE f s = {}) = (s = {})
IMAGE_DELETE = |- !f x s. ~x IN s ==> (IMAGE f(s DELETE x) = IMAGE f s)
IMAGE_UNION =
|- !f s t. IMAGE f(s UNION t) = (IMAGE f s) UNION (IMAGE f t)
IMAGE_SUBSET =
|- !s t. s SUBSET t ==> (!f. (IMAGE f s) SUBSET (IMAGE f t))
IMAGE_INTER =
|- !f s t. (IMAGE f(s INTER t)) SUBSET ((IMAGE f s) INTER (IMAGE f t))
lemma = |- !s x. x IN s ==> (!f. (f x) IN (IMAGE f s))
SET_MINIMUM =
|- !s M. (?x. x IN s) = (?x. x IN s /\ (!y. y IN s ==> (M x) <= (M y)))
INJ_DEF =
|- !f s t.
INJ f s t =
(!x. x IN s ==> (f x) IN t) /\
(!x y. x IN s /\ y IN s ==> (f x = f y) ==> (x = y))
INJ_ID = |- !s. INJ(\x. x)s s
INJ_COMPOSE = |- !f g s t u. INJ f s t /\ INJ g t u ==> INJ(g o f)s u
INJ_EMPTY = |- !f. (!s. INJ f{}s) /\ (!s. INJ f s{} = (s = {}))
SURJ_DEF =
|- !f s t.
SURJ f s t =
(!x. x IN s ==> (f x) IN t) /\
(!x. x IN t ==> (?y. y IN s /\ (f y = x)))
SURJ_ID = |- !s. SURJ(\x. x)s s
SURJ_COMPOSE =
|- !f g s t u. SURJ f s t /\ SURJ g t u ==> SURJ(g o f)s u
SURJ_EMPTY =
|- !f. (!s. SURJ f{}s = (s = {})) /\ (!s. SURJ f s{} = (s = {}))
IMAGE_SURJ = |- !f s t. SURJ f s t = (IMAGE f s = t)
BIJ_DEF = |- !f s t. BIJ f s t = INJ f s t /\ SURJ f s t
BIJ_ID = |- !s. BIJ(\x. x)s s
BIJ_EMPTY =
|- !f. (!s. BIJ f{}s = (s = {})) /\ (!s. BIJ f s{} = (s = {}))
BIJ_COMPOSE = |- !f g s t u. BIJ f s t /\ BIJ g t u ==> BIJ(g o f)s u
lemma1 =
|- !f s.
(!x y. x IN s /\ y IN s ==> (f x = f y) ==> (x = y)) =
(!y. y IN s ==> (!x. x IN s /\ (f x = f y) = y IN s /\ (x = y)))
lemma2 = |- !f s. ?g. !t. INJ f s t ==> (!x. x IN s ==> (g(f x) = x))
LINV_DEF = |- !f s t. INJ f s t ==> (!x. x IN s ==> (LINV f s(f x) = x))
lemma3 = |- !f s. ?g. !t. SURJ f s t ==> (!x. x IN t ==> (f(g x) = x))
RINV_DEF =
|- !f s t. SURJ f s t ==> (!x. x IN t ==> (f(RINV f s x) = x))
card_rel_def =
"(!s. R s 0 = (s = {})) /\
(!s n. R s(SUC n) = (?x. x IN s /\ R(s DELETE x)n))"
: term
Theorem num_Axiom autoloading from theory `prim_rec` ...
num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
CARD_REL_EXISTS =
|- ?R.
(!s. R s 0 = (s = {})) /\
(!s n. R s(SUC n) = (?x. x IN s /\ R(s DELETE x)n))
CARD_REL_DEL_LEMMA =
.. |- !n s x.
x IN s ==> R(s DELETE x)n ==> (!y. y IN s ==> R(s DELETE y)n)
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
CARD_REL_UNIQUE = .. |- !n s. R s n ==> (!m. R s m ==> (n = m))
CARD_REL_EXISTS_LEMMA = .. |- !s. ?n. R s n
CARD_REL_THM = .. |- !m s. ((@n. R s n) = m) = R s m
CARD_EXISTS =
|- ?CARD.
(CARD{} = 0) /\
(!s x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s)))
CARD_DEF =
|- (CARD{} = 0) /\
(!s x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s)))
CARD_EMPTY = |- CARD{} = 0
CARD_INSERT =
|- !s x. CARD(x INSERT s) = (x IN s => CARD s | SUC(CARD s))
CARD_EQ_0 = |- !s. (CARD s = 0) = (s = {})
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
CARD_DELETE =
|- !s x. CARD(s DELETE x) = (x IN s => (CARD s) - 1 | CARD s)
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
lemma1 = |- !n m. (SUC n) <= (SUC m) = n <= m
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
lemma2 = |- !n m. n <= (SUC m) = n <= m \/ (n = SUC m)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
CARD_INTER_LESS_EQ = |- !s t. (CARD(s INTER t)) <= (CARD s)
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
CARD_UNION =
|- !s t. (CARD(s UNION t)) + (CARD(s INTER t)) = (CARD s) + (CARD t)
lemma = |- !n m. n <= (SUC m) = n <= m \/ (n = SUC m)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
CARD_SUBSET = |- !s t. t SUBSET s ==> (CARD t) <= (CARD s)
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
CARD_PSUBSET = |- !s t. t PSUBSET s ==> (CARD t) < (CARD s)
CARD_SING = |- !x. CARD{x} = 1
SING_IFF_CARD1 = |- !s. SING s = (CARD s = 1)
Theorem SUB_PLUS autoloading from theory `arithmetic` ...
SUB_PLUS = |- !a b c. a - (b + c) = (a - b) - c
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
CARD_DIFF = |- !t s. CARD(s DIFF t) = (CARD s) - (CARD(s INTER t))
Theorem SUB_LESS_0 autoloading from theory `arithmetic` ...
SUB_LESS_0 = |- !n m. m < n = 0 < (n - m)
LESS_CARD_DIFF = |- !t s. (CARD t) < (CARD s) ==> 0 < (CARD(s DIFF t))
echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `finite_sets`;;'\
'compilet `set_ind`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory finite_sets loaded
() : void
SET_INDUCT_TAC = - : tactic
Calling Lisp compiler
File set_ind compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `finite_sets`;;'\
'compilet `fset_conv`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory finite_sets loaded
() : void
IN_CONV = - : (conv -> conv)
DELETE_CONV = - : (conv -> conv)
UNION_CONV = - : (conv -> conv)
INSERT_CONV = - : (conv -> conv)
IMAGE_CONV = - : (conv -> conv -> conv)
Calling Lisp compiler
File fset_conv compiled
() : void
#===> library finite_sets rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/finite_sets'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/res_quan'
rm -f res_quan.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_res_quan`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
RESQ_FORALL = |- !P B. RES_FORALL P B = (!x. P x ==> B x)
RESQ_EXISTS = |- !P B. RES_EXISTS P B = (?x. P x /\ B x)
RESQ_SELECT = |- !P B. RES_SELECT P B = (@x. P x /\ B x)
RESQ_ABSTRACT = |- !P B. RES_ABSTRACT P B = (\x. (P x => B x | ARB))
RESQ_FORALL_CONJ_DIST =
|- !P Q R. (!i :: P. Q i /\ R i) = (!i :: P. Q i) /\ (!i :: P. R i)
RESQ_FORALL_DISJ_DIST =
|- !P Q R.
(!i :: \i. P i \/ Q i. R i) = (!i :: P. R i) /\ (!i :: Q. R i)
RESQ_FORALL_UNIQUE = |- !P j. (!i :: $= j. P i) = P j
RESQ_FORALL_FORALL =
|- !P R x. (!x. !i :: P. R i x) = (!i :: P. !x. R i x)
RESQ_FORALL_REORDER =
|- !P Q R. (!i :: P. !j :: Q. R i j) = (!j :: Q. !i :: P. R i j)
RESQ_EXISTS_DISJ_DIST =
|- !P Q R. (?i :: P. Q i \/ R i) = (?i :: P. Q i) \/ (?i :: P. R i)
RESQ_DISJ_EXISTS_DIST =
|- !P Q R.
(?i :: \i. P i \/ Q i. R i) = (?i :: P. R i) \/ (?i :: Q. R i)
RESQ_EXISTS_UNIQUE = |- !P j. (?i :: $= j. P i) = P j
RESQ_EXISTS_REORDER =
|- !P Q R. (?i :: P. ?j :: Q. R i j) = (?j :: Q. ?i :: P. R i j)
() : void
File mk_res_quan loaded
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `cond_rewr`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
match_aa =
-
: (term -> term -> ((term # term) list # (type # type) list) list)
match_ok = - : (* list -> ((** # *) list # *** list) list -> bool)
match_aal =
-
: (term list -> term -> term list -> ((term # term) list # term) list)
subset = - : (* list -> * list -> bool)
match_asm =
-
: (term list ->
term list ->
((term # term) list # term list) ->
term list ->
((term # term) list # term list))
var_cap =
-
: (thm -> term list -> term list -> term list -> (term list # thm))
MATCH_SUBS1 =
-
: (thm ->
term list ->
term list ->
((term # term) list # (type # type) list) ->
(term list # thm))
MATCH_SUBS =
-
: (thm ->
term list ->
term list ->
((term # term) list # (type # type) list) list ->
(term list # thm list))
COND_REWR_TAC =
-
: ((term -> term -> ((term # term) list # (type # type) list) list) ->
thm_tactic)
-
: ((term -> term -> ((term # term) list # (type # type) list) list) ->
thm_tactic)
COND_REWR_TAC =
-
: ((term -> term -> ((term # term) list # (type # type) list) list) ->
thm_tactic)
search_top_down =
-
: (term -> term -> ((term # term) list # (type # type) list) list)
COND_REWR_CANON = - : (thm -> thm)
COND_REWRITE1_TAC = - : thm_tactic
COND_REWR_CONV =
-
: ((term -> term -> ((term # term) list # (type # type) list) list) ->
thm ->
conv)
COND_REWRITE1_CONV = - : (thm list -> thm -> conv)
Calling Lisp compiler
File cond_rewr compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_theory `res_quan`;;'\
'loadf `cond_rewr`;;'\
'compilet `res_rules`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory res_quan loaded
() : void
................() : void
rtheory = `res_quan` : string
mk_resq_forall = - : ((term # term # term) -> term)
mk_resq_exists = - : ((term # term # term) -> term)
mk_resq_select = - : ((term # term # term) -> term)
mk_resq_abstract = - : ((term # term # term) -> term)
list_mk_resq_forall = - : (((term # term) list # term) -> term)
list_mk_resq_exists = - : (((term # term) list # term) -> term)
dest_resq_forall = - : (term -> (term # term # term))
dest_resq_exists = - : (term -> (term # term # term))
dest_resq_select = - : (term -> (term # term # term))
dest_resq_abstract = - : (term -> (term # term # term))
strip_resq_forall = - : (term -> ((term # term) list # term))
strip_resq_exists = - : (term -> ((term # term) list # term))
is_resq_forall = - : (term -> bool)
is_resq_exists = - : (term -> bool)
is_resq_select = - : (term -> bool)
is_resq_abstract = - : (term -> bool)
RESQ_SPEC = - : (term -> thm -> thm)
RESQ_SPECL = - : (term list -> thm -> thm)
RESQ_SPEC_ALL = - : (thm -> thm)
GQSPEC = - : (term -> thm -> thm)
GQSPECL = - : (term list -> thm -> thm)
GQSPEC_ALL = - : (thm -> thm)
RESQ_HALF_SPEC = - : (thm -> thm)
RESQ_HALF_EXISTS = - : (thm -> thm)
RESQ_GEN = - : ((term # term) -> thm -> thm)
RESQ_GENL = - : ((term # term) list -> thm -> thm)
RESQ_GEN_ALL = - : (thm -> thm)
RESQ_MATCH_MP = - : (thm -> thm -> thm)
RESQ_HALF_GEN_TAC = - : tactic
RESQ_GEN_TAC = - : tactic
GGEN_TAC = - : tactic
RESQ_EXISTS_TAC = - : (term -> tactic)
MATCH_MP = - : (thm -> thm -> thm)
check = - : (string -> * list -> * list)
check_res = - : (thm -> thm)
RESQ_IMP_RES_THEN = - : thm_tactical
RESQ_RES_THEN = - : (thm_tactic -> tactic)
((-), -) : (thm_tactical # (thm_tactic -> tactic))
RESQ_IMP_RES_THEN = - : thm_tactical
RESQ_RES_THEN = - : (thm_tactic -> tactic)
RESQ_IMP_RES_TAC = - : thm_tactic
RESQ_RES_TAC = - : tactic
LHS_CONV = - : (conv -> conv)
RHS_CONV = - : (conv -> conv)
BOTH_CONV = - : (conv -> conv)
LEFT_THENC_RIGHT = - : (conv -> conv -> conv)
RF_BODY_CONV = - : (conv -> conv)
RF_PRED_CONV = - : (conv -> conv)
RF_CONV = - : (conv -> conv)
PRED_THENC_BODY = - : (conv -> conv -> conv)
RESQ_FORALL_CONV = - : conv
LIST_RESQ_FORALL_CONV = - : conv
IMP_RESQ_FORALL_CONV = - : conv
RESQ_FORALL_AND_CONV = - : conv
AND_RESQ_FORALL_CONV = - : conv
RESQ_FORALL_SWAP_CONV = - : conv
RESQ_EXISTS_CONV = - : conv
RESQ_REWR_CANON = - : (thm -> thm)
RESQ_REWRITE1_TAC = - : thm_tactic
RESQ_REWRITE1_CONV = - : (thm list -> thm -> conv)
check_varstruct = - : (term -> term list)
check_lhs = - : (term -> term list)
get_type = - : (term -> type -> type)
RESQ_DEF_EXISTS_RULE = - : conv
new_gen_resq_definition = - : (string -> (string # term) -> thm)
new_resq_definition = - : ((string # term) -> thm)
new_infix_resq_definition = - : ((string # term) -> thm)
new_binder_resq_definition = - : ((string # term) -> thm)
((-), (-), -)
: (((string # term) -> thm) #
((string # term) -> thm) #
((string # term) -> thm))
new_resq_definition = - : ((string # term) -> thm)
new_infix_resq_definition = - : ((string # term) -> thm)
new_binder_resq_definition = - : ((string # term) -> thm)
Calling Lisp compiler
File res_rules compiled
() : void
#===> library res_quan rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/res_quan'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/wellorder'
\
echo 'set_flag(`abort_when_fail`,true);;' \
'loadt `mk_wellorder`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
false : bool
Run time: 0.0s
ty = ":* # * -> bool" : type
Run time: 0.0s
set_wo_map = - : (void -> void)
unset_wo_map = - : (void -> void)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
PBETA_TAC = - : tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
ANTE_RES_THEN = - : thm_tactical
Run time: 0.0s
IMP_RES_THEN = - : thm_tactical
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
less = |- !l x y. wo_less l(x,y) = l(x,y) /\ ~(x = y)
Run time: 0.0s
Intermediate theorems generated: 2
subset = |- !P Q. P wo_subset Q = (!x. P x ==> Q x)
Run time: 0.0s
Intermediate theorems generated: 2
Union = |- !P. wo_Union P = (\x. ?p. P p /\ p x)
Run time: 0.0s
Intermediate theorems generated: 2
fl = |- !l x. wo_fl l x = (?y. l(x,y) \/ l(y,x))
Run time: 0.0s
Intermediate theorems generated: 2
poset =
|- !l.
wo_poset l =
(!x. wo_fl l x ==> l(x,x)) /\
(!x y z. l(x,y) /\ l(y,z) ==> l(x,z)) /\
(!x y. l(x,y) /\ l(y,x) ==> (x = y))
Run time: 0.0s
Intermediate theorems generated: 2
chain = |- !l P. wo_chain l P = (!x y. P x /\ P y ==> l(x,y) \/ l(y,x))
Run time: 0.0s
Intermediate theorems generated: 2
woset =
|- !l.
wo_woset l =
(!x. wo_fl l x ==> l(x,x)) /\
(!x y z. l(x,y) /\ l(y,z) ==> l(x,z)) /\
(!x y. l(x,y) /\ l(y,x) ==> (x = y)) /\
(!x y. wo_fl l x /\ wo_fl l y ==> l(x,y) \/ l(y,x)) /\
(!P.
(!x. P x ==> wo_fl l x) /\ (?x. P x) ==>
(?y. P y /\ (!z. P z ==> l(y,z))))
Run time: 0.0s
Intermediate theorems generated: 2
inseg = |- !l m. l wo_inseg m = (!x y. l(x,y) = m(x,y) /\ wo_fl l y)
Run time: 0.1s
Intermediate theorems generated: 2
linseg = |- !l a. wo_linseg l a = (\(x,y). l(x,y) /\ wo_less l(y,a))
Run time: 0.0s
Intermediate theorems generated: 2
ordinal =
|- !l.
wo_ordinal l =
wo_woset l /\ (!x. wo_fl l x ==> (x = (@y. ~wo_less l(y,x))))
Run time: 0.0s
Intermediate theorems generated: 2
() : void
Run time: 0.0s
SUBSET_REFL = |- !P. P subset P
Run time: 0.0s
Intermediate theorems generated: 22
SUBSET_ANTISYM = |- !P Q. P subset Q /\ Q subset P ==> (P = Q)
Run time: 0.0s
Intermediate theorems generated: 100
SUBSET_TRANS = |- !P Q R. P subset Q /\ Q subset R ==> P subset R
Run time: 0.0s
Intermediate theorems generated: 121
POSET_REFL = |- !l. poset l ==> (!x. fl l x ==> l(x,x))
POSET_TRANS = |- !l. poset l ==> (!x y z. l(x,y) /\ l(y,z) ==> l(x,z))
POSET_ANTISYM = |- !l. poset l ==> (!x y. l(x,y) /\ l(y,x) ==> (x = y))
Run time: 0.0s
Intermediate theorems generated: 16
POSET_FLEQ = |- !l. poset l ==> (!x. fl l x = l(x,x))
Run time: 0.0s
Intermediate theorems generated: 34
CHAIN_SUBSET = |- !l P Q. chain l P /\ Q subset P ==> chain l Q
Run time: 0.1s
Intermediate theorems generated: 90
WOSET_REFL = |- !l. woset l ==> (!x. fl l x ==> l(x,x))
WOSET_TRANS = |- !l. woset l ==> (!x y z. l(x,y) /\ l(y,z) ==> l(x,z))
WOSET_ANTISYM = |- !l. woset l ==> (!x y. l(x,y) /\ l(y,x) ==> (x = y))
WOSET_TOTAL =
|- !l. woset l ==> (!x y. fl l x /\ fl l y ==> l(x,y) \/ l(y,x))
WOSET_WELL =
|- !l.
woset l ==>
(!P.
(!x. P x ==> fl l x) /\ (?x. P x) ==>
(?y. P y /\ (!z. P z ==> l(y,z))))
Run time: 0.0s
Intermediate theorems generated: 24
WOSET_POSET = |- !l. woset l ==> poset l
Run time: 0.0s
Intermediate theorems generated: 98
WOSET_FLEQ = |- !l. woset l ==> (!x. fl l x = l(x,x))
Run time: 0.0s
Intermediate theorems generated: 8
WOSET_TRANS_LESS =
|- !l. woset l ==> (!x y z. less l(x,y) /\ l(y,z) ==> less l(x,z))
Run time: 0.0s
Intermediate theorems generated: 144
WOSET =
|- !l.
woset l =
(!x y. l(x,y) /\ l(y,x) ==> (x = y)) /\
(!P.
(!x. P x ==> fl l x) /\ (?x. P x) ==>
(?y. P y /\ (!z. P z ==> l(y,z))))
Run time: 0.2s
Intermediate theorems generated: 1294
PAIRED_EXT = |- !l m. (!x y. l(x,y) = m(x,y)) = (l = m)
Run time: 0.0s
Intermediate theorems generated: 63
WOSET_REFL = |- !l. woset l ==> (!x. fl l x ==> l(x,x))
WOSET_TRANS = |- !l. woset l ==> (!x y z. l(x,y) /\ l(y,z) ==> l(x,z))
WOSET_ANTISYM = |- !l. woset l ==> (!x y. l(x,y) /\ l(y,x) ==> (x = y))
WOSET_TOTAL =
|- !l. woset l ==> (!x y. fl l x /\ fl l y ==> l(x,y) \/ l(y,x))
WOSET_WELL =
|- !l.
woset l ==>
(!P.
(!x. P x ==> fl l x) /\ (?x. P x) ==>
(?y. P y /\ (!z. P z ==> l(y,z))))
Run time: 0.0s
Intermediate theorems generated: 24
WOSET_TRANS_LE =
|- !l. woset l ==> (!x y z. l(x,y) /\ less l(y,z) ==> less l(x,z))
Run time: 0.0s
Intermediate theorems generated: 143
WOSET_WELL_CONTRAPOS =
|- !l.
woset l ==>
(!P.
(!x. P x ==> fl l x) /\ (?x. P x) ==>
(?y. P y /\ (!z. less l(z,y) ==> ~P z)))
Run time: 0.0s
Intermediate theorems generated: 109
WOSET_TOTAL_LE =
|- !l. woset l ==> (!x y. fl l x /\ fl l y ==> l(x,y) \/ less l(y,x))
Run time: 0.1s
Intermediate theorems generated: 138
WOSET_TOTAL_LT =
|- !l.
woset l ==>
(!x y. fl l x /\ fl l y ==> (x = y) \/ less l(x,y) \/ less l(y,x))
Run time: 0.0s
Intermediate theorems generated: 172
WO_INDUCT =
|- !P l.
woset l /\ (!x. fl l x /\ (!y. less l(y,x) ==> P y) ==> P x) ==>
(!x. fl l x ==> P x)
Run time: 0.0s
Intermediate theorems generated: 469
WO_INDUCT_TAC = - : tactic
Run time: 0.0s
Intermediate theorems generated: 2
AGREE_LEMMA =
|- !l h ms m n f g z.
woset l /\
(!x. fl l(ms x)) /\
(!f f' x.
(!y. less l(ms y,ms x) ==> (f y = f' y)) ==> (h f x = h f' x)) /\
(!x. l(ms x,m) ==> (f x = h f x)) /\
(!x. l(ms x,n) ==> (g x = h g x)) /\
l(ms z,m) /\
l(ms z,n) ==>
(f z = g z)
Run time: 0.1s
Intermediate theorems generated: 1165
WO_RECURSE_LOCAL =
|- !l h ms.
woset l /\
(!x. fl l(ms x)) /\
(!f f' x.
(!y. less l(ms y,ms x) ==> (f y = f' y)) ==> (h f x = h f' x)) ==>
(!n. ?f. !x. l(ms x,n) ==> (f x = h f x))
Run time: 0.2s
Intermediate theorems generated: 1556
WO_RECURSE_EXISTS =
|- !l h ms.
woset l /\
(!x. fl l(ms x)) /\
(!f f' x.
(!y. less l(ms y,ms x) ==> (f y = f' y)) ==> (h f x = h f' x)) ==>
(?f. !x. f x = h f x)
Run time: 0.0s
Intermediate theorems generated: 444
WO_RECURSE =
|- !l h ms.
woset l /\
(!x. fl l(ms x)) /\
(!f g x.
(!y. less l(ms y,ms x) ==> (f y = g y)) ==> (h f x = h g x)) ==>
(?! f. !x. f x = h f x)
Run time: 0.1s
Intermediate theorems generated: 280
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Run time: 0.0s
FL_NUM = |- !n. fl(\(m,n). m <= n)n
Run time: 0.0s
Intermediate theorems generated: 39
Theorem WOP autoloading from theory `arithmetic` ...
WOP = |- !P. (?n. P n) ==> (?n. P n /\ (!m. m < n ==> ~P m))
Run time: 0.0s
Theorem NOT_LESS_EQUAL autoloading from theory `arithmetic` ...
NOT_LESS_EQUAL = |- !m n. ~m <= n = n < m
Run time: 0.0s
Theorem LESS_EQUAL_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQUAL_ANTISYM = |- !n m. n <= m /\ m <= n ==> (n = m)
Run time: 0.0s
WOSET_NUM = |- woset(\(m,n). m <= n)
Run time: 0.0s
Intermediate theorems generated: 148
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
Run time: 0.0s
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Run time: 0.0s
Intermediate theorems generated: 1
WO_RECURSE_NUM =
|- !h ms.
(!f g x. (!y. (ms y) < (ms x) ==> (f y = g y)) ==> (h f x = h g x)) ==>
(?! f. !x. f x = h f x)
Run time: 0.1s
Intermediate theorems generated: 259
UNION_FL = |- !P l. fl(Union P)x = (?l. P l /\ fl l x)
Run time: 0.0s
Intermediate theorems generated: 170
UNION_INSEG = |- !P l. (!m. P m ==> m inseg l) ==> (Union P) inseg l
Run time: 0.0s
Intermediate theorems generated: 232
INSEG_SUBSET = |- !l m. m inseg l ==> (!x y. m(x,y) ==> l(x,y))
Run time: 0.0s
Intermediate theorems generated: 68
INSEG_SUBSET_FL = |- !l m. m inseg l ==> (!x. fl m x ==> fl l x)
Run time: 0.0s
Intermediate theorems generated: 187
INSEG_WOSET = |- !l m. m inseg l /\ woset l ==> woset m
Run time: 0.0s
Intermediate theorems generated: 401
LINSEG_INSEG = |- !l a. woset l ==> (linseg l a) inseg l
Run time: 0.1s
Intermediate theorems generated: 240
LINSEG_WOSET = |- !l a. woset l ==> woset(linseg l a)
Run time: 0.0s
Intermediate theorems generated: 39
LINSEG_FL = |- !l a x. woset l ==> (fl(linseg l a)x = less l(x,a))
Run time: 0.0s
Intermediate theorems generated: 142
INSEG_PROPER_SUBSET =
|- !l m. m inseg l /\ ~(l = m) ==> (?x y. l(x,y) /\ ~m(x,y))
Run time: 0.1s
Intermediate theorems generated: 213
INSEG_PROPER_SUBSET_FL =
|- !l m. m inseg l /\ ~(l = m) ==> (?a. fl l a /\ ~fl m a)
Run time: 0.0s
Intermediate theorems generated: 107
INSEG_LINSEG =
|- !l m.
woset l ==>
(m inseg l = (m = l) \/ (?a. fl l a /\ (m = linseg l a)))
Run time: 0.1s
Intermediate theorems generated: 1172
EXTEND_FL =
|- !l x. woset l ==> (fl(\(x,y). l(x,y) /\ l(y,a))x = l(x,a))
Run time: 0.0s
Intermediate theorems generated: 143
EXTEND_INSEG =
|- !l a. woset l /\ fl l a ==> (\(x,y). l(x,y) /\ l(y,a)) inseg l
Run time: 0.1s
Intermediate theorems generated: 57
EXTEND_LINSEG =
|- !l a.
woset l /\ fl l a ==>
(\(x,y). linseg l a(x,y) \/ (y = a) /\ (fl(linseg l a)x \/ (x = a))) inseg
l
Run time: 0.1s
Intermediate theorems generated: 489
ORDINAL_CHAINED =
|- !l m. ordinal l /\ ordinal m ==> m inseg l \/ l inseg m
Run time: 0.1s
Intermediate theorems generated: 997
FL_SUC =
|- !l a.
fl(\(x,y). l(x,y) \/ (y = a) /\ (fl l x \/ (x = a)))x =
fl l x \/ (x = a)
Run time: 0.1s
Intermediate theorems generated: 659
ORDINAL_SUC =
|- !l.
ordinal l /\ (?x. ~fl l x) ==>
ordinal
(\(x,y).
l(x,y) \/ (y = (@y. ~fl l y)) /\ (fl l x \/ (x = (@y. ~fl l y))))
Run time: 0.2s
Intermediate theorems generated: 2338
ORDINAL_UNION = |- !P. (!l. P l ==> ordinal l) ==> ordinal(Union P)
Run time: 0.2s
Intermediate theorems generated: 2015
ORDINAL_UNION_LEMMA =
|- !l x. ordinal l ==> fl l x ==> fl(Union ordinal)x
Run time: 0.0s
Intermediate theorems generated: 30
ORDINAL_UP =
|- !l.
ordinal l ==> (!x. fl l x) \/ (?m x. ordinal m /\ fl m x /\ ~fl l x)
Run time: 0.1s
Intermediate theorems generated: 154
WO_LEMMA = |- ?l. ordinal l /\ (!x. fl l x)
Run time: 0.0s
Intermediate theorems generated: 135
WO_FL_RESTRICT =
|- !l.
woset l ==> (!P. fl(\(x,y). P x /\ P y /\ l(x,y))x = P x /\ fl l x)
Run time: 0.1s
Intermediate theorems generated: 392
WO = |- !P. ?l. woset l /\ (fl l = P)
Run time: 0.0s
Intermediate theorems generated: 403
HP =
|- !l.
poset l ==>
(?P. chain l P /\ (!Q. chain l Q /\ P subset Q ==> (Q = P)))
Run time: 0.2s
Intermediate theorems generated: 2506
ZL =
|- !l.
poset l /\ (!P. chain l P ==> (?y. fl l y /\ (!x. P x ==> l(x,y)))) ==>
(?y. fl l y /\ (!x. l(y,x) ==> (y = x)))
Run time: 0.0s
Intermediate theorems generated: 795
kl_tm = "\(c1,c2). C subset c1 /\ c1 subset c2 /\ chain l c2" : term
Run time: 0.0s
KL_POSET_LEMMA =
|- poset(\(c1,c2). C subset c1 /\ c1 subset c2 /\ chain l c2)
Run time: 0.1s
Intermediate theorems generated: 386
KL =
|- !l.
poset l ==>
(!C.
chain l C ==>
(?P.
(chain l P /\ C subset P) /\
(!R. chain l R /\ P subset R ==> (R = P))))
Run time: 0.2s
Intermediate theorems generated: 1083
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File mk_wellorder loaded
() : void
Run time: 3.4s
Intermediate theorems generated: 22538
#make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/wellorder'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/abs_theory'
Making ../../Library/abs_theory/monoid_def.th...
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
true : bool
false : bool
false : bool
Run time: 0.0s
() : void
Run time: 0.0s
true : bool
Run time: 0.0s
.loading abs_theory
.Extending help search path......................................() : void
Run time: 0.1s
SYM_RULE = - : (thm -> thm)
Run time: 0.0s
/bin/rm: cannot remove 'monoid_def.th': No such file or directory
1 : int
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 1
MONOID = |- !f. ?! fn. !f' x. fn(monoid f' x) = f f' x
Run time: 0.0s
Intermediate theorems generated: 431
() : void
Run time: 0.0s
Intermediate theorems generated: 2
"!f. (!a. (op m a f = a) /\ (op m f a = a)) ==> (f = e m)"
3 ["!x y z. op m x(op m y z) = op m(op m x y)z" ]
2 ["!x. op m(e m)x = x" ]
1 ["!x. op m x(e m) = x" ]
() : void
Run time: 0.0s
Intermediate theorems generated: 1
OK..
"f = e m"
4 ["!x y z. op m x(op m y z) = op m(op m x y)z" ]
3 ["!x. op m(e m)x = x" ]
2 ["!x. op m x(e m) = x" ]
1 ["!a. (op m a f = a) /\ (op m f a = a)" ]
() : void
Run time: 0.0s
Intermediate theorems generated: 6
OK..
"f = e m"
5 ["!x y z. op m x(op m y z) = op m(op m x y)z" ]
4 ["!x. op m(e m)x = x" ]
3 ["!x. op m x(e m) = x" ]
2 ["!a. (op m a f = a) /\ (op m f a = a)" ]
1 ["e m = op m(e m)f" ]
() : void
Run time: 0.0s
Intermediate theorems generated: 10
OK..
"f = op m(e m)f"
5 ["!x y z. op m x(op m y z) = op m(op m x y)z" ]
4 ["!x. op m(e m)x = x" ]
3 ["!x. op m x(e m) = x" ]
2 ["!a. (op m a f = a) /\ (op m f a = a)" ]
1 ["e m = op m(e m)f" ]
() : void
Run time: 0.0s
Intermediate theorems generated: 4
OK..
goal proved
. |- f = op m(e m)f
.. |- f = e m
.. |- f = e m
. |- !f. (!a. (op m a f = a) /\ (op m f a = a)) ==> (f = e m)
Previous subproof:
goal proved
() : void
Run time: 0.1s
Intermediate theorems generated: 43
IDENTITY_UNIQUE =
. |- !f. (!a. (op m a f = a) /\ (op m f a = a)) ==> (f = e m)
Run time: 0.0s
Intermediate theorems generated: 36
. |- !f. (!a. (op m a f = a) /\ (op m f a = a)) ==> (f = e m)
Run time: 0.0s
Intermediate theorems generated: 2
OP_DETERMINES_IDENTITY = .. |- (op m1 = op m2) ==> (e m1 = e m2)
Run time: 0.0s
Intermediate theorems generated: 73
.. |- (op m1 = op m2) ==> (e m1 = e m2)
Run time: 0.0s
Intermediate theorems generated: 4
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File ../../Library/abs_theory/monoid_def.ml loaded
() : void
Run time: 0.2s
Intermediate theorems generated: 614
Making ../../Library/abs_theory/group_def.th...
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
true : bool
false : bool
false : bool
Run time: 0.0s
() : void
Run time: 0.0s
true : bool
Run time: 0.0s
.loading abs_theory
.Extending help search path......................................() : void
Run time: 0.1s
SYM_RULE = - : (thm -> thm)
Run time: 0.0s
/bin/rm: cannot remove 'group_def.th': No such file or directory
1 : int
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 1
Theory monoid_def loaded
() : void
Run time: 0.0s
Intermediate theorems generated: 6
GROUP = |- !f. ?! fn. !f0 x f1. fn(group f0 x f1) = f f0 x f1
Run time: 0.1s
Intermediate theorems generated: 601
() : void
Run time: 0.0s
Intermediate theorems generated: 2
GROUP_EXTENDS_MONOID = ... |- IS_MONOID(monoid(fn g)(id g))
Run time: 0.0s
Intermediate theorems generated: 144
IDENTITY_UNIQUE =
... |- !f. (!a. (fn g a f = a) /\ (fn g f a = a)) ==> (f = id g)
Run time: 0.0s
Intermediate theorems generated: 144
":(*)group" : type
Run time: 0.0s
Intermediate theorems generated: 3
... |- !f. (!a. (fn g a f = a) /\ (fn g f a = a)) ==> (f = id g)
Run time: 0.1s
Intermediate theorems generated: 6
LEFT_CANCELLATION = ... |- !x y a. (fn g a x = fn g a y) ==> (x = y)
Run time: 0.0s
Intermediate theorems generated: 67
INVERSE_INVERSE_LEMMA = |- !g. IS_GROUP g ==> (!a. inv g(inv g a) = a)
Run time: 0.0s
Intermediate theorems generated: 45
ALTERNATE_INVERSE_INVERSE_LEMMA =
|- !g. IS_GROUP g ==> (!a. inv g(inv g a) = a)
Run time: 0.0s
Intermediate theorems generated: 69
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File ../../Library/abs_theory/group_def.ml loaded
() : void
Run time: 0.3s
Intermediate theorems generated: 1089
Making ../../Library/abs_theory/example.th...
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
true : bool
false : bool
false : bool
Run time: 0.0s
() : void
Run time: 0.0s
true : bool
Run time: 0.0s
.loading abs_theory
.Extending help search path......................................() : void
Run time: 0.1s
/bin/rm: cannot remove 'example.th': No such file or directory
1 : int
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 1
Loading library taut ...
Updating help search path
........................................
Library taut loaded.
() : void
Run time: 0.0s
Intermediate theorems generated: 153
Theory group_def loaded
() : void
Run time: 0.0s
Intermediate theorems generated: 7
Theorem I_THM autoloading from theory `combin` ...
I_THM = |- !x. I x = x
Run time: 0.0s
GROUP_THOBS = |- IS_GROUP(group(\x y. ~(x = y))F I)
Run time: 0.1s
Intermediate theorems generated: 378
|- !f. (!a. (~(a = f) = a) /\ (~(f = a) = a)) ==> ~f
Run time: 0.0s
Intermediate theorems generated: 733
|- !x y a. (~(a = x) = ~(a = y)) ==> (x = y)
Run time: 0.0s
Intermediate theorems generated: 732
|- !a. I(I a) = a
Run time: 0.2s
Intermediate theorems generated: 1106
concrete_rep = "group(\x y. x = y)T I" : term
Run time: 0.0s
GROUP_THOBS = |- IS_GROUP(group(\x y. x = y)T I)
Run time: 0.0s
Intermediate theorems generated: 356
inst_func = - : (string -> thm)
Run time: 0.0s
[|- !f. (!a. ((a = f) = a) /\ ((f = a) = a)) ==> f;
|- !x y a. ((a = x) = (a = y)) ==> (x = y);
|- !a. I(I a) = a]
: thm list
Run time: 0.3s
Intermediate theorems generated: 2546
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File ../../Library/abs_theory/example.ml loaded
() : void
Run time: 0.8s
Intermediate theorems generated: 6013
===> abs_theory rebuilt on Thu Jan 19 18:04:56 UTC 2023
Making abs_theory.ml
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
true : bool
false : bool
false : bool
Run time: 0.0s
() : void
Run time: 0.0s
() : void
loading abs_theory
() : void
Extending help search path() : void
int_to_term = - : (int -> term)
term_to_int = - : (term -> int)
for = - : (int -> * list -> * list)
ol = - : ((* -> *) list -> * -> *)
X_SPEC = - : (term -> term -> thm -> thm)
CONJ_IMP = - : (thm -> thm)
abs_type_info = - : (thm -> type)
dest_all_type = - : (type -> (string # type list))
string_from_type = - : (type -> string)
ty_str = - : (string -> type list -> string)
def_prefix = `abs_def_` : string
new_abstract_representation =
-
: (string -> (string # type) list -> thm)
get_abs_defs = - : (string -> thm list)
instantiate_abstract_definition =
-
: (string -> string -> thm -> (term # term) list -> thm)
thobs = [] : (type # thm) list
thobs_prefix = `thobs_` : string
new_theory_obligations = - : ((string # term) -> void)
get_thobs = - : (string -> (type # thm) list)
orelsef = - : ((* -> **) -> (* -> **) -> * -> **)
() : void
D = - : (((* -> **) # (* -> ***)) -> * -> (** # ***))
() : void
make_abs_goal = - : (goal -> goal)
prove_abs_thm = - : ((string # term # tactic) -> thm)
ABS_TAC_PROOF = - : ((goal # tactic) -> thm)
set_abs_goal = - : (goal -> void)
g = - : (term -> void)
STRIP_THOBS_THEN = - : (thm_tactic -> tactic)
STRIP_THOBS_TAC = - : tactic
new_abstract_parent = - : (string -> void)
EXPAND_THOBS_TAC = - : (string -> tactic)
instantiate_abstract_theorem =
-
: (string -> string -> (term # term) list -> proof)
close_theory_orig = - : (void -> void)
close_theory = - : (void -> void)
new_theory_orig = - : (string -> void)
new_theory = - : (string -> void)
((-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
-)
: (((goal # tactic) -> thm) #
(string -> tactic) #
tactic #
(thm_tactic -> tactic) #
(thm -> type) #
(void -> void) #
(term -> void) #
(string -> string -> thm -> (term # term) list -> thm) #
(string -> string -> (term # term) list -> proof) #
(string -> void) #
(string -> (string # type) list -> thm) #
(string -> void) #
((string # term) -> void) #
((string # term # tactic) -> thm) #
(goal -> void))
ABS_TAC_PROOF = - : ((goal # tactic) -> thm)
EXPAND_THOBS_TAC = - : (string -> tactic)
STRIP_THOBS_TAC = - : tactic
STRIP_THOBS_THEN = - : (thm_tactic -> tactic)
abs_type_info = - : (thm -> type)
close_theory = - : (void -> void)
g = - : (term -> void)
instantiate_abstract_definition =
-
: (string -> string -> thm -> (term # term) list -> thm)
instantiate_abstract_theorem =
-
: (string -> string -> (term # term) list -> proof)
new_abstract_parent = - : (string -> void)
new_abstract_representation =
-
: (string -> (string # type) list -> thm)
new_theory = - : (string -> void)
new_theory_obligations = - : ((string # term) -> void)
prove_abs_thm = - : ((string # term # tactic) -> thm)
set_abs_goal = - : (goal -> void)
Calling Lisp compiler
File abs_theory compiled
() : void
Run time: 0.3s
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/abs_theory'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/reals'
cd theories; make all
make[5]: Entering directory '/<<PKGBUILDDIR>>/Library/reals/theories'
\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `hrat.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.0s
define_equivalence_type =
-
: (string ->
thm ->
(term # string # bool) list ->
thm list ->
thm list ->
thm list)
Run time: 0.0s
File equiv loaded
() : void
Run time: 0.1s
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Run time: 0.0s
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
Run time: 0.0s
Theorem PRE autoloading from theory `prim_rec` ...
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
Run time: 0.0s
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
Run time: 0.0s
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Run time: 0.0s
UNSUCK_TAC = - : tactic
Run time: 0.0s
Intermediate theorems generated: 336
trat_1 = |- trat_1 = 0,0
Run time: 0.0s
Intermediate theorems generated: 2
trat_inv = |- !x y. trat_inv(x,y) = y,x
Run time: 0.0s
Intermediate theorems generated: 2
trat_add =
|- !x y x' y'.
(x,y) trat_add (x',y') =
PRE(((SUC x) * (SUC y')) + ((SUC x') * (SUC y))),
PRE((SUC y) * (SUC y'))
Run time: 0.0s
Intermediate theorems generated: 2
trat_mul =
|- !x y x' y'.
(x,y) trat_mul (x',y') =
PRE((SUC x) * (SUC x')),PRE((SUC y) * (SUC y'))
Run time: 0.0s
Intermediate theorems generated: 2
trat_sucint =
|- (trat_sucint 0 = trat_1) /\
(!n. trat_sucint(SUC n) = (trat_sucint n) trat_add trat_1)
Run time: 0.0s
Intermediate theorems generated: 136
trat_eq =
|- !x y x' y'.
(x,y) trat_eq (x',y') = ((SUC x) * (SUC y') = (SUC x') * (SUC y))
Run time: 0.0s
Intermediate theorems generated: 2
TRAT_EQ_REFL = |- !p. p trat_eq p
Run time: 0.0s
Intermediate theorems generated: 22
TRAT_EQ_SYM = |- !p q. p trat_eq q = q trat_eq p
Run time: 0.0s
Intermediate theorems generated: 37
Theorem MULT_ASSOC autoloading from theory `arithmetic` ...
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
Run time: 0.0s
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
Run time: 0.1s
Theorem MULT_SUC_EQ autoloading from theory `arithmetic` ...
MULT_SUC_EQ = |- !p m n. (n * (SUC p) = m * (SUC p)) = (n = m)
Run time: 0.0s
TRAT_EQ_TRANS = |- !p q r. p trat_eq q /\ q trat_eq r ==> p trat_eq r
Run time: 0.0s
Intermediate theorems generated: 152
TRAT_EQ_AP = |- !p q. (p = q) ==> p trat_eq q
Run time: 0.0s
Intermediate theorems generated: 8
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
Run time: 0.0s
TRAT_ADD_SYM_EQ = |- !h i. h trat_add i = i trat_add h
Run time: 0.0s
Intermediate theorems generated: 62
TRAT_MUL_SYM_EQ = |- !h i. h trat_mul i = i trat_mul h
Run time: 0.0s
Intermediate theorems generated: 58
TRAT_INV_WELLDEFINED =
|- !p q. p trat_eq q ==> (trat_inv p) trat_eq (trat_inv q)
Run time: 0.0s
Intermediate theorems generated: 61
Theorem RIGHT_ADD_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
Run time: 0.0s
TRAT_ADD_WELLDEFINED =
|- !p q r. p trat_eq q ==> (p trat_add r) trat_eq (q trat_add r)
Run time: 0.1s
Intermediate theorems generated: 297
TRAT_ADD_WELLDEFINED2 =
|- !p1 p2 q1 q2.
p1 trat_eq p2 /\ q1 trat_eq q2 ==>
(p1 trat_add q1) trat_eq (p2 trat_add q2)
Run time: 0.0s
Intermediate theorems generated: 65
TRAT_MUL_WELLDEFINED =
|- !p q r. p trat_eq q ==> (p trat_mul r) trat_eq (q trat_mul r)
Run time: 0.0s
Intermediate theorems generated: 207
TRAT_MUL_WELLDEFINED2 =
|- !p1 p2 q1 q2.
p1 trat_eq p2 /\ q1 trat_eq q2 ==>
(p1 trat_mul q1) trat_eq (p2 trat_mul q2)
Run time: 0.0s
Intermediate theorems generated: 65
TRAT_ADD_SYM = |- !h i. (h trat_add i) trat_eq (i trat_add h)
Run time: 0.0s
Intermediate theorems generated: 15
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Run time: 0.0s
TRAT_ADD_ASSOC =
|- !h i j.
(h trat_add (i trat_add j)) trat_eq ((h trat_add i) trat_add j)
Run time: 0.1s
Intermediate theorems generated: 297
TRAT_MUL_SYM = |- !h i. (h trat_mul i) trat_eq (i trat_mul h)
Run time: 0.0s
Intermediate theorems generated: 15
TRAT_MUL_ASSOC =
|- !h i j.
(h trat_mul (i trat_mul j)) trat_eq ((h trat_mul i) trat_mul j)
Run time: 0.0s
Intermediate theorems generated: 189
Theorem LEFT_ADD_DISTRIB autoloading from theory `arithmetic` ...
LEFT_ADD_DISTRIB = |- !m n p. p * (m + n) = (p * m) + (p * n)
Run time: 0.0s
TRAT_LDISTRIB =
|- !h i j.
(h trat_mul (i trat_add j)) trat_eq
((h trat_mul i) trat_add (h trat_mul j))
Run time: 0.1s
Intermediate theorems generated: 611
TRAT_MUL_LID = |- !h. (trat_1 trat_mul h) trat_eq h
Run time: 0.0s
Intermediate theorems generated: 127
TRAT_MUL_LINV = |- !h. ((trat_inv h) trat_mul h) trat_eq trat_1
Run time: 0.1s
Intermediate theorems generated: 136
Theorem ADD_INV_0_EQ autoloading from theory `arithmetic` ...
ADD_INV_0_EQ = |- !m n. (m + n = m) = (n = 0)
Run time: 0.0s
TRAT_NOZERO = |- !h i. ~(h trat_add i) trat_eq h
Run time: 0.0s
Intermediate theorems generated: 250
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
Run time: 0.0s
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
Run time: 0.0s
Theorem LESS_LESS_CASES autoloading from theory `arithmetic` ...
LESS_LESS_CASES = |- !m n. (m = n) \/ m < n \/ n < m
Run time: 0.0s
TRAT_ADD_TOTAL =
|- !h i.
h trat_eq i \/
(?d. h trat_eq (i trat_add d)) \/
(?d. i trat_eq (h trat_add d))
Run time: 0.1s
Intermediate theorems generated: 599
TRAT_SUCINT_0 = |- !n. (trat_sucint n) trat_eq (n,0)
Run time: 0.0s
Intermediate theorems generated: 233
Theorem LESS_ADD_NONZERO autoloading from theory `arithmetic` ...
LESS_ADD_NONZERO = |- !m n. ~(n = 0) ==> m < (m + n)
Run time: 0.0s
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
Run time: 0.0s
Theorem LESS_MONO_MULT autoloading from theory `arithmetic` ...
LESS_MONO_MULT = |- !m n p. m <= n ==> (m * p) <= (n * p)
Run time: 0.0s
Theorem SUB_ADD autoloading from theory `arithmetic` ...
SUB_ADD = |- !m n. n <= m ==> ((m - n) + n = m)
Run time: 0.0s
Theorem RIGHT_SUB_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_SUB_DISTRIB = |- !m n p. (m - n) * p = (m * p) - (n * p)
Run time: 0.0s
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Run time: 0.0s
Theorem SUB_EQ_0 autoloading from theory `arithmetic` ...
SUB_EQ_0 = |- !m n. (m - n = 0) = m <= n
Run time: 0.0s
TRAT_ARCH = |- !h. ?n d. (trat_sucint n) trat_eq (h trat_add d)
Run time: 0.0s
Intermediate theorems generated: 395
TRAT_SUCINT =
|- (trat_sucint 0) trat_eq trat_1 /\
(!n. (trat_sucint(SUC n)) trat_eq ((trat_sucint n) trat_add trat_1))
Run time: 0.0s
Intermediate theorems generated: 37
TRAT_EQ_EQUIV = |- !p q. p trat_eq q = ($trat_eq p = $trat_eq q)
Run time: 0.0s
Intermediate theorems generated: 73
HRAT_ADD_SYM = |- !h i. h hrat_add i = i hrat_add h
HRAT_ADD_ASSOC =
|- !h i j. h hrat_add (i hrat_add j) = (h hrat_add i) hrat_add j
HRAT_MUL_SYM = |- !h i. h hrat_mul i = i hrat_mul h
HRAT_MUL_ASSOC =
|- !h i j. h hrat_mul (i hrat_mul j) = (h hrat_mul i) hrat_mul j
HRAT_LDISTRIB =
|- !h i j.
h hrat_mul (i hrat_add j) = (h hrat_mul i) hrat_add (h hrat_mul j)
HRAT_MUL_LID = |- !h. hrat_1 hrat_mul h = h
HRAT_MUL_LINV = |- !h. (hrat_inv h) hrat_mul h = hrat_1
HRAT_NOZERO = |- !h i. ~(h hrat_add i = h)
HRAT_ADD_TOTAL =
|- !h i. (h = i) \/ (?d. h = i hrat_add d) \/ (?d. i = h hrat_add d)
HRAT_ARCH = |- !h. ?n d. hrat_sucint n = h hrat_add d
HRAT_SUCINT =
|- (hrat_sucint 0 = hrat_1) /\
(!n. hrat_sucint(SUC n) = (hrat_sucint n) hrat_add hrat_1)
Run time: 0.6s
Intermediate theorems generated: 6487
HRAT_ADD_SYM = |- !h i. h hrat_add i = i hrat_add h
Run time: 0.0s
Intermediate theorems generated: 5
HRAT_ADD_ASSOC =
|- !h i j. h hrat_add (i hrat_add j) = (h hrat_add i) hrat_add j
Run time: 0.0s
Intermediate theorems generated: 7
HRAT_MUL_SYM = |- !h i. h hrat_mul i = i hrat_mul h
Run time: 0.0s
Intermediate theorems generated: 5
HRAT_MUL_ASSOC =
|- !h i j. h hrat_mul (i hrat_mul j) = (h hrat_mul i) hrat_mul j
Run time: 0.1s
Intermediate theorems generated: 7
HRAT_LDISTRIB =
|- !h i j.
h hrat_mul (i hrat_add j) = (h hrat_mul i) hrat_add (h hrat_mul j)
Run time: 0.0s
Intermediate theorems generated: 7
HRAT_MUL_LID = |- !h. hrat_1 hrat_mul h = h
Run time: 0.0s
Intermediate theorems generated: 3
HRAT_MUL_LINV = |- !h. (hrat_inv h) hrat_mul h = hrat_1
Run time: 0.0s
Intermediate theorems generated: 3
HRAT_NOZERO = |- !h i. ~(h hrat_add i = h)
Run time: 0.0s
Intermediate theorems generated: 5
HRAT_ADD_TOTAL =
|- !h i. (h = i) \/ (?d. h = i hrat_add d) \/ (?d. i = h hrat_add d)
Run time: 0.0s
Intermediate theorems generated: 5
HRAT_ARCH = |- !h. ?n d. hrat_sucint n = h hrat_add d
Run time: 0.0s
Intermediate theorems generated: 3
HRAT_SUCINT =
|- (hrat_sucint 0 = hrat_1) /\
(!n. hrat_sucint(SUC n) = (hrat_sucint n) hrat_add hrat_1)
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File hrat.ml loaded
() : void
Run time: 1.6s
Intermediate theorems generated: 11032
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `hreal.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory HRAT loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.1s
() : void
Run time: 0.0s
hrat_lt = |- !x y. x hrat_lt y = (?d. y = x hrat_add d)
Run time: 0.0s
Intermediate theorems generated: 2
Theorem HRAT_NOZERO autoloading from theory `HRAT` ...
HRAT_NOZERO = |- !h i. ~(h hrat_add i = h)
Run time: 0.0s
HRAT_LT_REFL = |- !x. ~x hrat_lt x
Run time: 0.0s
Intermediate theorems generated: 41
Theorem HRAT_ADD_ASSOC autoloading from theory `HRAT` ...
HRAT_ADD_ASSOC =
|- !h i j. h hrat_add (i hrat_add j) = (h hrat_add i) hrat_add j
Run time: 0.0s
HRAT_LT_TRANS = |- !x y z. x hrat_lt y /\ y hrat_lt z ==> x hrat_lt z
Run time: 0.0s
Intermediate theorems generated: 63
HRAT_LT_ANTISYM = |- !x y. ~(x hrat_lt y /\ y hrat_lt x)
Run time: 0.0s
Intermediate theorems generated: 24
Theorem HRAT_ADD_TOTAL autoloading from theory `HRAT` ...
HRAT_ADD_TOTAL =
|- !h i. (h = i) \/ (?d. h = i hrat_add d) \/ (?d. i = h hrat_add d)
Run time: 0.0s
HRAT_LT_TOTAL = |- !x y. (x = y) \/ x hrat_lt y \/ y hrat_lt x
Run time: 0.0s
Intermediate theorems generated: 49
Theorem HRAT_MUL_LID autoloading from theory `HRAT` ...
HRAT_MUL_LID = |- !h. hrat_1 hrat_mul h = h
Run time: 0.0s
Theorem HRAT_MUL_SYM autoloading from theory `HRAT` ...
HRAT_MUL_SYM = |- !h i. h hrat_mul i = i hrat_mul h
Run time: 0.0s
HRAT_MUL_RID = |- !x. x hrat_mul hrat_1 = x
Run time: 0.0s
Intermediate theorems generated: 14
Theorem HRAT_MUL_LINV autoloading from theory `HRAT` ...
HRAT_MUL_LINV = |- !h. (hrat_inv h) hrat_mul h = hrat_1
Run time: 0.0s
HRAT_MUL_RINV = |- !x. x hrat_mul (hrat_inv x) = hrat_1
Run time: 0.0s
Intermediate theorems generated: 14
Theorem HRAT_LDISTRIB autoloading from theory `HRAT` ...
HRAT_LDISTRIB =
|- !h i j.
h hrat_mul (i hrat_add j) = (h hrat_mul i) hrat_add (h hrat_mul j)
Run time: 0.0s
HRAT_RDISTRIB =
|- !x y z.
(x hrat_add y) hrat_mul z = (x hrat_mul z) hrat_add (y hrat_mul z)
Run time: 0.1s
Intermediate theorems generated: 22
HRAT_LT_ADDL = |- !x y. x hrat_lt (x hrat_add y)
Run time: 0.0s
Intermediate theorems generated: 13
Theorem HRAT_ADD_SYM autoloading from theory `HRAT` ...
HRAT_ADD_SYM = |- !h i. h hrat_add i = i hrat_add h
Run time: 0.0s
HRAT_LT_ADDR = |- !x y. y hrat_lt (x hrat_add y)
Run time: 0.0s
Intermediate theorems generated: 19
HRAT_LT_GT = |- !x y. x hrat_lt y ==> ~y hrat_lt x
Run time: 0.0s
Intermediate theorems generated: 78
HRAT_LT_NE = |- !x y. x hrat_lt y ==> ~(x = y)
Run time: 0.0s
Intermediate theorems generated: 33
HRAT_EQ_LADD = |- !x y z. (x hrat_add y = x hrat_add z) = (y = z)
Run time: 0.0s
Intermediate theorems generated: 126
Theorem HRAT_MUL_ASSOC autoloading from theory `HRAT` ...
HRAT_MUL_ASSOC =
|- !h i j. h hrat_mul (i hrat_mul j) = (h hrat_mul i) hrat_mul j
Run time: 0.0s
HRAT_EQ_LMUL = |- !x y z. (x hrat_mul y = x hrat_mul z) = (y = z)
Run time: 0.0s
Intermediate theorems generated: 50
HRAT_LT_ADD2 =
|- !u v x y.
u hrat_lt x /\ v hrat_lt y ==> (u hrat_add v) hrat_lt (x hrat_add y)
Run time: 0.0s
Intermediate theorems generated: 79
HRAT_LT_LADD =
|- !x y z. (z hrat_add x) hrat_lt (z hrat_add y) = x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 77
HRAT_LT_RADD =
|- !x y z. (x hrat_add z) hrat_lt (y hrat_add z) = x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 21
HRAT_LT_MUL2 =
|- !u v x y.
u hrat_lt x /\ v hrat_lt y ==> (u hrat_mul v) hrat_lt (x hrat_mul y)
Run time: 0.1s
Intermediate theorems generated: 100
HRAT_LT_LMUL =
|- !x y z. (z hrat_mul x) hrat_lt (z hrat_mul y) = x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 149
HRAT_LT_RMUL =
|- !x y z. (x hrat_mul z) hrat_lt (y hrat_mul z) = x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 21
HRAT_LT_LMUL1 = |- !x y. (x hrat_mul y) hrat_lt y = x hrat_lt hrat_1
Run time: 0.0s
Intermediate theorems generated: 21
HRAT_LT_RMUL1 = |- !x y. (x hrat_mul y) hrat_lt x = y hrat_lt hrat_1
Run time: 0.0s
Intermediate theorems generated: 18
HRAT_GT_LMUL1 = |- !x y. y hrat_lt (x hrat_mul y) = hrat_1 hrat_lt x
Run time: 0.0s
Intermediate theorems generated: 22
HRAT_LT_L1 =
|- !x y. ((hrat_inv x) hrat_mul y) hrat_lt hrat_1 = y hrat_lt x
Run time: 0.0s
Intermediate theorems generated: 10
HRAT_LT_R1 =
|- !x y. (x hrat_mul (hrat_inv y)) hrat_lt hrat_1 = x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 10
HRAT_GT_L1 =
|- !x y. hrat_1 hrat_lt ((hrat_inv x) hrat_mul y) = x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 10
HRAT_INV_MUL =
|- !x y. hrat_inv(x hrat_mul y) = (hrat_inv x) hrat_mul (hrat_inv y)
Run time: 0.1s
Intermediate theorems generated: 85
HRAT_UP = |- !x. ?y. x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 13
HRAT_DOWN = |- !x. ?y. y hrat_lt x
Run time: 0.0s
Intermediate theorems generated: 45
HRAT_DOWN2 = |- !x y. ?z. z hrat_lt x /\ z hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 154
HRAT_MEAN = |- !x y. x hrat_lt y ==> (?z. x hrat_lt z /\ z hrat_lt y)
Run time: 0.0s
Intermediate theorems generated: 133
isacut =
|- !C.
isacut C =
(?x. C x) /\
(?x. ~C x) /\
(!x y. C x /\ y hrat_lt x ==> C y) /\
(!x. C x ==> (?y. C y /\ x hrat_lt y))
Run time: 0.0s
Intermediate theorems generated: 2
cut_of_hrat = |- !x. cut_of_hrat x = (\y. y hrat_lt x)
Run time: 0.1s
Intermediate theorems generated: 2
ISACUT_HRAT = |- !h. isacut(cut_of_hrat h)
Run time: 0.0s
Intermediate theorems generated: 221
hreal_tydef = |- ?rep. TYPE_DEFINITION isacut rep
Run time: 0.0s
Intermediate theorems generated: 4
hreal_tybij =
|- (!a. hreal(cut a) = a) /\ (!r. isacut r = (cut(hreal r) = r))
Run time: 0.0s
Intermediate theorems generated: 4
EQUAL_CUTS = |- !X Y. (cut X = cut Y) ==> (X = Y)
Run time: 0.0s
Intermediate theorems generated: 24
CUT_ISACUT = |- !X. isacut(cut X)
Run time: 0.0s
Intermediate theorems generated: 26
CUT_PROPERTIES =
|- (?x. cut X x) /\
(?x. ~cut X x) /\
(!x y. cut X x /\ y hrat_lt x ==> cut X y) /\
(!x. cut X x ==> (?y. cut X y /\ x hrat_lt y))
Run time: 0.0s
Intermediate theorems generated: 3
CUT_NONEMPTY = |- !X. ?x. cut X x
Run time: 0.0s
Intermediate theorems generated: 37
CUT_BOUNDED = |- !X. ?x. ~cut X x
Run time: 0.0s
Intermediate theorems generated: 37
CUT_DOWN = |- !X x y. cut X x /\ y hrat_lt x ==> cut X y
Run time: 0.0s
Intermediate theorems generated: 49
CUT_UP = |- !X x. cut X x ==> (?y. cut X y /\ x hrat_lt y)
Run time: 0.1s
Intermediate theorems generated: 42
CUT_UBOUND = |- !X x y. ~cut X x /\ x hrat_lt y ==> ~cut X y
Run time: 0.0s
Intermediate theorems generated: 102
CUT_STRADDLE = |- !X x y. cut X x /\ ~cut X y ==> x hrat_lt y
Run time: 0.0s
Intermediate theorems generated: 137
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Run time: 0.0s
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
Run time: 0.0s
Theorem HRAT_SUCINT autoloading from theory `HRAT` ...
HRAT_SUCINT =
|- (hrat_sucint 0 = hrat_1) /\
(!n. hrat_sucint(SUC n) = (hrat_sucint n) hrat_add hrat_1)
Run time: 0.0s
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Run time: 0.1s
Theorem HRAT_ARCH autoloading from theory `HRAT` ...
HRAT_ARCH = |- !h. ?n d. hrat_sucint n = h hrat_add d
Run time: 0.0s
CUT_NEARTOP_ADD = |- !X e. ?x. cut X x /\ ~cut X(x hrat_add e)
Run time: 0.0s
Intermediate theorems generated: 303
CUT_NEARTOP_MUL =
|- !X u. hrat_1 hrat_lt u ==> (?x. cut X x /\ ~cut X(u hrat_mul x))
Run time: 0.0s
Intermediate theorems generated: 234
hreal_1 = |- hreal_1 = hreal(cut_of_hrat hrat_1)
Run time: 0.0s
Intermediate theorems generated: 2
hreal_add =
|- !X Y.
X hreal_add Y =
hreal(\w. ?x y. (w = x hrat_add y) /\ cut X x /\ cut Y y)
Run time: 0.1s
Intermediate theorems generated: 2
hreal_mul =
|- !X Y.
X hreal_mul Y =
hreal(\w. ?x y. (w = x hrat_mul y) /\ cut X x /\ cut Y y)
Run time: 0.0s
Intermediate theorems generated: 2
hreal_inv =
|- !X.
hreal_inv X =
hreal
(\w.
?d. d hrat_lt hrat_1 /\ (!x. cut X x ==> (w hrat_mul x) hrat_lt d))
Run time: 0.0s
Intermediate theorems generated: 2
hreal_sup = |- !P. hreal_sup P = hreal(\w. ?X. P X /\ cut X w)
Run time: 0.0s
Intermediate theorems generated: 2
hreal_lt = |- !X Y. X hreal_lt Y = ~(X = Y) /\ (!x. cut X x ==> cut Y x)
Run time: 0.0s
Intermediate theorems generated: 2
HREAL_INV_ISACUT =
|- !X.
isacut
(\w.
?d. d hrat_lt hrat_1 /\ (!x. cut X x ==> (w hrat_mul x) hrat_lt d))
Run time: 0.1s
Intermediate theorems generated: 502
HREAL_ADD_ISACUT =
|- !X Y. isacut(\w. ?x y. (w = x hrat_add y) /\ cut X x /\ cut Y y)
Run time: 0.0s
Intermediate theorems generated: 521
HREAL_MUL_ISACUT =
|- !X Y. isacut(\w. ?x y. (w = x hrat_mul y) /\ cut X x /\ cut Y y)
Run time: 0.0s
Intermediate theorems generated: 537
HREAL_ADD_SYM = |- !X Y. X hreal_add Y = Y hreal_add X
Run time: 0.0s
Intermediate theorems generated: 124
HREAL_MUL_SYM = |- !X Y. X hreal_mul Y = Y hreal_mul X
Run time: 0.1s
Intermediate theorems generated: 124
HREAL_ADD_ASSOC =
|- !X Y Z. X hreal_add (Y hreal_add Z) = (X hreal_add Y) hreal_add Z
Run time: 0.0s
Intermediate theorems generated: 490
HREAL_MUL_ASSOC =
|- !X Y Z. X hreal_mul (Y hreal_mul Z) = (X hreal_mul Y) hreal_mul Z
Run time: 0.1s
Intermediate theorems generated: 490
HREAL_LDISTRIB =
|- !X Y Z.
X hreal_mul (Y hreal_add Z) =
(X hreal_mul Y) hreal_add (X hreal_mul Z)
Run time: 0.1s
Intermediate theorems generated: 935
HREAL_MUL_LID = |- !X. hreal_1 hreal_mul X = X
Run time: 0.0s
Intermediate theorems generated: 278
HREAL_MUL_LINV = |- !X. (hreal_inv X) hreal_mul X = hreal_1
Run time: 0.1s
Intermediate theorems generated: 485
HREAL_NOZERO = |- !X Y. ~(X hreal_add Y = X)
Run time: 0.0s
Intermediate theorems generated: 155
hreal_sub =
|- !Y X. Y hreal_sub X = hreal(\w. ?x. ~cut X x /\ cut Y(x hrat_add w))
Run time: 0.0s
Intermediate theorems generated: 2
HREAL_LT_LEMMA = |- !X Y. X hreal_lt Y ==> (?x. ~cut X x /\ cut Y x)
Run time: 0.1s
Intermediate theorems generated: 210
HREAL_SUB_ISACUT =
|- !X Y.
X hreal_lt Y ==> isacut(\w. ?x. ~cut X x /\ cut Y(x hrat_add w))
Run time: 0.0s
Intermediate theorems generated: 400
HREAL_SUB_ADD =
|- !X Y. X hreal_lt Y ==> ((Y hreal_sub X) hreal_add X = Y)
Run time: 0.1s
Intermediate theorems generated: 837
HREAL_LT_TOTAL = |- !X Y. (X = Y) \/ X hreal_lt Y \/ Y hreal_lt X
Run time: 0.1s
Intermediate theorems generated: 492
HREAL_LT = |- !X Y. X hreal_lt Y = (?D. Y = X hreal_add D)
Run time: 0.0s
Intermediate theorems generated: 196
HREAL_ADD_TOTAL =
|- !X Y. (X = Y) \/ (?D. Y = X hreal_add D) \/ (?D. X = Y hreal_add D)
Run time: 0.1s
Intermediate theorems generated: 19
HREAL_SUP_ISACUT =
|- !P.
(?X. P X) /\ (?Y. !X. P X ==> X hreal_lt Y) ==>
isacut(\w. ?X. P X /\ cut X w)
Run time: 0.0s
Intermediate theorems generated: 349
HREAL_SUP =
|- !P.
(?X. P X) /\ (?Y. !X. P X ==> X hreal_lt Y) ==>
(!Y. (?X. P X /\ Y hreal_lt X) = Y hreal_lt (hreal_sup P))
Run time: 0.1s
Intermediate theorems generated: 553
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File hreal.ml loaded
() : void
Run time: 1.9s
Intermediate theorems generated: 10456
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `realax.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory HREAL loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.1s
() : void
Run time: 0.0s
Intermediate theorems generated: 12
() : void
Run time: 0.0s
define_equivalence_type =
-
: (string ->
thm ->
(term # string # bool) list ->
thm list ->
thm list ->
thm list)
Run time: 0.0s
File equiv loaded
() : void
Run time: 0.0s
Theorem HREAL_LDISTRIB autoloading from theory `HREAL` ...
HREAL_LDISTRIB =
|- !X Y Z.
X hreal_mul (Y hreal_add Z) =
(X hreal_mul Y) hreal_add (X hreal_mul Z)
Run time: 0.0s
Theorem HREAL_MUL_SYM autoloading from theory `HREAL` ...
HREAL_MUL_SYM = |- !X Y. X hreal_mul Y = Y hreal_mul X
Run time: 0.0s
HREAL_RDISTRIB =
|- !x y z.
(x hreal_add y) hreal_mul z =
(x hreal_mul z) hreal_add (y hreal_mul z)
Run time: 0.0s
Intermediate theorems generated: 22
Theorem HREAL_NOZERO autoloading from theory `HREAL` ...
HREAL_NOZERO = |- !X Y. ~(X hreal_add Y = X)
Run time: 0.0s
HREAL_EQ_ADDR = |- !x y. ~(x hreal_add y = x)
Run time: 0.0s
Intermediate theorems generated: 5
HREAL_EQ_ADDL = |- !x y. ~(x = x hreal_add y)
Run time: 0.0s
Intermediate theorems generated: 11
Theorem HREAL_ADD_ASSOC autoloading from theory `HREAL` ...
HREAL_ADD_ASSOC =
|- !X Y Z. X hreal_add (Y hreal_add Z) = (X hreal_add Y) hreal_add Z
Run time: 0.0s
Theorem HREAL_ADD_TOTAL autoloading from theory `HREAL` ...
HREAL_ADD_TOTAL =
|- !X Y. (X = Y) \/ (?D. Y = X hreal_add D) \/ (?D. X = Y hreal_add D)
Run time: 0.0s
HREAL_EQ_LADD = |- !x y z. (x hreal_add y = x hreal_add z) = (y = z)
Run time: 0.0s
Intermediate theorems generated: 94
Theorem HREAL_LT autoloading from theory `HREAL` ...
HREAL_LT = |- !X Y. X hreal_lt Y = (?D. Y = X hreal_add D)
Run time: 0.0s
HREAL_LT_REFL = |- !x. ~x hreal_lt x
Run time: 0.0s
Intermediate theorems generated: 33
HREAL_LT_ADDL = |- !x y. x hreal_lt (x hreal_add y)
Run time: 0.0s
Intermediate theorems generated: 13
HREAL_LT_NE = |- !x y. x hreal_lt y ==> ~(x = y)
Run time: 0.0s
Intermediate theorems generated: 23
HREAL_LT_ADDR = |- !x y. ~(x hreal_add y) hreal_lt x
Run time: 0.0s
Intermediate theorems generated: 56
HREAL_LT_GT = |- !x y. x hreal_lt y ==> ~y hreal_lt x
Run time: 0.0s
Intermediate theorems generated: 66
Theorem HREAL_ADD_SYM autoloading from theory `HREAL` ...
HREAL_ADD_SYM = |- !X Y. X hreal_add Y = Y hreal_add X
Run time: 0.0s
HREAL_LT_ADD2 =
|- !x1 x2 y1 y2.
x1 hreal_lt y1 /\ x2 hreal_lt y2 ==>
(x1 hreal_add x2) hreal_lt (y1 hreal_add y2)
Run time: 0.0s
Intermediate theorems generated: 79
HREAL_LT_LADD =
|- !x y z. (x hreal_add y) hreal_lt (x hreal_add z) = y hreal_lt z
Run time: 0.0s
Intermediate theorems generated: 77
CANCEL_CONV = - : ((thm # thm # thm list) -> conv)
Run time: 0.0s
CANCEL_TAC = - : tactic
Run time: 0.0s
Intermediate theorems generated: 106
treal_0 = |- treal_0 = hreal_1,hreal_1
Run time: 0.0s
Intermediate theorems generated: 2
treal_1 = |- treal_1 = hreal_1 hreal_add hreal_1,hreal_1
Run time: 0.0s
Intermediate theorems generated: 2
treal_neg = |- !x y. treal_neg(x,y) = y,x
Run time: 0.0s
Intermediate theorems generated: 2
treal_add =
|- !x1 y1 x2 y2.
(x1,y1) treal_add (x2,y2) = x1 hreal_add x2,y1 hreal_add y2
Run time: 0.0s
Intermediate theorems generated: 2
treal_mul =
|- !x1 y1 x2 y2.
(x1,y1) treal_mul (x2,y2) =
(x1 hreal_mul x2) hreal_add (y1 hreal_mul y2),
(x1 hreal_mul y2) hreal_add (y1 hreal_mul x2)
Run time: 0.0s
Intermediate theorems generated: 2
treal_lt =
|- !x1 y1 x2 y2.
(x1,y1) treal_lt (x2,y2) =
(x1 hreal_add y2) hreal_lt (x2 hreal_add y1)
Run time: 0.0s
Intermediate theorems generated: 2
treal_inv =
|- !x y.
treal_inv(x,y) =
((x = y) =>
treal_0 |
(y hreal_lt x =>
((hreal_inv(x hreal_sub y)) hreal_add hreal_1,hreal_1) |
(hreal_1,(hreal_inv(y hreal_sub x)) hreal_add hreal_1)))
Run time: 0.0s
Intermediate theorems generated: 2
treal_eq =
|- !x1 y1 x2 y2.
(x1,y1) treal_eq (x2,y2) = (x1 hreal_add y2 = x2 hreal_add y1)
Run time: 0.0s
Intermediate theorems generated: 2
TREAL_EQ_REFL = |- !x. x treal_eq x
Run time: 0.0s
Intermediate theorems generated: 22
TREAL_EQ_SYM = |- !x y. x treal_eq y = y treal_eq x
Run time: 0.0s
Intermediate theorems generated: 37
TREAL_EQ_TRANS =
|- !x y z. x treal_eq y /\ y treal_eq z ==> x treal_eq z
Run time: 0.1s
Intermediate theorems generated: 1147
TREAL_EQ_EQUIV = |- !p q. p treal_eq q = ($treal_eq p = $treal_eq q)
Run time: 0.0s
Intermediate theorems generated: 73
TREAL_EQ_AP = |- !p q. (p = q) ==> p treal_eq q
Run time: 0.0s
Intermediate theorems generated: 8
TREAL_10 = |- ~treal_1 treal_eq treal_0
Run time: 0.0s
Intermediate theorems generated: 32
TREAL_ADD_SYM = |- !x y. x treal_add y = y treal_add x
Run time: 0.0s
Intermediate theorems generated: 44
TREAL_MUL_SYM = |- !x y. x treal_mul y = y treal_mul x
Run time: 0.0s
Intermediate theorems generated: 75
TREAL_ADD_ASSOC =
|- !x y z. x treal_add (y treal_add z) = (x treal_add y) treal_add z
Run time: 0.0s
Intermediate theorems generated: 63
Theorem HREAL_MUL_ASSOC autoloading from theory `HREAL` ...
HREAL_MUL_ASSOC =
|- !X Y Z. X hreal_mul (Y hreal_mul Z) = (X hreal_mul Y) hreal_mul Z
Run time: 0.0s
TREAL_MUL_ASSOC =
|- !x y z. x treal_mul (y treal_mul z) = (x treal_mul y) treal_mul z
Run time: 0.0s
Intermediate theorems generated: 388
TREAL_LDISTRIB =
|- !x y z.
x treal_mul (y treal_add z) =
(x treal_mul y) treal_add (x treal_mul z)
Run time: 0.1s
Intermediate theorems generated: 345
TREAL_ADD_LID = |- !x. (treal_0 treal_add x) treal_eq x
Run time: 0.0s
Intermediate theorems generated: 158
Theorem HREAL_MUL_LID autoloading from theory `HREAL` ...
HREAL_MUL_LID = |- !X. hreal_1 hreal_mul X = X
Run time: 0.0s
TREAL_MUL_LID = |- !x. (treal_1 treal_mul x) treal_eq x
Run time: 0.0s
Intermediate theorems generated: 217
TREAL_ADD_LINV = |- !x. ((treal_neg x) treal_add x) treal_eq treal_0
Run time: 0.0s
Intermediate theorems generated: 169
Theorem HREAL_SUB_ADD autoloading from theory `HREAL` ...
HREAL_SUB_ADD =
|- !X Y. X hreal_lt Y ==> ((Y hreal_sub X) hreal_add X = Y)
Run time: 0.0s
Theorem HREAL_MUL_LINV autoloading from theory `HREAL` ...
HREAL_MUL_LINV = |- !X. (hreal_inv X) hreal_mul X = hreal_1
Run time: 0.0s
Theorem HREAL_LT_TOTAL autoloading from theory `HREAL` ...
HREAL_LT_TOTAL = |- !X Y. (X = Y) \/ X hreal_lt Y \/ Y hreal_lt X
Run time: 0.0s
TREAL_MUL_LINV =
|- !x.
~x treal_eq treal_0 ==> ((treal_inv x) treal_mul x) treal_eq treal_1
Run time: 0.2s
Intermediate theorems generated: 3953
TREAL_LT_TOTAL = |- !x y. x treal_eq y \/ x treal_lt y \/ y treal_lt x
Run time: 0.1s
Intermediate theorems generated: 48
TREAL_LT_REFL = |- !x. ~x treal_lt x
Run time: 0.0s
Intermediate theorems generated: 24
TREAL_LT_TRANS =
|- !x y z. x treal_lt y /\ y treal_lt z ==> x treal_lt z
Run time: 0.0s
Intermediate theorems generated: 1063
TREAL_LT_ADD =
|- !x y z. y treal_lt z ==> (x treal_add y) treal_lt (x treal_add z)
Run time: 0.1s
Intermediate theorems generated: 1045
TREAL_LT_MUL =
|- !x y.
treal_0 treal_lt x /\ treal_0 treal_lt y ==>
treal_0 treal_lt (x treal_mul y)
Run time: 0.1s
Intermediate theorems generated: 866
treal_of_hreal = |- !x. treal_of_hreal x = x hreal_add hreal_1,hreal_1
Run time: 0.0s
Intermediate theorems generated: 2
hreal_of_treal = |- !x y. hreal_of_treal(x,y) = (@d. x = y hreal_add d)
Run time: 0.0s
Intermediate theorems generated: 2
TREAL_BIJ =
|- (!h. hreal_of_treal(treal_of_hreal h) = h) /\
(!r.
treal_0 treal_lt r = (treal_of_hreal(hreal_of_treal r)) treal_eq r)
Run time: 0.0s
Intermediate theorems generated: 986
TREAL_ISO =
|- !h i. h hreal_lt i ==> (treal_of_hreal h) treal_lt (treal_of_hreal i)
Run time: 0.1s
Intermediate theorems generated: 450
TREAL_BIJ_WELLDEF =
|- !h i. h treal_eq i ==> (hreal_of_treal h = hreal_of_treal i)
Run time: 0.1s
Intermediate theorems generated: 1446
TREAL_NEG_WELLDEF =
|- !x1 x2. x1 treal_eq x2 ==> (treal_neg x1) treal_eq (treal_neg x2)
Run time: 0.0s
Intermediate theorems generated: 58
TREAL_ADD_WELLDEFR =
|- !x1 x2 y.
x1 treal_eq x2 ==> (x1 treal_add y) treal_eq (x2 treal_add y)
Run time: 0.1s
Intermediate theorems generated: 1044
TREAL_ADD_WELLDEF =
|- !x1 x2 y1 y2.
x1 treal_eq x2 /\ y1 treal_eq y2 ==>
(x1 treal_add y1) treal_eq (x2 treal_add y2)
Run time: 0.0s
Intermediate theorems generated: 65
TREAL_MUL_WELLDEFR =
|- !x1 x2 y.
x1 treal_eq x2 ==> (x1 treal_mul y) treal_eq (x2 treal_mul y)
Run time: 0.0s
Intermediate theorems generated: 183
TREAL_MUL_WELLDEF =
|- !x1 x2 y1 y2.
x1 treal_eq x2 /\ y1 treal_eq y2 ==>
(x1 treal_mul y1) treal_eq (x2 treal_mul y2)
Run time: 0.0s
Intermediate theorems generated: 65
TREAL_LT_WELLDEFR =
|- !x1 x2 y. x1 treal_eq x2 ==> (x1 treal_lt y = x2 treal_lt y)
Run time: 0.1s
Intermediate theorems generated: 519
TREAL_LT_WELLDEFL =
|- !x y1 y2. y1 treal_eq y2 ==> (x treal_lt y1 = x treal_lt y2)
Run time: 0.0s
Intermediate theorems generated: 612
TREAL_LT_WELLDEF =
|- !x1 x2 y1 y2.
x1 treal_eq x2 /\ y1 treal_eq y2 ==>
(x1 treal_lt y1 = x2 treal_lt y2)
Run time: 0.0s
Intermediate theorems generated: 60
TREAL_INV_WELLDEF =
|- !x1 x2. x1 treal_eq x2 ==> (treal_inv x1) treal_eq (treal_inv x2)
Run time: 0.2s
Intermediate theorems generated: 2545
REAL_10 = |- ~(r1 = r0)
REAL_ADD_SYM = |- !x y. x real_add y = y real_add x
REAL_MUL_SYM = |- !x y. x real_mul y = y real_mul x
REAL_ADD_ASSOC =
|- !x y z. x real_add (y real_add z) = (x real_add y) real_add z
REAL_MUL_ASSOC =
|- !x y z. x real_mul (y real_mul z) = (x real_mul y) real_mul z
REAL_LDISTRIB =
|- !x y z.
x real_mul (y real_add z) = (x real_mul y) real_add (x real_mul z)
REAL_ADD_LID = |- !x. r0 real_add x = x
REAL_MUL_LID = |- !x. r1 real_mul x = x
REAL_ADD_LINV = |- !x. (real_neg x) real_add x = r0
REAL_MUL_LINV = |- !x. ~(x = r0) ==> ((real_inv x) real_mul x = r1)
REAL_LT_TOTAL = |- !x y. (x = y) \/ x real_lt y \/ y real_lt x
REAL_LT_REFL = |- !x. ~x real_lt x
REAL_LT_TRANS = |- !x y z. x real_lt y /\ y real_lt z ==> x real_lt z
REAL_LT_IADD =
|- !x y z. y real_lt z ==> (x real_add y) real_lt (x real_add z)
REAL_LT_MUL =
|- !x y. r0 real_lt x /\ r0 real_lt y ==> r0 real_lt (x real_mul y)
REAL_BIJ =
|- (!h. hreal_of_real(real_of_hreal h) = h) /\
(!r. r0 real_lt r = (real_of_hreal(hreal_of_real r) = r))
REAL_ISO =
|- !h i. h hreal_lt i ==> (real_of_hreal h) real_lt (real_of_hreal i)
Run time: 0.9s
Intermediate theorems generated: 7766
REAL_ISO_EQ =
|- !h i. h hreal_lt i = (real_of_hreal h) real_lt (real_of_hreal i)
Run time: 0.0s
Intermediate theorems generated: 98
REAL_POS = |- !X. r0 real_lt (real_of_hreal X)
Run time: 0.0s
Intermediate theorems generated: 20
SUP_ALLPOS_LEMMA1 =
|- (!x. P x ==> r0 real_lt x) ==>
((?x. P x /\ y real_lt x) =
(?X. P(real_of_hreal X) /\ y real_lt (real_of_hreal X)))
Run time: 0.0s
Intermediate theorems generated: 68
SUP_ALLPOS_LEMMA2 = |- P(real_of_hreal X) = (\h. P(real_of_hreal h))X
Run time: 0.1s
Intermediate theorems generated: 5
SUP_ALLPOS_LEMMA3 =
|- (!x. P x ==> r0 real_lt x) /\
(?x. P x) /\
(?z. !x. P x ==> x real_lt z) ==>
(?X. (\h. P(real_of_hreal h))X) /\
(?Y. !X. (\h. P(real_of_hreal h))X ==> X hreal_lt Y)
Run time: 0.0s
Intermediate theorems generated: 135
SUP_ALLPOS_LEMMA4 =
|- !y. ~r0 real_lt y ==> (!x. y real_lt (real_of_hreal x))
Run time: 0.0s
Intermediate theorems generated: 75
Theorem HREAL_SUP autoloading from theory `HREAL` ...
HREAL_SUP =
|- !P.
(?X. P X) /\ (?Y. !X. P X ==> X hreal_lt Y) ==>
(!Y. (?X. P X /\ Y hreal_lt X) = Y hreal_lt (hreal_sup P))
Run time: 0.0s
REAL_SUP_ALLPOS =
|- !P.
(!x. P x ==> r0 real_lt x) /\
(?x. P x) /\
(?z. !x. P x ==> x real_lt z) ==>
(?s. !y. (?x. P x /\ y real_lt x) = y real_lt s)
Run time: 0.1s
Intermediate theorems generated: 199
[|- ~(r1 = r0);
|- !x y. x real_add y = y real_add x;
|- !x y. x real_mul y = y real_mul x;
|- !x y z. x real_add (y real_add z) = (x real_add y) real_add z;
|- !x y z. x real_mul (y real_mul z) = (x real_mul y) real_mul z;
|- !x y z.
x real_mul (y real_add z) = (x real_mul y) real_add (x real_mul z);
|- !x. r0 real_add x = x;
|- !x. r1 real_mul x = x;
|- !x. (real_neg x) real_add x = r0;
|- !x. ~(x = r0) ==> ((real_inv x) real_mul x = r1);
|- !x y. (x = y) \/ x real_lt y \/ y real_lt x;
|- !x. ~x real_lt x;
|- !x y z. x real_lt y /\ y real_lt z ==> x real_lt z;
|- !x y z. y real_lt z ==> (x real_add y) real_lt (x real_add z);
|- !x y. r0 real_lt x /\ r0 real_lt y ==> r0 real_lt (x real_mul y)]
: thm list
Run time: 0.2s
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File realax.ml loaded
() : void
Run time: 3.0s
Intermediate theorems generated: 26795
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `real.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory REALAX loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.0s
() : void
Run time: 0.0s
real_sub = |- !x y. x real_sub y = x real_add (real_neg y)
Run time: 0.0s
Intermediate theorems generated: 2
real_le = |- !x y. x real_le y = ~y real_lt x
Run time: 0.0s
Intermediate theorems generated: 2
real_gt = |- !x y. x real_gt y = y real_lt x
Run time: 0.0s
Intermediate theorems generated: 2
real_ge = |- !x y. x real_ge y = y real_le x
Run time: 0.0s
Intermediate theorems generated: 2
real_div = |- !x y. x / y = x real_mul (real_inv y)
Run time: 0.0s
Intermediate theorems generated: 2
real_of_num =
|- (real_of_num 0 = r0) /\
(!n. real_of_num(SUC n) = (real_of_num n) real_add r1)
Run time: 0.0s
Intermediate theorems generated: 136
REAL_0 = |- r0 = real_of_num 0
Run time: 0.1s
Intermediate theorems generated: 11
REAL_1 = |- r1 = real_of_num 1
Run time: 0.0s
Intermediate theorems generated: 23
() : void
Run time: 0.0s
[] : (string # string) list
Run time: 0.0s
gonk = - : (string list -> thm)
Run time: 0.0s
reeducate = - : (string -> void)
Run time: 0.0s
() : void
Run time: 0.0s
REAL_10 = |- ~(& 1 = & 0)
Run time: 0.0s
Intermediate theorems generated: 4
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Intermediate theorems generated: 2
REAL_MUL_SYM = |- !x y. x * y = y * x
Run time: 0.0s
Intermediate theorems generated: 2
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.0s
Intermediate theorems generated: 2
REAL_MUL_ASSOC = |- !x y z. x * (y * z) = (x * y) * z
Run time: 0.0s
Intermediate theorems generated: 2
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Intermediate theorems generated: 7
REAL_MUL_LID = |- !x. (& 1) * x = x
Run time: 0.0s
Intermediate theorems generated: 7
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Intermediate theorems generated: 4
REAL_MUL_LINV = |- !x. ~(x = & 0) ==> ((inv x) * x = & 1)
Run time: 0.0s
Intermediate theorems generated: 8
REAL_LDISTRIB = |- !x y z. x * (y + z) = (x * y) + (x * z)
Run time: 0.0s
Intermediate theorems generated: 2
REAL_LT_TOTAL = |- !x y. (x = y) \/ x < y \/ y < x
Run time: 0.0s
Intermediate theorems generated: 2
REAL_LT_REFL = |- !x. ~x < x
Run time: 0.0s
Intermediate theorems generated: 2
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.0s
Intermediate theorems generated: 2
REAL_LT_IADD = |- !x y z. y < z ==> (x + y) < (x + z)
Run time: 0.0s
Intermediate theorems generated: 2
REAL_LT_MUL = |- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x * y)
Run time: 0.0s
Intermediate theorems generated: 15
REAL_SUP_ALLPOS =
|- !P.
(!x. P x ==> (& 0) < x) /\ (?x. P x) /\ (?z. !x. P x ==> x < z) ==>
(?s. !y. (?x. P x /\ y < x) = y < s)
Run time: 0.0s
Intermediate theorems generated: 12
REAL_ADD_RID = |- !x. x + (& 0) = x
Run time: 0.0s
Intermediate theorems generated: 14
REAL_ADD_RINV = |- !x. x + (-- x) = & 0
Run time: 0.0s
Intermediate theorems generated: 14
REAL_MUL_RID = |- !x. x * (& 1) = x
Run time: 0.0s
Intermediate theorems generated: 14
REAL_MUL_RINV = |- !x. ~(x = & 0) ==> (x * (inv x) = & 1)
Run time: 0.0s
Intermediate theorems generated: 15
REAL_RDISTRIB = |- !x y z. (x + y) * z = (x * z) + (y * z)
Run time: 0.0s
Intermediate theorems generated: 22
REAL_EQ_LADD = |- !x y z. (x + y = x + z) = (y = z)
Run time: 0.0s
Intermediate theorems generated: 50
REAL_EQ_RADD = |- !x y z. (x + z = y + z) = (x = y)
Run time: 0.0s
Intermediate theorems generated: 21
REAL_ADD_LID_UNIQ = |- !x y. (x + y = y) = (x = & 0)
Run time: 0.0s
Intermediate theorems generated: 21
REAL_ADD_RID_UNIQ = |- !x y. (x + y = x) = (y = & 0)
Run time: 0.0s
Intermediate theorems generated: 18
REAL_LNEG_UNIQ = |- !x y. (x + y = & 0) = (x = -- y)
Run time: 0.0s
Intermediate theorems generated: 10
REAL_RNEG_UNIQ = |- !x y. (x + y = & 0) = (y = -- x)
Run time: 0.0s
Intermediate theorems generated: 18
REAL_NEG_ADD = |- !x y. --(x + y) = (-- x) + (-- y)
Run time: 0.0s
Intermediate theorems generated: 101
REAL_MUL_LZERO = |- !x. (& 0) * x = & 0
Run time: 0.1s
Intermediate theorems generated: 40
REAL_MUL_RZERO = |- !x. x * (& 0) = & 0
Run time: 0.0s
Intermediate theorems generated: 14
REAL_NEG_LMUL = |- !x y. --(x * y) = (-- x) * y
Run time: 0.0s
Intermediate theorems generated: 62
REAL_NEG_RMUL = |- !x y. --(x * y) = x * (-- y)
Run time: 0.0s
Intermediate theorems generated: 18
REAL_NEGNEG = |- !x. --(-- x) = x
Run time: 0.0s
Intermediate theorems generated: 33
REAL_NEG_MUL2 = |- !x y. (-- x) * (-- y) = x * y
Run time: 0.0s
Intermediate theorems generated: 56
REAL_ENTIRE = |- !x y. (x * y = & 0) = (x = & 0) \/ (y = & 0)
Run time: 0.0s
Intermediate theorems generated: 116
REAL_LT_LADD = |- !x y z. (x + y) < (x + z) = y < z
Run time: 0.0s
Intermediate theorems generated: 54
REAL_LT_RADD = |- !x y z. (x + z) < (y + z) = x < y
Run time: 0.0s
Intermediate theorems generated: 21
REAL_NOT_LT = |- !x y. ~x < y = y <= x
Run time: 0.0s
Intermediate theorems generated: 15
REAL_LT_ANTISYM = |- !x y. ~(x < y /\ y < x)
Run time: 0.0s
Intermediate theorems generated: 24
REAL_LT_GT = |- !x y. x < y ==> ~y < x
Run time: 0.0s
Intermediate theorems generated: 26
REAL_NOT_LE = |- !x y. ~x <= y = y < x
Run time: 0.0s
Intermediate theorems generated: 19
REAL_LE_TOTAL = |- !x y. x <= y \/ y <= x
Run time: 0.0s
Intermediate theorems generated: 55
REAL_LET_TOTAL = |- !x y. x <= y \/ y < x
Run time: 0.0s
Intermediate theorems generated: 28
REAL_LTE_TOTAL = |- !x y. x < y \/ y <= x
Run time: 0.1s
Intermediate theorems generated: 27
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
Intermediate theorems generated: 21
REAL_LE_LT = |- !x y. x <= y = x < y \/ (x = y)
Run time: 0.0s
Intermediate theorems generated: 93
REAL_LT_LE = |- !x y. x < y = x <= y /\ ~(x = y)
Run time: 0.0s
Intermediate theorems generated: 125
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
Intermediate theorems generated: 22
REAL_LTE_TRANS = |- !x y z. x < y /\ y <= z ==> x < z
Run time: 0.0s
Intermediate theorems generated: 47
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.1s
Intermediate theorems generated: 46
REAL_LE_TRANS = |- !x y z. x <= y /\ y <= z ==> x <= z
Run time: 0.0s
Intermediate theorems generated: 51
REAL_LE_ANTISYM = |- !x y. x <= y /\ y <= x = (x = y)
Run time: 0.0s
Intermediate theorems generated: 94
REAL_LET_ANTISYM = |- !x y. ~(x < y /\ y <= x)
Run time: 0.0s
Intermediate theorems generated: 32
REAL_LTE_ANTSYM = |- !x y. ~(x <= y /\ y < x)
Run time: 0.0s
Intermediate theorems generated: 15
REAL_NEG_LT0 = |- !x. (-- x) < (& 0) = (& 0) < x
Run time: 0.0s
Intermediate theorems generated: 24
REAL_NEG_GT0 = |- !x. (& 0) < (-- x) = x < (& 0)
Run time: 0.0s
Intermediate theorems generated: 25
REAL_NEG_LE0 = |- !x. (-- x) <= (& 0) = (& 0) <= x
Run time: 0.0s
Intermediate theorems generated: 25
REAL_NEG_GE0 = |- !x. (& 0) <= (-- x) = x <= (& 0)
Run time: 0.0s
Intermediate theorems generated: 25
REAL_LT_NEGTOTAL = |- !x. (x = & 0) \/ (& 0) < x \/ (& 0) < (-- x)
Run time: 0.0s
Intermediate theorems generated: 79
REAL_LE_NEGTOTAL = |- !x. (& 0) <= x \/ (& 0) <= (-- x)
Run time: 0.0s
Intermediate theorems generated: 73
REAL_LE_MUL = |- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x * y)
Run time: 0.1s
Intermediate theorems generated: 276
REAL_LE_SQUARE = |- !x. (& 0) <= (x * x)
Run time: 0.0s
Intermediate theorems generated: 68
REAL_LE_01 = |- (& 0) <= (& 1)
Run time: 0.0s
Intermediate theorems generated: 6
REAL_LT_01 = |- (& 0) < (& 1)
Run time: 0.0s
Intermediate theorems generated: 29
REAL_LE_LADD = |- !x y z. (x + y) <= (x + z) = y <= z
Run time: 0.0s
Intermediate theorems generated: 20
REAL_LE_RADD = |- !x y z. (x + z) <= (y + z) = x <= y
Run time: 0.0s
Intermediate theorems generated: 20
REAL_LT_ADD2 = |- !w x y z. w < x /\ y < z ==> (w + y) < (x + z)
Run time: 0.0s
Intermediate theorems generated: 55
REAL_LE_ADD2 = |- !w x y z. w <= x /\ y <= z ==> (w + y) <= (x + z)
Run time: 0.0s
Intermediate theorems generated: 55
REAL_LE_ADD = |- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x + y)
Run time: 0.0s
Intermediate theorems generated: 22
REAL_LT_ADD = |- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x + y)
Run time: 0.0s
Intermediate theorems generated: 22
REAL_LT_ADDNEG = |- !x y z. y < (x + (-- z)) = (y + z) < x
Run time: 0.0s
Intermediate theorems generated: 48
REAL_LT_ADDNEG2 = |- !x y z. (x + (-- y)) < z = x < (z + y)
Run time: 0.0s
Intermediate theorems generated: 49
REAL_LT_ADD1 = |- !x y. x <= y ==> x < (y + (& 1))
Run time: 0.0s
Intermediate theorems generated: 75
REAL_SUB_ADD = |- !x y. (x - y) + y = x
Run time: 0.0s
Intermediate theorems generated: 50
REAL_SUB_ADD2 = |- !x y. y + (x - y) = x
Run time: 0.0s
Intermediate theorems generated: 16
REAL_SUB_REFL = |- !x. x - x = & 0
Run time: 0.0s
Intermediate theorems generated: 20
REAL_SUB_0 = |- !x y. (x - y = & 0) = (x = y)
Run time: 0.1s
Intermediate theorems generated: 33
REAL_LE_DOUBLE = |- !x. (& 0) <= (x + x) = (& 0) <= x
Run time: 0.0s
Intermediate theorems generated: 72
REAL_LE_NEGL = |- !x. (-- x) <= x = (& 0) <= x
Run time: 0.0s
Intermediate theorems generated: 25
REAL_LE_NEGR = |- !x. x <= (-- x) = x <= (& 0)
Run time: 0.0s
Intermediate theorems generated: 42
REAL_NEG_EQ0 = |- !x. (-- x = & 0) = (x = & 0)
Run time: 0.0s
Intermediate theorems generated: 45
REAL_NEG_0 = |- --(& 0) = & 0
Run time: 0.1s
Intermediate theorems generated: 9
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
Intermediate theorems generated: 32
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
Intermediate theorems generated: 28
REAL_SUB_LE = |- !x y. (& 0) <= (x - y) = y <= x
Run time: 0.0s
Intermediate theorems generated: 28
REAL_ADD_SUB = |- !x y. (x + y) - x = y
Run time: 0.0s
Intermediate theorems generated: 61
REAL_EQ_LMUL = |- !x y z. (x * y = x * z) = (x = & 0) \/ (y = z)
Run time: 0.1s
Intermediate theorems generated: 122
REAL_EQ_RMUL = |- !x y z. (x * z = y * z) = (z = & 0) \/ (x = y)
Run time: 0.0s
Intermediate theorems generated: 21
REAL_SUB_LDISTRIB = |- !x y z. x * (y - z) = (x * y) - (x * z)
Run time: 0.0s
Intermediate theorems generated: 39
REAL_SUB_RDISTRIB = |- !x y z. (x - y) * z = (x * z) - (y * z)
Run time: 0.0s
Intermediate theorems generated: 22
REAL_NEG_EQ = |- !x y. (-- x = y) = (x = -- y)
Run time: 0.0s
Intermediate theorems generated: 30
REAL_NEG_MINUS1 = |- !x. -- x = (--(& 1)) * x
Run time: 0.1s
Intermediate theorems generated: 30
REAL_INV_NZ = |- !x. ~(x = & 0) ==> ~(inv x = & 0)
Run time: 0.0s
Intermediate theorems generated: 35
REAL_INVINV = |- !x. ~(x = & 0) ==> (inv(inv x) = x)
Run time: 0.0s
Intermediate theorems generated: 114
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
Intermediate theorems generated: 43
REAL_INV_POS = |- !x. (& 0) < x ==> (& 0) < (inv x)
Run time: 0.1s
Intermediate theorems generated: 133
REAL_LT_LMUL_0 = |- !x y. (& 0) < x ==> ((& 0) < (x * y) = (& 0) < y)
Run time: 0.0s
Intermediate theorems generated: 87
REAL_LT_RMUL_0 = |- !x y. (& 0) < y ==> ((& 0) < (x * y) = (& 0) < x)
Run time: 0.0s
Intermediate theorems generated: 18
REAL_LT_LMUL = |- !x y z. (& 0) < x ==> ((x * y) < (x * z) = y < z)
Run time: 0.0s
Intermediate theorems generated: 57
REAL_LT_RMUL = |- !x y z. (& 0) < z ==> ((x * z) < (y * z) = x < y)
Run time: 0.0s
Intermediate theorems generated: 22
REAL_LT_RMUL_IMP = |- !x y z. x < y /\ (& 0) < z ==> (x * z) < (y * z)
Run time: 0.0s
Intermediate theorems generated: 29
REAL_LT_LMUL_IMP = |- !x y z. y < z /\ (& 0) < x ==> (x * y) < (x * z)
Run time: 0.0s
Intermediate theorems generated: 29
REAL_LINV_UNIQ = |- !x y. (x * y = & 1) ==> (x = inv y)
Run time: 0.0s
Intermediate theorems generated: 111
REAL_RINV_UNIQ = |- !x y. (x * y = & 1) ==> (y = inv x)
Run time: 0.0s
Intermediate theorems generated: 18
REAL_NEG_INV = |- !x. ~(x = & 0) ==> (--(inv x) = inv(-- x))
Run time: 0.1s
Intermediate theorems generated: 71
REAL_INV_1OVER = |- !x. inv x = (& 1) / x
Run time: 0.0s
Intermediate theorems generated: 19
REAL_LE_ADDR = |- !x y. x <= (x + y) = (& 0) <= y
Run time: 0.0s
Intermediate theorems generated: 20
REAL_LE_ADDL = |- !x y. y <= (x + y) = (& 0) <= x
Run time: 0.0s
Intermediate theorems generated: 17
REAL_LT_ADDR = |- !x y. x < (x + y) = (& 0) < y
Run time: 0.0s
Intermediate theorems generated: 20
REAL_LT_ADDL = |- !x y. y < (x + y) = (& 0) < x
Run time: 0.1s
Intermediate theorems generated: 17
REAL = |- !n. &(SUC n) = (& n) + (& 1)
Run time: 0.0s
Intermediate theorems generated: 19
REAL_POS = |- !n. (& 0) <= (& n)
Run time: 0.0s
Intermediate theorems generated: 70
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 num_lt (SUC n)
Run time: 0.0s
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m num_lt n = n num_le m
Run time: 0.1s
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) num_le (SUC m) = n num_le m
Run time: 0.0s
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 num_le n
Run time: 0.0s
REAL_LE = |- !m n. (& m) <= (& n) = m num_le n
Run time: 0.0s
Intermediate theorems generated: 321
REAL_LT = |- !m n. (& m) < (& n) = m num_lt n
Run time: 0.0s
Intermediate theorems generated: 48
Theorem LESS_EQUAL_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQUAL_ANTISYM = |- !n m. n num_le m /\ m num_le n ==> (n = m)
Run time: 0.0s
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m num_le m
Run time: 0.0s
REAL_INJ = |- !m n. (& m = & n) = (m = n)
Run time: 0.1s
Intermediate theorems generated: 57
Definition ADD autoloading from theory `arithmetic` ...
ADD =
|- (!n. 0 num_add n = n) /\ (!m n. (SUC m) num_add n = SUC(m num_add n))
Run time: 0.0s
Intermediate theorems generated: 1
REAL_ADD = |- !m n. (& m) + (& n) = &(m num_add n)
Run time: 0.0s
Intermediate theorems generated: 131
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 num_mul m = 0) /\
(m num_mul 0 = 0) /\
(1 num_mul m = m) /\
(m num_mul 1 = m) /\
((SUC m) num_mul n = (m num_mul n) num_add n) /\
(m num_mul (SUC n) = m num_add (m num_mul n))
Run time: 0.0s
REAL_MUL = |- !m n. (& m) * (& n) = &(m num_mul n)
Run time: 0.0s
Intermediate theorems generated: 148
REAL_INV1 = |- inv(& 1) = & 1
Run time: 0.1s
Intermediate theorems generated: 26
REAL_OVER1 = |- !x. x / (& 1) = x
Run time: 0.0s
Intermediate theorems generated: 22
REAL_DIV_REFL = |- !x. ~(x = & 0) ==> (x / x = & 1)
Run time: 0.0s
Intermediate theorems generated: 19
REAL_DIV_LZERO = |- !x. (& 0) / x = & 0
Run time: 0.0s
Intermediate theorems generated: 20
REAL_LT_NZ = |- !n. ~(& n = & 0) = (& 0) < (& n)
Run time: 0.1s
Intermediate theorems generated: 90
REAL_NZ_IMP_LT = |- !n. ~(n = 0) ==> (& 0) < (& n)
Run time: 0.0s
Intermediate theorems generated: 28
REAL_LT_RDIV_0 = |- !y z. (& 0) < z ==> ((& 0) < (y / z) = (& 0) < y)
Run time: 0.0s
Intermediate theorems generated: 40
REAL_LT_RDIV = |- !x y z. (& 0) < z ==> ((x / z) < (y / z) = x < y)
Run time: 0.0s
Intermediate theorems generated: 44
REAL_LT_FRACTION_0 =
|- !n d. ~(n = 0) ==> ((& 0) < (d / (& n)) = (& 0) < d)
Run time: 0.0s
Intermediate theorems generated: 44
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m num_lt n /\ n num_lt p ==> m num_lt p
Run time: 0.1s
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n num_lt 0
Run time: 0.0s
REAL_LT_MULTIPLE = |- !n d. 1 num_lt n ==> (d < ((& n) * d) = (& 0) < d)
Run time: 0.0s
Intermediate theorems generated: 268
REAL_LT_FRACTION = |- !n d. 1 num_lt n ==> ((d / (& n)) < d = (& 0) < d)
Run time: 0.0s
Intermediate theorems generated: 184
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
Run time: 0.0s
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.1s
Intermediate theorems generated: 27
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n num_lt (SUC n)
Run time: 0.0s
REAL_LT_HALF2 = |- !d. (d / (& 2)) < d = (& 0) < d
Run time: 0.0s
Intermediate theorems generated: 22
REAL_DOUBLE = |- !x. x + x = (& 2) * x
Run time: 0.0s
Intermediate theorems generated: 37
REAL_DIV_LMUL = |- !x y. ~(y = & 0) ==> (y * (x / y) = x)
Run time: 0.1s
Intermediate theorems generated: 70
REAL_DIV_RMUL = |- !x y. ~(y = & 0) ==> ((x / y) * y = x)
Run time: 0.0s
Intermediate theorems generated: 17
REAL_HALF_DOUBLE = |- !x. (x / (& 2)) + (x / (& 2)) = x
Run time: 0.0s
Intermediate theorems generated: 51
REAL_DOWN = |- !x. (& 0) < x ==> (?y. (& 0) < y /\ y < x)
Run time: 0.0s
Intermediate theorems generated: 24
REAL_DOWN2 =
|- !x y. (& 0) < x /\ (& 0) < y ==> (?z. (& 0) < z /\ z < x /\ z < y)
Run time: 0.1s
Intermediate theorems generated: 145
REAL_SUB_SUB = |- !x y. (x - y) - x = -- y
Run time: 0.0s
Intermediate theorems generated: 91
REAL_LT_ADD_SUB = |- !x y z. (x + y) < z = x < (z - y)
Run time: 0.0s
Intermediate theorems generated: 23
REAL_LT_SUB_RADD = |- !x y z. (x - y) < z = x < (z + y)
Run time: 0.0s
Intermediate theorems generated: 25
REAL_LT_SUB_LADD = |- !x y z. x < (y - z) = (x + z) < y
Run time: 0.1s
Intermediate theorems generated: 57
REAL_LE_SUB_LADD = |- !x y z. x <= (y - z) = (x + z) <= y
Run time: 0.0s
Intermediate theorems generated: 38
REAL_LE_SUB_RADD = |- !x y z. (x - y) <= z = x <= (z + y)
Run time: 0.0s
Intermediate theorems generated: 38
REAL_LT_NEG = |- !x y. (-- x) < (-- y) = y < x
Run time: 0.0s
Intermediate theorems generated: 79
REAL_LE_NEG = |- !x y. (-- x) <= (-- y) = y <= x
Run time: 0.0s
Intermediate theorems generated: 37
REAL_ADD2_SUB2 = |- !a b c d. (a + b) - (c + d) = (a - c) + (b - d)
Run time: 0.0s
Intermediate theorems generated: 73
REAL_SUB_LZERO = |- !x. (& 0) - x = -- x
Run time: 0.0s
Intermediate theorems generated: 20
REAL_SUB_RZERO = |- !x. x - (& 0) = x
Run time: 0.1s
Intermediate theorems generated: 22
REAL_LET_ADD2 = |- !w x y z. w <= x /\ y < z ==> (w + y) < (x + z)
Run time: 0.0s
Intermediate theorems generated: 58
REAL_LTE_ADD2 = |- !w x y z. w < x /\ y <= z ==> (w + y) < (x + z)
Run time: 0.0s
Intermediate theorems generated: 33
REAL_LET_ADD = |- !x y. (& 0) <= x /\ (& 0) < y ==> (& 0) < (x + y)
Run time: 0.0s
Intermediate theorems generated: 33
REAL_LTE_ADD = |- !x y. (& 0) < x /\ (& 0) <= y ==> (& 0) < (x + y)
Run time: 0.1s
Intermediate theorems generated: 33
REAL_LT_MUL2 =
|- !x1 x2 y1 y2.
(& 0) <= x1 /\ (& 0) <= y1 /\ x1 < x2 /\ y1 < y2 ==>
(x1 * y1) < (x2 * y2)
Run time: 0.0s
Intermediate theorems generated: 344
REAL_LT_INV = |- !x y. (& 0) < x /\ x < y ==> (inv y) < (inv x)
Run time: 0.0s
Intermediate theorems generated: 282
REAL_SUB_LNEG = |- !x y. (-- x) - y = --(x + y)
Run time: 0.0s
Intermediate theorems generated: 23
REAL_SUB_RNEG = |- !x y. x - (-- y) = x + y
Run time: 0.1s
Intermediate theorems generated: 22
REAL_SUB_NEG2 = |- !x y. (-- x) - (-- y) = y - x
Run time: 0.0s
Intermediate theorems generated: 40
REAL_SUB_TRIANGLE = |- !a b c. (a - b) + (b - c) = a - c
Run time: 0.0s
Intermediate theorems generated: 93
REAL_EQ_SUB_LADD = |- !x y z. (x = y - z) = (x + z = y)
Run time: 0.1s
Intermediate theorems generated: 24
REAL_EQ_SUB_RADD = |- !x y z. (x - y = z) = (x = z + y)
Run time: 0.0s
Intermediate theorems generated: 17
REAL_INV_MUL =
|- !x y. ~(x = & 0) /\ ~(y = & 0) ==> (inv(x * y) = (inv x) * (inv y))
Run time: 0.0s
Intermediate theorems generated: 142
REAL_LE_LMUL = |- !x y z. (& 0) < x ==> ((x * y) <= (x * z) = y <= z)
Run time: 0.1s
Intermediate theorems generated: 43
REAL_LE_RMUL = |- !x y z. (& 0) < z ==> ((x * z) <= (y * z) = x <= y)
Run time: 0.0s
Intermediate theorems generated: 22
REAL_SUB_INV2 =
|- !x y.
~(x = & 0) /\ ~(y = & 0) ==> ((inv x) - (inv y) = (y - x) / (x * y))
Run time: 0.0s
Intermediate theorems generated: 153
REAL_SUB_SUB2 = |- !x y. x - (x - y) = y
Run time: 0.1s
Intermediate theorems generated: 40
REAL_ADD_SUB2 = |- !x y. x - (x + y) = -- y
Run time: 0.0s
Intermediate theorems generated: 36
REAL_MEAN = |- !x y. x < y ==> (?z. x < z /\ z < y)
Run time: 0.0s
Intermediate theorems generated: 91
REAL_EQ_LMUL2 = |- !x y z. ~(x = & 0) ==> ((y = z) = (x * y = x * z))
Run time: 0.1s
Intermediate theorems generated: 35
REAL_LE_MUL2 =
|- !x1 x2 y1 y2.
(& 0) <= x1 /\ (& 0) <= y1 /\ x1 <= x2 /\ y1 <= y2 ==>
(x1 * y1) <= (x2 * y2)
Run time: 0.0s
Intermediate theorems generated: 345
REAL_LE_LDIV = |- !x y z. (& 0) < x /\ y <= (z * x) ==> (y / x) <= z
Run time: 0.1s
Intermediate theorems generated: 102
REAL_LE_RDIV = |- !x y z. (& 0) < x /\ (y * x) <= z ==> y <= (z / x)
Run time: 0.0s
Intermediate theorems generated: 101
REAL_LT_1 = |- !x y. (& 0) <= x /\ x < y ==> (x / y) < (& 1)
Run time: 0.0s
Intermediate theorems generated: 120
REAL_LE_LMUL_IMP =
|- !x y z. (& 0) <= x /\ y <= z ==> (x * y) <= (x * z)
Run time: 0.1s
Intermediate theorems generated: 65
REAL_LE_RMUL_IMP =
|- !x y z. (& 0) <= x /\ y <= z ==> (y * x) <= (z * x)
Run time: 0.0s
Intermediate theorems generated: 26
REAL_EQ_IMP_LE = |- !x y. (x = y) ==> x <= y
Run time: 0.0s
Intermediate theorems generated: 8
REAL_INV_LT1 = |- !x. (& 0) < x /\ x < (& 1) ==> (& 1) < (inv x)
Run time: 0.0s
Intermediate theorems generated: 290
REAL_POS_NZ = |- !x. (& 0) < x ==> ~(x = & 0)
Run time: 0.0s
Intermediate theorems generated: 17
REAL_EQ_RMUL_IMP = |- !x y z. ~(z = & 0) /\ (x * z = y * z) ==> (x = y)
Run time: 0.1s
Intermediate theorems generated: 36
REAL_EQ_LMUL_IMP = |- !x y z. ~(x = & 0) /\ (x * y = x * z) ==> (y = z)
Run time: 0.0s
Intermediate theorems generated: 28
Theorem FACT_LESS autoloading from theory `arithmetic` ...
FACT_LESS = |- !n. 0 num_lt (FACT n)
Run time: 0.0s
REAL_FACT_NZ = |- !n. ~(&(FACT n) = & 0)
Run time: 0.0s
Intermediate theorems generated: 25
REAL_DIFFSQ = |- !x y. (x + y) * (x - y) = (x * x) - (y * y)
Run time: 0.1s
Intermediate theorems generated: 165
REAL_POSSQ = |- !x. (& 0) < (x * x) = ~(x = & 0)
Run time: 0.0s
Intermediate theorems generated: 68
REAL_SUMSQ = |- !x y. ((x * x) + (y * y) = & 0) = (x = & 0) /\ (y = & 0)
Run time: 0.1s
Intermediate theorems generated: 163
REAL_EQ_NEG = |- !x y. (-- x = -- y) = (x = y)
Run time: 0.0s
Intermediate theorems generated: 36
REAL_DIV_MUL2 =
|- !x z. ~(x = & 0) /\ ~(z = & 0) ==> (!y. y / z = (x * y) / (x * z))
Run time: 0.0s
Intermediate theorems generated: 169
REAL_MIDDLE1 = |- !a b. a <= b ==> a <= ((a + b) / (& 2))
Run time: 0.1s
Intermediate theorems generated: 89
REAL_MIDDLE2 = |- !a b. a <= b ==> ((a + b) / (& 2)) <= b
Run time: 0.0s
Intermediate theorems generated: 87
abs = |- !x. abs x = ((& 0) <= x => x | -- x)
Run time: 0.1s
Intermediate theorems generated: 2
ABS_ZERO = |- !x. (abs x = & 0) = (x = & 0)
Run time: 0.0s
Intermediate theorems generated: 52
ABS_0 = |- abs(& 0) = & 0
Run time: 0.0s
Intermediate theorems generated: 9
ABS_1 = |- abs(& 1) = & 1
Run time: 0.1s
Intermediate theorems generated: 31
ABS_NEG = |- !x. abs(-- x) = abs x
Run time: 0.0s
Intermediate theorems generated: 178
ABS_TRIANGLE = |- !x y. (abs(x + y)) <= ((abs x) + (abs y))
Run time: 0.1s
Intermediate theorems generated: 604
ABS_POS = |- !x. (& 0) <= (abs x)
Run time: 0.0s
Intermediate theorems generated: 67
ABS_MUL = |- !x y. abs(x * y) = (abs x) * (abs y)
Run time: 0.1s
Intermediate theorems generated: 385
ABS_LT_MUL2 =
|- !w x y z. (abs w) < y /\ (abs x) < z ==> (abs(w * x)) < (y * z)
Run time: 0.1s
Intermediate theorems generated: 56
ABS_SUB = |- !x y. abs(x - y) = abs(y - x)
Run time: 0.0s
Intermediate theorems generated: 31
ABS_NZ = |- !x. ~(x = & 0) = (& 0) < (abs x)
Run time: 0.0s
Intermediate theorems generated: 139
ABS_INV = |- !x. ~(x = & 0) ==> (abs(inv x) = inv(abs x))
Run time: 0.1s
Intermediate theorems generated: 105
ABS_ABS = |- !x. abs(abs x) = abs x
Run time: 0.0s
Intermediate theorems generated: 27
ABS_LE = |- !x. x <= (abs x)
Run time: 0.1s
Intermediate theorems generated: 75
ABS_REFL = |- !x. (abs x = x) = (& 0) <= x
Run time: 0.0s
Intermediate theorems generated: 156
ABS_N = |- !n. abs(& n) = & n
Run time: 0.0s
Intermediate theorems generated: 21
ABS_BETWEEN =
|- !x y d. (& 0) < d /\ (x - d) < y /\ y < (x + d) = (abs(y - x)) < d
Run time: 0.1s
Intermediate theorems generated: 372
ABS_BOUND = |- !x y d. (abs(x - y)) < d ==> y < (x + d)
Run time: 0.0s
Intermediate theorems generated: 54
ABS_STILLNZ = |- !x y. (abs(x - y)) < (abs y) ==> ~(x = & 0)
Run time: 0.0s
Intermediate theorems generated: 56
ABS_CASES = |- !x. (x = & 0) \/ (& 0) < (abs x)
Run time: 0.0s
Intermediate theorems generated: 29
ABS_BETWEEN1 = |- !x y z. x < z /\ (abs(y - x)) < (z - x) ==> y < z
Run time: 0.1s
Intermediate theorems generated: 102
ABS_SIGN = |- !x y. (abs(x - y)) < y ==> (& 0) < x
Run time: 0.0s
Intermediate theorems generated: 22
ABS_SIGN2 = |- !x y. (abs(x - y)) < (-- y) ==> x < (& 0)
Run time: 0.0s
Intermediate theorems generated: 68
ABS_DIV = |- !y. ~(y = & 0) ==> (!x. abs(x / y) = (abs x) / (abs y))
Run time: 0.1s
Intermediate theorems generated: 41
ABS_CIRCLE =
|- !x y h. (abs h) < ((abs y) - (abs x)) ==> (abs(x + h)) < (abs y)
Run time: 0.0s
Intermediate theorems generated: 61
REAL_SUB_ABS = |- !x y. ((abs x) - (abs y)) <= (abs(x - y))
Run time: 0.1s
Intermediate theorems generated: 94
ABS_SUB_ABS = |- !x y. (abs((abs x) - (abs y))) <= (abs(x - y))
Run time: 0.0s
Intermediate theorems generated: 80
ABS_BETWEEN2 =
|- !x0 x y0 y.
x0 < y0 /\
(abs(x - x0)) < ((y0 - x0) / (& 2)) /\
(abs(y - y0)) < ((y0 - x0) / (& 2)) ==>
x < y
Run time: 0.1s
Intermediate theorems generated: 935
ABS_BOUNDS = |- !x k. (abs x) <= k = (-- k) <= x /\ x <= k
Run time: 0.0s
Intermediate theorems generated: 250
pow = |- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
Run time: 0.1s
Intermediate theorems generated: 175
POW_0 = |- !n. (& 0) pow (SUC n) = & 0
Run time: 0.0s
Intermediate theorems generated: 56
POW_NZ = |- !c n. ~(c = & 0) ==> ~(c pow n = & 0)
Run time: 0.0s
Intermediate theorems generated: 108
POW_INV = |- !c. ~(c = & 0) ==> (!n. inv(c pow n) = (inv c) pow n)
Run time: 0.0s
Intermediate theorems generated: 126
POW_ABS = |- !c n. (abs c) pow n = abs(c pow n)
Run time: 0.0s
Intermediate theorems generated: 83
POW_PLUS1 =
|- !e. (& 0) < e ==> (!n. ((& 1) + ((& n) * e)) <= (((& 1) + e) pow n))
Run time: 0.1s
Intermediate theorems generated: 298
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 num_add m = m) /\
(m num_add 0 = m) /\
((SUC m) num_add n = SUC(m num_add n)) /\
(m num_add (SUC n) = SUC(m num_add n))
Run time: 0.0s
POW_ADD = |- !c m n. c pow (m num_add n) = (c pow m) * (c pow n)
Run time: 0.1s
Intermediate theorems generated: 152
POW_1 = |- !x. x pow 1 = x
Run time: 0.0s
Intermediate theorems generated: 34
POW_2 = |- !x. x pow 2 = x * x
Run time: 0.0s
Intermediate theorems generated: 32
POW_POS = |- !x. (& 0) <= x ==> (!n. (& 0) <= (x pow n))
Run time: 0.1s
Intermediate theorems generated: 68
POW_LE = |- !n x y. (& 0) <= x /\ x <= y ==> (x pow n) <= (y pow n)
Run time: 0.0s
Intermediate theorems generated: 160
POW_M1 = |- !n. abs((--(& 1)) pow n) = & 1
Run time: 0.1s
Intermediate theorems generated: 80
POW_MUL = |- !n x y. (x * y) pow n = (x pow n) * (y pow n)
Run time: 0.0s
Intermediate theorems generated: 135
REAL_LE_POW2 = |- !x. (& 0) <= (x pow 2)
Run time: 0.1s
Intermediate theorems generated: 14
ABS_POW2 = |- !x. abs(x pow 2) = x pow 2
Run time: 0.0s
Intermediate theorems generated: 13
REAL_POW2_ABS = |- !x. (abs x) pow 2 = x pow 2
Run time: 0.1s
Intermediate theorems generated: 62
REAL_LE1_POW2 = |- !x. (& 1) <= x ==> (& 1) <= (x pow 2)
Run time: 0.0s
Intermediate theorems generated: 54
REAL_LT1_POW2 = |- !x. (& 1) < x ==> (& 1) < (x pow 2)
Run time: 0.0s
Intermediate theorems generated: 54
POW_POS_LT = |- !x n. (& 0) < x ==> (& 0) < (x pow (SUC n))
Run time: 0.0s
Intermediate theorems generated: 73
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m num_le (SUC m)
Run time: 0.0s
POW_2_LE1 = |- !n. (& 1) <= ((& 2) pow n)
Run time: 0.1s
Intermediate theorems generated: 118
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m num_add 1
Run time: 0.0s
POW_2_LT = |- !n. (& n) < ((& 2) pow n)
Run time: 0.0s
Intermediate theorems generated: 103
POW_MINUS1 = |- !n. (--(& 1)) pow (2 num_mul n) = & 1
Run time: 0.1s
Intermediate theorems generated: 231
REAL_SUP_SOMEPOS =
|- !P.
(?x. P x /\ (& 0) < x) /\ (?z. !x. P x ==> x < z) ==>
(?s. !y. (?x. P x /\ y < x) = y < s)
Run time: 0.1s
Intermediate theorems generated: 325
SUP_LEMMA1 =
|- !d.
(!y. (?x. (\x. P(x + d))x /\ y < x) = y < s) ==>
(!y. (?x. P x /\ y < x) = y < (s + d))
Run time: 0.0s
Intermediate theorems generated: 119
SUP_LEMMA2 = |- (?x. P x) ==> (?d x. (\x. P(x + d))x /\ (& 0) < x)
Run time: 0.1s
Intermediate theorems generated: 121
SUP_LEMMA3 =
|- !d. (?z. !x. P x ==> x < z) ==> (?z. !x. (\x. P(x + d))x ==> x < z)
Run time: 0.0s
Intermediate theorems generated: 42
REAL_SUP_EXISTS =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x < z) ==>
(?s. !y. (?x. P x /\ y < x) = y < s)
Run time: 0.1s
Intermediate theorems generated: 45
sup = |- !P. sup P = (@s. !y. (?x. P x /\ y < x) = y < s)
Run time: 0.0s
Intermediate theorems generated: 2
REAL_SUP =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x < z) ==>
(!y. (?x. P x /\ y < x) = y < (sup P))
Run time: 0.1s
Intermediate theorems generated: 31
REAL_SUP_UBOUND =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x < z) ==> (!y. P y ==> y <= (sup P))
Run time: 0.0s
Intermediate theorems generated: 87
SETOK_LE_LT =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x <= z) =
(?x. P x) /\ (?z. !x. P x ==> x < z)
Run time: 0.1s
Intermediate theorems generated: 53
REAL_SUP_LE =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x <= z) ==>
(!y. (?x. P x /\ y < x) = y < (sup P))
Run time: 0.0s
Intermediate theorems generated: 15
REAL_SUP_UBOUND_LE =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x <= z) ==> (!y. P y ==> y <= (sup P))
Run time: 0.1s
Intermediate theorems generated: 15
REAL_ARCH = |- !x. (& 0) < x ==> (!y. ?n. y < ((& n) * x))
Run time: 0.1s
Intermediate theorems generated: 342
Theorem PRE autoloading from theory `prim_rec` ...
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
Run time: 0.0s
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Run time: 0.0s
REAL_ARCH_LEAST =
|- !y.
(& 0) < y ==>
(!x. (& 0) <= x ==> (?n. ((& n) * y) <= x /\ x < ((&(SUC n)) * y)))
Run time: 0.0s
Intermediate theorems generated: 222
sum =
|- (!n f. sum n 0 f = & 0) /\
(!n m f. sum n(SUC m)f = (sum n m f) + (f(n num_add m)))
Run time: 0.1s
Intermediate theorems generated: 202
Sum_DEF = |- !m n f. Sum(m,n)f = sum m n f
Run time: 0.0s
Intermediate theorems generated: 2
Sum =
|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
Run time: 0.1s
Intermediate theorems generated: 51
SUM_TWO = |- !f n p. (Sum(0,n)f) + (Sum(n,p)f) = Sum(0,n num_add p)f
Run time: 0.1s
Intermediate theorems generated: 109
SUM_DIFF = |- !f m n. Sum(m,n)f = (Sum(0,m num_add n)f) - (Sum(0,m)f)
Run time: 0.0s
Intermediate theorems generated: 30
ABS_SUM = |- !f m n. (abs(Sum(m,n)f)) <= (Sum(m,n)(\n'. abs(f n')))
Run time: 0.1s
Intermediate theorems generated: 103
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m num_le (m num_add n)
Run time: 0.0s
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m num_add n = n num_add m
Run time: 0.0s
SUM_LE =
|- !f g m n.
(!r. m num_le r /\ r num_lt (n num_add m) ==> (f r) <= (g r)) ==>
(Sum(m,n)f) <= (Sum(m,n)g)
Run time: 0.0s
Intermediate theorems generated: 272
SUM_EQ =
|- !f g m n.
(!r. m num_le r /\ r num_lt (n num_add m) ==> (f r = g r)) ==>
(Sum(m,n)f = Sum(m,n)g)
Run time: 0.1s
Intermediate theorems generated: 82
SUM_POS = |- !f. (!n. (& 0) <= (f n)) ==> (!m n. (& 0) <= (Sum(m,n)f))
Run time: 0.0s
Intermediate theorems generated: 78
SUM_POS_GEN =
|- !f m.
(!n. m num_le n ==> (& 0) <= (f n)) ==> (!n. (& 0) <= (Sum(m,n)f))
Run time: 0.0s
Intermediate theorems generated: 91
SUM_ABS =
|- !f m n. abs(Sum(m,n)(\m. abs(f m))) = Sum(m,n)(\m. abs(f m))
Run time: 0.1s
Intermediate theorems generated: 42
SUM_ABS_LE = |- !f m n. (abs(Sum(m,n)f)) <= (Sum(m,n)(\n'. abs(f n')))
Run time: 0.0s
Intermediate theorems generated: 105
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m num_add (n num_add p) = (m num_add n) num_add p
Run time: 0.0s
Theorem LESS_EQUAL_ADD autoloading from theory `arithmetic` ...
LESS_EQUAL_ADD = |- !m n. m num_le n ==> (?p. n = m num_add p)
Run time: 0.0s
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n num_ge m = m num_le n
Run time: 0.0s
SUM_ZERO =
|- !f N.
(!n. n num_ge N ==> (f n = & 0)) ==>
(!m n. m num_ge N ==> (Sum(m,n)f = & 0))
Run time: 0.1s
Intermediate theorems generated: 145
SUM_ADD =
|- !f g m n. Sum(m,n)(\n'. (f n') + (g n')) = (Sum(m,n)f) + (Sum(m,n)g)
Run time: 0.1s
Intermediate theorems generated: 133
SUM_CMUL = |- !f c m n. Sum(m,n)(\n'. c * (f n')) = c * (Sum(m,n)f)
Run time: 0.0s
Intermediate theorems generated: 100
SUM_NEG = |- !f n d. Sum(n,d)(\n'. --(f n')) = --(Sum(n,d)f)
Run time: 0.1s
Intermediate theorems generated: 89
SUM_SUB =
|- !f g m n. Sum(m,n)(\n. (f n) - (g n)) = (Sum(m,n)f) - (Sum(m,n)g)
Run time: 0.0s
Intermediate theorems generated: 74
Theorem LESS_MONO_ADD autoloading from theory `arithmetic` ...
LESS_MONO_ADD =
|- !m n p. m num_lt n ==> (m num_add p) num_lt (n num_add p)
Run time: 0.0s
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m num_lt n ==> m num_le n
Run time: 0.0s
Theorem LESS_EQ_IMP_LESS_SUC autoloading from theory `arithmetic` ...
LESS_EQ_IMP_LESS_SUC = |- !n m. n num_le m ==> n num_lt (SUC m)
Run time: 0.1s
SUM_SUBST =
|- !f g m n.
(!p. m num_le p /\ p num_lt (m num_add n) ==> (f p = g p)) ==>
(Sum(m,n)f = Sum(m,n)g)
Run time: 0.0s
Intermediate theorems generated: 221
SUM_NSUB =
|- !n f c. (Sum(0,n)f) - ((& n) * c) = Sum(0,n)(\p. (f p) - c)
Run time: 0.1s
Intermediate theorems generated: 239
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m num_lt n ==> m num_lt (SUC n)
Run time: 0.0s
SUM_BOUND =
|- !f K m n.
(!p. m num_le p /\ p num_lt (m num_add n) ==> (f p) <= K) ==>
(Sum(m,n)f) <= ((& n) * K)
Run time: 0.1s
Intermediate theorems generated: 226
SUM_GROUP =
|- !n k f. Sum(0,n)(\m. Sum(m num_mul k,k)f) = Sum(0,n num_mul k)f
Run time: 0.1s
Intermediate theorems generated: 169
SUM_1 = |- !f n. Sum(n,1)f = f n
Run time: 0.0s
Intermediate theorems generated: 56
SUM_2 = |- !f n. Sum(n,2)f = (f n) + (f(n num_add 1))
Run time: 0.1s
Intermediate theorems generated: 81
SUM_OFFSET =
|- !f n k.
Sum(0,n)(\m. f(m num_add k)) = (Sum(0,n num_add k)f) - (Sum(0,k)f)
Run time: 0.0s
Intermediate theorems generated: 141
SUM_REINDEX =
|- !f m k n. Sum(m num_add k,n)f = Sum(m,n)(\r. f(r num_add k))
Run time: 0.1s
Intermediate theorems generated: 117
SUM_0 = |- !m n. Sum(m,n)(\r. & 0) = & 0
Run time: 0.1s
Intermediate theorems generated: 72
Theorem ADD_SUC autoloading from theory `arithmetic` ...
ADD_SUC = |- !m n. SUC(m num_add n) = m num_add (SUC n)
Run time: 0.0s
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Run time: 0.0s
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n num_lt n
Run time: 0.0s
Theorem LESS_ADD_SUC autoloading from theory `arithmetic` ...
LESS_ADD_SUC = |- !m n. m num_lt (m num_add (SUC n))
Run time: 0.0s
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) num_lt (SUC n) = m num_lt n
Run time: 0.0s
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) num_sub 1 = m
Run time: 0.0s
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n num_lt m ==> (?p. m = n num_add (p num_add 1))
Run time: 0.0s
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m num_le n = m num_lt n \/ (m = n)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m num_lt n = (SUC m) num_le n
Run time: 0.0s
Theorem LESS_CASES autoloading from theory `arithmetic` ...
LESS_CASES = |- !m n. m num_lt n \/ n num_le m
Run time: 0.0s
SUM_PERMUTE_0 =
|- !n p.
(!y. y num_lt n ==> (?! x. x num_lt n /\ (p x = y))) ==>
(!f. Sum(0,n)(\n'. f(p n')) = Sum(0,n)f)
Run time: 0.3s
Intermediate theorems generated: 2469
SUM_CANCEL =
|- !f n d.
Sum(n,d)(\n'. (f(SUC n')) - (f n')) = (f(n num_add d)) - (f n)
Run time: 0.1s
Intermediate theorems generated: 206
() : void
Run time: 0.1s
Intermediate theorems generated: 1
File real.ml loaded
() : void
Run time: 9.8s
Intermediate theorems generated: 23746
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `topology.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory REAL loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.1s
[] : (string # string) list
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 11
() : void
Run time: 0.0s
() : void
Run time: 0.0s
re_Union = |- !S. re_Union S = (\x. ?s. S s /\ s x)
Run time: 0.0s
Intermediate theorems generated: 2
re_union = |- !P Q. P re_union Q = (\x. P x \/ Q x)
Run time: 0.0s
Intermediate theorems generated: 2
re_intersect = |- !P Q. P re_intersect Q = (\x. P x /\ Q x)
Run time: 0.0s
Intermediate theorems generated: 2
re_null = |- re_null = (\x. F)
Run time: 0.0s
Intermediate theorems generated: 2
re_universe = |- re_universe = (\x. T)
Run time: 0.0s
Intermediate theorems generated: 2
re_subset = |- !P Q. P re_subset Q = (!x. P x ==> Q x)
Run time: 0.0s
Intermediate theorems generated: 2
re_compl = |- !S. re_compl S = (\x. ~S x)
Run time: 0.0s
Intermediate theorems generated: 2
SUBSET_REFL = |- !S. S re_subset S
Run time: 0.0s
Intermediate theorems generated: 16
COMPL_MEM = |- !S x. S x = ~re_compl S x
Run time: 0.0s
Intermediate theorems generated: 23
SUBSET_ANTISYM = |- !P Q. P re_subset Q /\ Q re_subset P = (P = Q)
Run time: 0.1s
Intermediate theorems generated: 99
SUBSET_TRANS =
|- !P Q R. P re_subset Q /\ Q re_subset R ==> P re_subset R
Run time: 0.0s
Intermediate theorems generated: 49
istopology =
|- !L.
istopology L =
L re_null /\
L re_universe /\
(!a b. L a /\ L b ==> L(a re_intersect b)) /\
(!P. P re_subset L ==> L(re_Union P))
Run time: 0.0s
Intermediate theorems generated: 2
topology_tydef = |- ?rep. TYPE_DEFINITION istopology rep
Run time: 0.0s
Intermediate theorems generated: 86
topology_tybij =
|- (!a. topology(open a) = a) /\
(!r. istopology r = (open(topology r) = r))
Run time: 0.0s
Intermediate theorems generated: 4
TOPOLOGY =
|- !L.
open L re_null /\
open L re_universe /\
(!x y. open L x /\ open L y ==> open L(x re_intersect y)) /\
(!P. P re_subset (open L) ==> open L(re_Union P))
Run time: 0.0s
Intermediate theorems generated: 34
TOPOLOGY_UNION = |- !L P. P re_subset (open L) ==> open L(re_Union P)
Run time: 0.0s
Intermediate theorems generated: 45
neigh =
|- !top N x. neigh top(N,x) = (?P. open top P /\ P re_subset N /\ P x)
Run time: 0.0s
Intermediate theorems generated: 2
OPEN_OWN_NEIGH = |- !S top x. open top S /\ S x ==> neigh top(S,x)
Run time: 0.1s
Intermediate theorems generated: 40
OPEN_UNOPEN =
|- !S top. open top S = (re_Union(\P. open top P /\ P re_subset S) = S)
Run time: 0.0s
Intermediate theorems generated: 212
OPEN_SUBOPEN =
|- !S top.
open top S = (!x. S x ==> (?P. P x /\ open top P /\ P re_subset S))
Run time: 0.0s
Intermediate theorems generated: 245
OPEN_NEIGH =
|- !S top.
open top S = (!x. S x ==> (?N. neigh top(N,x) /\ N re_subset S))
Run time: 0.0s
Intermediate theorems generated: 170
closed = |- !L S. closed L S = open L(re_compl S)
Run time: 0.1s
Intermediate theorems generated: 2
limpt =
|- !top x S.
limpt top x S =
(!N. neigh top(N,x) ==> (?y. ~(x = y) /\ S y /\ N y))
Run time: 0.0s
Intermediate theorems generated: 2
CLOSED_LIMPT = |- !top S. closed top S = (!x. limpt top x S ==> S x)
Run time: 0.0s
Intermediate theorems generated: 433
ismet =
|- !m.
ismet m =
(!x y. (m(x,y) = & 0) = (x = y)) /\
(!x y z. (m(y,z)) <= ((m(x,y)) + (m(x,z))))
Run time: 0.0s
Intermediate theorems generated: 2
Theorem REAL_LE_ADD2 autoloading from theory `REAL` ...
REAL_LE_ADD2 = |- !w x y z. w <= x /\ y <= z ==> (w + y) <= (x + z)
Run time: 0.0s
Theorem REAL_LE_01 autoloading from theory `REAL` ...
REAL_LE_01 = |- (& 0) <= (& 1)
Run time: 0.0s
Theorem REAL_LE_REFL autoloading from theory `REAL` ...
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
Theorem REAL_ADD_RID autoloading from theory `REAL` ...
REAL_ADD_RID = |- !x. x + (& 0) = x
Run time: 0.0s
Theorem REAL_ADD_LID autoloading from theory `REAL` ...
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Theorem REAL_10 autoloading from theory `REAL` ...
REAL_10 = |- ~(& 1 = & 0)
Run time: 0.0s
metric_tydef = |- ?rep. TYPE_DEFINITION ismet rep
Run time: 0.0s
Intermediate theorems generated: 560
metric_tybij =
|- (!a. metric(dist a) = a) /\ (!r. ismet r = (dist(metric r) = r))
Run time: 0.0s
Intermediate theorems generated: 4
METRIC_ISMET = |- !m. ismet(dist m)
Run time: 0.0s
Intermediate theorems generated: 20
METRIC_ZERO = |- !m x y. (dist m(x,y) = & 0) = (x = y)
Run time: 0.1s
Intermediate theorems generated: 41
METRIC_SAME = |- !m x. dist m(x,x) = & 0
Run time: 0.0s
Intermediate theorems generated: 16
Theorem REAL_LT_ADD2 autoloading from theory `REAL` ...
REAL_LT_ADD2 = |- !w x y z. w < x /\ y < z ==> (w + y) < (x + z)
Run time: 0.0s
Theorem REAL_NOT_LE autoloading from theory `REAL` ...
REAL_NOT_LE = |- !x y. ~x <= y = y < x
Run time: 0.0s
METRIC_POS = |- !m x y. (& 0) <= (dist m(x,y))
Run time: 0.0s
Intermediate theorems generated: 91
Theorem REAL_LE_ANTISYM autoloading from theory `REAL` ...
REAL_LE_ANTISYM = |- !x y. x <= y /\ y <= x = (x = y)
Run time: 0.0s
METRIC_SYM = |- !m x y. dist m(x,y) = dist m(y,x)
Run time: 0.0s
Intermediate theorems generated: 99
METRIC_TRIANGLE =
|- !m x y z. (dist m(x,z)) <= ((dist m(x,y)) + (dist m(y,z)))
Run time: 0.0s
Intermediate theorems generated: 52
Theorem REAL_LE_LT autoloading from theory `REAL` ...
REAL_LE_LT = |- !x y. x <= y = x < y \/ (x = y)
Run time: 0.0s
METRIC_NZ = |- !m x y. ~(x = y) ==> (& 0) < (dist m(x,y))
Run time: 0.1s
Intermediate theorems generated: 78
mtop =
|- !m.
mtop m =
topology
(\S. !x. S x ==> (?e. (& 0) < e /\ (!y. (dist m(x,y)) < e ==> S y)))
Run time: 0.0s
Intermediate theorems generated: 2
Theorem REAL_LT_TRANS autoloading from theory `REAL` ...
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_LT_TOTAL autoloading from theory `REAL` ...
REAL_LT_TOTAL = |- !x y. (x = y) \/ x < y \/ y < x
Run time: 0.0s
Theorem REAL_LT_01 autoloading from theory `REAL` ...
REAL_LT_01 = |- (& 0) < (& 1)
Run time: 0.0s
mtop_istopology =
|- !m.
istopology
(\S. !x. S x ==> (?e. (& 0) < e /\ (!y. (dist m(x,y)) < e ==> S y)))
Run time: 0.1s
Intermediate theorems generated: 544
MTOP_OPEN =
|- !m.
open(mtop m)S =
(!x. S x ==> (?e. (& 0) < e /\ (!y. (dist m(x,y)) < e ==> S y)))
Run time: 0.0s
Intermediate theorems generated: 38
ball = |- !m x e. B m(x,e) = (\y. (dist m(x,y)) < e)
Run time: 0.0s
Intermediate theorems generated: 2
Theorem REAL_LET_TRANS autoloading from theory `REAL` ...
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_ADD_SYM autoloading from theory `REAL` ...
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Theorem REAL_LT_SUB_LADD autoloading from theory `REAL` ...
REAL_LT_SUB_LADD = |- !x y z. x < (y - z) = (x + z) < y
Run time: 0.0s
Theorem REAL_SUB_LT autoloading from theory `REAL` ...
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
BALL_OPEN = |- !m x e. (& 0) < e ==> open(mtop m)(B m(x,e))
Run time: 0.0s
Intermediate theorems generated: 161
BALL_NEIGH = |- !m x e. (& 0) < e ==> neigh(mtop m)(B m(x,e),x)
Run time: 0.1s
Intermediate theorems generated: 76
MTOP_LIMPT =
|- !m x S.
limpt(mtop m)x S =
(!e. (& 0) < e ==> (?y. ~(x = y) /\ S y /\ (dist m(x,y)) < e))
Run time: 0.0s
Intermediate theorems generated: 298
Theorem REAL_ADD_LINV autoloading from theory `REAL` ...
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Theorem REAL_ADD_ASSOC autoloading from theory `REAL` ...
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.0s
Definition real_sub autoloading from theory `REAL` ...
real_sub = |- !x y. x - y = x + (-- y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem ABS_TRIANGLE autoloading from theory `REAL` ...
ABS_TRIANGLE = |- !x y. (abs(x + y)) <= ((abs x) + (abs y))
Run time: 0.0s
Theorem ABS_NEG autoloading from theory `REAL` ...
ABS_NEG = |- !x. abs(-- x) = abs x
Run time: 0.0s
Theorem REAL_NEG_SUB autoloading from theory `REAL` ...
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
Theorem REAL_SUB_0 autoloading from theory `REAL` ...
REAL_SUB_0 = |- !x y. (x - y = & 0) = (x = y)
Run time: 0.0s
Theorem ABS_ZERO autoloading from theory `REAL` ...
ABS_ZERO = |- !x. (abs x = & 0) = (x = & 0)
Run time: 0.0s
ISMET_R1 = |- ismet(\(x,y). abs(y - x))
Run time: 0.0s
Intermediate theorems generated: 204
mr1 = |- mr1 = metric(\(x,y). abs(y - x))
Run time: 0.0s
Intermediate theorems generated: 2
MR1_DEF = |- !x y. dist mr1(x,y) = abs(y - x)
Run time: 0.0s
Intermediate theorems generated: 32
Theorem REAL_ADD_SUB autoloading from theory `REAL` ...
REAL_ADD_SUB = |- !x y. (x + y) - x = y
Run time: 0.0s
MR1_ADD = |- !x d. dist mr1(x,x + d) = abs d
Run time: 0.0s
Intermediate theorems generated: 25
Theorem REAL_SUB_SUB autoloading from theory `REAL` ...
REAL_SUB_SUB = |- !x y. (x - y) - x = -- y
Run time: 0.0s
MR1_SUB = |- !x d. dist mr1(x,x - d) = abs d
Run time: 0.0s
Intermediate theorems generated: 30
Definition abs autoloading from theory `REAL` ...
abs = |- !x. abs x = ((& 0) <= x => x | -- x)
Run time: 0.0s
Intermediate theorems generated: 1
MR1_ADD_LE = |- !x d. (& 0) <= d ==> (dist mr1(x,x + d) = d)
Run time: 0.1s
Intermediate theorems generated: 34
MR1_SUB_LE = |- !x d. (& 0) <= d ==> (dist mr1(x,x - d) = d)
Run time: 0.0s
Intermediate theorems generated: 34
Theorem REAL_LT_IMP_LE autoloading from theory `REAL` ...
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
MR1_ADD_LT = |- !x d. (& 0) < d ==> (dist mr1(x,x + d) = d)
Run time: 0.0s
Intermediate theorems generated: 11
MR1_SUB_LT = |- !x d. (& 0) < d ==> (dist mr1(x,x - d) = d)
Run time: 0.0s
Intermediate theorems generated: 11
Theorem ABS_BETWEEN1 autoloading from theory `REAL` ...
ABS_BETWEEN1 = |- !x y z. x < z /\ (abs(y - x)) < (z - x) ==> y < z
Run time: 0.0s
MR1_BETWEEN1 = |- !x y z. x < z /\ (dist mr1(x,y)) < (z - x) ==> y < z
Run time: 0.0s
Intermediate theorems generated: 29
Theorem REAL_LT_IMP_NE autoloading from theory `REAL` ...
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
Theorem REAL_ADD_RID_UNIQ autoloading from theory `REAL` ...
REAL_ADD_RID_UNIQ = |- !x y. (x + y = x) = (y = & 0)
Run time: 0.0s
Theorem REAL_LT_HALF2 autoloading from theory `REAL` ...
REAL_LT_HALF2 = |- !d. (d / (& 2)) < d = (& 0) < d
Run time: 0.0s
Theorem REAL_LT_HALF1 autoloading from theory `REAL` ...
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.0s
MR1_LIMPT = |- !x. limpt(mtop mr1)x re_universe
Run time: 0.0s
Intermediate theorems generated: 143
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File topology.ml loaded
() : void
Run time: 1.3s
Intermediate theorems generated: 4132
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `nets.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory TOPOLOGY loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.0s
real_interface_map =
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
[] : (string # string) list
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 30
() : void
Run time: 0.1s
() : void
Run time: 0.0s
dorder =
|- !g.
dorder g =
(!x y.
g x x /\ g y y ==> (?z. g z z /\ (!w. g w z ==> g w x /\ g w y)))
Run time: 0.0s
Intermediate theorems generated: 2
tends =
|- !s l top g.
(s tends l)(top,g) =
(!N. neigh top(N,l) ==> (?n. g n n /\ (!m. g m n ==> N(s m))))
Run time: 0.0s
Intermediate theorems generated: 2
bounded =
|- !m g f.
bounded(m,g)f =
(?k x N. g N N /\ (!n. g n N ==> (dist m(f n,x)) < k))
Run time: 0.0s
Intermediate theorems generated: 2
tendsto =
|- !m x y z.
tendsto(m,x)y z =
(& 0) < (dist m(x,y)) /\ (dist m(x,y)) <= (dist m(x,z))
Run time: 0.0s
Intermediate theorems generated: 2
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
DORDER_LEMMA =
|- !g.
dorder g ==>
(!P Q.
(?n. g n n /\ (!m. g m n ==> P m)) /\
(?n. g n n /\ (!m. g m n ==> Q m)) ==>
(?n. g n n /\ (!m. g m n ==> P m /\ Q m)))
Run time: 0.0s
Intermediate theorems generated: 312
DORDER_THEN = - : ((thm -> *) -> thm -> *)
Run time: 0.0s
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m num_le n /\ n num_le p ==> m num_le p
Run time: 0.1s
Theorem LESS_EQ_CASES autoloading from theory `arithmetic` ...
LESS_EQ_CASES = |- !m n. m num_le n \/ n num_le m
Run time: 0.0s
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m num_le m
Run time: 0.0s
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n num_ge m = m num_le n
Run time: 0.0s
DORDER_NGE = |- dorder $num_ge
Run time: 0.0s
Intermediate theorems generated: 136
Theorem REAL_LE_TRANS autoloading from theory `REAL` ...
REAL_LE_TRANS = |- !x y z. x <= y /\ y <= z ==> x <= z
Run time: 0.0s
Theorem REAL_LE_TOTAL autoloading from theory `REAL` ...
REAL_LE_TOTAL = |- !x y. x <= y \/ y <= x
Run time: 0.0s
Theorem REAL_LE_REFL autoloading from theory `REAL` ...
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
DORDER_TENDSTO = |- !m x. dorder(tendsto(m,x))
Run time: 0.1s
Intermediate theorems generated: 257
Definition re_subset autoloading from theory `TOPOLOGY` ...
re_subset = |- !P Q. P re_subset Q = (!x. P x ==> Q x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem MTOP_OPEN autoloading from theory `TOPOLOGY` ...
MTOP_OPEN =
|- !m.
open(mtop m)S =
(!x. S x ==> (?e. (& 0) < e /\ (!y. (dist m(x,y)) < e ==> S y)))
Run time: 0.0s
Definition neigh autoloading from theory `TOPOLOGY` ...
neigh =
|- !top N x. neigh top(N,x) = (?P. open top P /\ P re_subset N /\ P x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem METRIC_SYM autoloading from theory `TOPOLOGY` ...
METRIC_SYM = |- !m x y. dist m(x,y) = dist m(y,x)
Run time: 0.0s
Definition ball autoloading from theory `TOPOLOGY` ...
ball = |- !m x e. B m(x,e) = (\y. (dist m(x,y)) < e)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem BALL_NEIGH autoloading from theory `TOPOLOGY` ...
BALL_NEIGH = |- !m x e. (& 0) < e ==> neigh(mtop m)(B m(x,e),x)
Run time: 0.0s
MTOP_TENDS =
|- !d g x x0.
(x --> x0)(mtop d,g) =
(!e.
(& 0) < e ==> (?n. g n n /\ (!m. g m n ==> (dist d(x m,x0)) < e)))
Run time: 0.1s
Intermediate theorems generated: 373
Theorem METRIC_TRIANGLE autoloading from theory `TOPOLOGY` ...
METRIC_TRIANGLE =
|- !m x y z. (dist m(x,z)) <= ((dist m(x,y)) + (dist m(y,z)))
Run time: 0.0s
Theorem REAL_NOT_LT autoloading from theory `REAL` ...
REAL_NOT_LT = |- !x y. ~x < y = y <= x
Run time: 0.0s
Theorem REAL_HALF_DOUBLE autoloading from theory `REAL` ...
REAL_HALF_DOUBLE = |- !x. (x / (& 2)) + (x / (& 2)) = x
Run time: 0.0s
Theorem REAL_LT_ADD2 autoloading from theory `REAL` ...
REAL_LT_ADD2 = |- !w x y z. w < x /\ y < z ==> (w + y) < (x + z)
Run time: 0.0s
Theorem METRIC_NZ autoloading from theory `TOPOLOGY` ...
METRIC_NZ = |- !m x y. ~(x = y) ==> (& 0) < (dist m(x,y))
Run time: 0.0s
Theorem REAL_LT_HALF1 autoloading from theory `REAL` ...
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.0s
MTOP_TENDS_UNIQ =
|- !g d.
dorder g ==>
(x --> x0)(mtop d,g) /\ (x --> x1)(mtop d,g) ==>
(x0 = x1)
Run time: 0.0s
Intermediate theorems generated: 313
SEQ_TENDS =
|- !d x x0.
(x --> x0)(mtop d,$num_ge) =
(!e. (& 0) < e ==> (?N. !n. n num_ge N ==> (dist d(x n,x0)) < e))
Run time: 0.0s
Intermediate theorems generated: 64
Theorem REAL_LT_IMP_LE autoloading from theory `REAL` ...
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
Definition re_universe autoloading from theory `TOPOLOGY` ...
re_universe = |- re_universe = (\x. T)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem MTOP_LIMPT autoloading from theory `TOPOLOGY` ...
MTOP_LIMPT =
|- !m x S.
limpt(mtop m)x S =
(!e. (& 0) < e ==> (?y. ~(x = y) /\ S y /\ (dist m(x,y)) < e))
Run time: 0.0s
LIM_TENDS =
|- !m1 m2 f x0 y0.
limpt(mtop m1)x0 re_universe ==>
((f --> y0)(mtop m2,tendsto(m1,x0)) =
(!e.
(& 0) < e ==>
(?d.
(& 0) < d /\
(!x.
(& 0) < (dist m1(x,x0)) /\ (dist m1(x,x0)) <= d ==>
(dist m2(f x,y0)) < e))))
Run time: 0.0s
Intermediate theorems generated: 459
Theorem REAL_LT_HALF2 autoloading from theory `REAL` ...
REAL_LT_HALF2 = |- !d. (d / (& 2)) < d = (& 0) < d
Run time: 0.0s
Theorem REAL_LET_TRANS autoloading from theory `REAL` ...
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.0s
LIM_TENDS2 =
|- !m1 m2 f x0 y0.
limpt(mtop m1)x0 re_universe ==>
((f --> y0)(mtop m2,tendsto(m1,x0)) =
(!e.
(& 0) < e ==>
(?d.
(& 0) < d /\
(!x.
(& 0) < (dist m1(x,x0)) /\ (dist m1(x,x0)) < d ==>
(dist m2(f x,y0)) < e))))
Run time: 0.1s
Intermediate theorems generated: 246
Theorem ABS_NEG autoloading from theory `REAL` ...
ABS_NEG = |- !x. abs(-- x) = abs x
Run time: 0.0s
Theorem REAL_SUB_LZERO autoloading from theory `REAL` ...
REAL_SUB_LZERO = |- !x. (& 0) - x = -- x
Run time: 0.0s
Theorem ABS_SUB autoloading from theory `REAL` ...
ABS_SUB = |- !x y. abs(x - y) = abs(y - x)
Run time: 0.0s
Theorem REAL_LT_RADD autoloading from theory `REAL` ...
REAL_LT_RADD = |- !x y z. (x + z) < (y + z) = x < y
Run time: 0.0s
Theorem REAL_ADD_SYM autoloading from theory `REAL` ...
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Theorem ABS_TRIANGLE autoloading from theory `REAL` ...
ABS_TRIANGLE = |- !x y. (abs(x + y)) <= ((abs x) + (abs y))
Run time: 0.0s
Theorem REAL_SUB_ADD autoloading from theory `REAL` ...
REAL_SUB_ADD = |- !x y. (x - y) + y = x
Run time: 0.0s
Theorem MR1_DEF autoloading from theory `TOPOLOGY` ...
MR1_DEF = |- !x y. dist mr1(x,y) = abs(y - x)
Run time: 0.0s
MR1_BOUNDED =
|- !g f.
bounded(mr1,g)f = (?k N. g N N /\ (!n. g n N ==> (abs(f n)) < k))
Run time: 0.1s
Intermediate theorems generated: 331
Theorem REAL_NEG_SUB autoloading from theory `REAL` ...
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
NET_NULL =
|- !g x x0.
(x --> x0)(mtop mr1,g) = ((\n. (x n) - x0) --> (& 0))(mtop mr1,g)
Run time: 0.0s
Intermediate theorems generated: 151
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 num_lt (SUC n)
Run time: 0.0s
Theorem REAL_LT autoloading from theory `REAL` ...
REAL_LT = |- !m n. (& m) < (& n) = m num_lt n
Run time: 0.0s
NET_CONV_BOUNDED =
|- !g x x0. (x --> x0)(mtop mr1,g) ==> bounded(mr1,g)x
Run time: 0.0s
Intermediate theorems generated: 119
Theorem REAL_LT_REFL autoloading from theory `REAL` ...
REAL_LT_REFL = |- !x. ~x < x
Run time: 0.1s
Theorem REAL_SUB_RZERO autoloading from theory `REAL` ...
REAL_SUB_RZERO = |- !x. x - (& 0) = x
Run time: 0.0s
Theorem ABS_NZ autoloading from theory `REAL` ...
ABS_NZ = |- !x. ~(x = & 0) = (& 0) < (abs x)
Run time: 0.0s
NET_CONV_NZ =
|- !g x x0.
(x --> x0)(mtop mr1,g) /\ ~(x0 = & 0) ==>
(?N. g N N /\ (!n. g n N ==> ~(x n = & 0)))
Run time: 0.0s
Intermediate theorems generated: 165
Theorem REAL_LT_INV autoloading from theory `REAL` ...
REAL_LT_INV = |- !x y. (& 0) < x /\ x < y ==> (inv y) < (inv x)
Run time: 0.0s
Theorem ABS_INV autoloading from theory `REAL` ...
ABS_INV = |- !x. ~(x = & 0) ==> (abs(inv x) = inv(abs x))
Run time: 0.0s
Theorem REAL_INJ autoloading from theory `REAL` ...
REAL_INJ = |- !m n. (& m = & n) = (m = n)
Run time: 0.0s
Theorem ABS_ABS autoloading from theory `REAL` ...
ABS_ABS = |- !x. abs(abs x) = abs x
Run time: 0.0s
Theorem REAL_MUL_LID autoloading from theory `REAL` ...
REAL_MUL_LID = |- !x. (& 1) * x = x
Run time: 0.0s
Theorem REAL_MUL_LINV autoloading from theory `REAL` ...
REAL_MUL_LINV = |- !x. ~(x = & 0) ==> ((inv x) * x = & 1)
Run time: 0.0s
Theorem REAL_MUL_SYM autoloading from theory `REAL` ...
REAL_MUL_SYM = |- !x y. x * y = y * x
Run time: 0.0s
Theorem REAL_MUL_ASSOC autoloading from theory `REAL` ...
REAL_MUL_ASSOC = |- !x y z. x * (y * z) = (x * y) * z
Run time: 0.0s
Definition real_div autoloading from theory `REAL` ...
real_div = |- !x y. x / y = x * (inv y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_RINV_UNIQ autoloading from theory `REAL` ...
REAL_RINV_UNIQ = |- !x y. (x * y = & 1) ==> (y = inv x)
Run time: 0.0s
Theorem REAL_LT_TRANS autoloading from theory `REAL` ...
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_LT_LADD autoloading from theory `REAL` ...
REAL_LT_LADD = |- !x y z. (x + y) < (x + z) = y < z
Run time: 0.0s
NET_CONV_IBOUNDED =
|- !g x x0.
(x --> x0)(mtop mr1,g) /\ ~(x0 = & 0) ==>
bounded(mr1,g)(\n. inv(x n))
Run time: 0.1s
Intermediate theorems generated: 493
NET_NULL_ADD =
|- !g.
dorder g ==>
(!x y.
(x --> (& 0))(mtop mr1,g) /\ (y --> (& 0))(mtop mr1,g) ==>
((\n. (x n) + (y n)) --> (& 0))(mtop mr1,g))
Run time: 0.0s
Intermediate theorems generated: 324
Theorem REAL_LT_MUL2 autoloading from theory `REAL` ...
REAL_LT_MUL2 =
|- !x1 x2 y1 y2.
(& 0) <= x1 /\ (& 0) <= y1 /\ x1 < x2 /\ y1 < y2 ==>
(x1 * y1) < (x2 * y2)
Run time: 0.0s
Theorem ABS_MUL autoloading from theory `REAL` ...
ABS_MUL = |- !x y. abs(x * y) = (abs x) * (abs y)
Run time: 0.0s
Theorem REAL_DIV_LMUL autoloading from theory `REAL` ...
REAL_DIV_LMUL = |- !x y. ~(y = & 0) ==> (y * (x / y) = x)
Run time: 0.0s
Theorem REAL_LT_RDIV_0 autoloading from theory `REAL` ...
REAL_LT_RDIV_0 = |- !y z. (& 0) < z ==> ((& 0) < (y / z) = (& 0) < y)
Run time: 0.0s
Theorem ABS_POS autoloading from theory `REAL` ...
ABS_POS = |- !x. (& 0) <= (abs x)
Run time: 0.0s
NET_NULL_MUL =
|- !g.
dorder g ==>
(!x y.
bounded(mr1,g)x /\ (y --> (& 0))(mtop mr1,g) ==>
((\n. (x n) * (y n)) --> (& 0))(mtop mr1,g))
Run time: 0.0s
Intermediate theorems generated: 484
Theorem REAL_LT_LMUL autoloading from theory `REAL` ...
REAL_LT_LMUL = |- !x y z. (& 0) < x ==> ((x * y) < (x * z) = y < z)
Run time: 0.0s
Theorem ABS_ZERO autoloading from theory `REAL` ...
ABS_ZERO = |- !x. (abs x = & 0) = (x = & 0)
Run time: 0.0s
Theorem REAL_INV_POS autoloading from theory `REAL` ...
REAL_INV_POS = |- !x. (& 0) < x ==> (& 0) < (inv x)
Run time: 0.0s
Theorem REAL_LT_MUL autoloading from theory `REAL` ...
REAL_LT_MUL = |- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x * y)
Run time: 0.0s
Definition abs autoloading from theory `REAL` ...
abs = |- !x. abs x = ((& 0) <= x => x | -- x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_MUL_LZERO autoloading from theory `REAL` ...
REAL_MUL_LZERO = |- !x. (& 0) * x = & 0
Run time: 0.0s
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n num_lt (SUC n)
Run time: 0.0s
NET_NULL_CMUL =
|- !g k x.
(x --> (& 0))(mtop mr1,g) ==>
((\n. k * (x n)) --> (& 0))(mtop mr1,g)
Run time: 0.0s
Intermediate theorems generated: 506
Theorem REAL_ADD_ASSOC autoloading from theory `REAL` ...
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.0s
Theorem REAL_NEG_ADD autoloading from theory `REAL` ...
REAL_NEG_ADD = |- !x y. --(x + y) = (-- x) + (-- y)
Run time: 0.0s
Definition real_sub autoloading from theory `REAL` ...
real_sub = |- !x y. x - y = x + (-- y)
Run time: 0.0s
Intermediate theorems generated: 1
NET_ADD =
|- !g.
dorder g ==>
(!x x0 y y0.
(x --> x0)(mtop mr1,g) /\ (y --> y0)(mtop mr1,g) ==>
((\n. (x n) + (y n)) --> (x0 + y0))(mtop mr1,g))
Run time: 0.0s
Intermediate theorems generated: 167
Theorem REAL_SUB_NEG2 autoloading from theory `REAL` ...
REAL_SUB_NEG2 = |- !x y. (-- x) - (-- y) = y - x
Run time: 0.0s
NET_NEG =
|- !g.
dorder g ==>
(!x x0.
(x --> x0)(mtop mr1,g) = ((\n. --(x n)) --> (-- x0))(mtop mr1,g))
Run time: 0.1s
Intermediate theorems generated: 121
NET_SUB =
|- !g.
dorder g ==>
(!x x0 y y0.
(x --> x0)(mtop mr1,g) /\ (y --> y0)(mtop mr1,g) ==>
((\n. (x n) - (y n)) --> (x0 - y0))(mtop mr1,g))
Run time: 0.0s
Intermediate theorems generated: 95
Theorem REAL_ADD_LID autoloading from theory `REAL` ...
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Theorem REAL_ADD_LINV autoloading from theory `REAL` ...
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Theorem REAL_NEG_RMUL autoloading from theory `REAL` ...
REAL_NEG_RMUL = |- !x y. --(x * y) = x * (-- y)
Run time: 0.0s
Theorem REAL_NEG_LMUL autoloading from theory `REAL` ...
REAL_NEG_LMUL = |- !x y. --(x * y) = (-- x) * y
Run time: 0.0s
Theorem REAL_RDISTRIB autoloading from theory `REAL` ...
REAL_RDISTRIB = |- !x y z. (x + y) * z = (x * z) + (y * z)
Run time: 0.0s
Theorem REAL_LDISTRIB autoloading from theory `REAL` ...
REAL_LDISTRIB = |- !x y z. x * (y + z) = (x * y) + (x * z)
Run time: 0.0s
NET_MUL =
|- !g.
dorder g ==>
(!x y x0 y0.
(x --> x0)(mtop mr1,g) /\ (y --> y0)(mtop mr1,g) ==>
((\n. (x n) * (y n)) --> (x0 * y0))(mtop mr1,g))
Run time: 0.1s
Intermediate theorems generated: 338
Theorem REAL_INV_NZ autoloading from theory `REAL` ...
REAL_INV_NZ = |- !x. ~(x = & 0) ==> ~(inv x = & 0)
Run time: 0.0s
Theorem ABS_LT_MUL2 autoloading from theory `REAL` ...
ABS_LT_MUL2 =
|- !w x y z. (abs w) < y /\ (abs x) < z ==> (abs(w * x)) < (y * z)
Run time: 0.0s
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m num_le n = m num_lt n \/ (m = n)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_LE autoloading from theory `REAL` ...
REAL_LE = |- !m n. (& m) <= (& n) = m num_le n
Run time: 0.0s
Theorem REAL_LT_IMP_NE autoloading from theory `REAL` ...
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
Theorem REAL_MUL_RINV autoloading from theory `REAL` ...
REAL_MUL_RINV = |- !x. ~(x = & 0) ==> (x * (inv x) = & 1)
Run time: 0.0s
Theorem REAL_MUL_RID autoloading from theory `REAL` ...
REAL_MUL_RID = |- !x. x * (& 1) = x
Run time: 0.0s
Theorem REAL_SUB_LDISTRIB autoloading from theory `REAL` ...
REAL_SUB_LDISTRIB = |- !x y z. x * (y - z) = (x * y) - (x * z)
Run time: 0.0s
NET_INV =
|- !g.
dorder g ==>
(!x x0.
(x --> x0)(mtop mr1,g) /\ ~(x0 = & 0) ==>
((\n. inv(x n)) --> (inv x0))(mtop mr1,g))
Run time: 0.1s
Intermediate theorems generated: 1253
NET_DIV =
|- !g.
dorder g ==>
(!x x0 y y0.
(x --> x0)(mtop mr1,g) /\ (y --> y0)(mtop mr1,g) /\ ~(y0 = & 0) ==>
((\n. (x n) / (y n)) --> (x0 / y0))(mtop mr1,g))
Run time: 0.1s
Intermediate theorems generated: 106
Theorem ABS_SUB_ABS autoloading from theory `REAL` ...
ABS_SUB_ABS = |- !x y. (abs((abs x) - (abs y))) <= (abs(x - y))
Run time: 0.0s
NET_ABS =
|- !x x0.
(x --> x0)(mtop mr1,g) ==> ((\n. abs(x n)) --> (abs x0))(mtop mr1,g)
Run time: 0.0s
Intermediate theorems generated: 128
Theorem ABS_BETWEEN2 autoloading from theory `REAL` ...
ABS_BETWEEN2 =
|- !x0 x y0 y.
x0 < y0 /\
(abs(x - x0)) < ((y0 - x0) / (& 2)) /\
(abs(y - y0)) < ((y0 - x0) / (& 2)) ==>
x < y
Run time: 0.0s
Theorem REAL_SUB_LT autoloading from theory `REAL` ...
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
Theorem REAL_NOT_LE autoloading from theory `REAL` ...
REAL_NOT_LE = |- !x y. ~x <= y = y < x
Run time: 0.0s
NET_LE =
|- !g.
dorder g ==>
(!x x0 y y0.
(x --> x0)(mtop mr1,g) /\
(y --> y0)(mtop mr1,g) /\
(?N. g N N /\ (!n. g n N ==> (x n) <= (y n))) ==>
x0 <= y0)
Run time: 0.1s
Intermediate theorems generated: 400
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File nets.ml loaded
() : void
Run time: 1.8s
Intermediate theorems generated: 7389
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `seq.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory NETS loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.0s
real_interface_map =
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
[] : (string # string) list
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 34
() : void
Run time: 0.1s
[(); ()] : void list
Run time: 0.0s
tends_num_real =
|- !x x0. x tends_num_real x0 = (x tends x0)(mtop mr1,$num_ge)
Run time: 0.0s
Intermediate theorems generated: 2
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
Theorem ABS_SUB autoloading from theory `REAL` ...
ABS_SUB = |- !x y. abs(x - y) = abs(y - x)
Run time: 0.0s
Theorem MR1_DEF autoloading from theory `TOPOLOGY` ...
MR1_DEF = |- !x y. dist mr1(x,y) = abs(y - x)
Run time: 0.0s
Theorem SEQ_TENDS autoloading from theory `NETS` ...
SEQ_TENDS =
|- !d x x0.
(x tends x0)(mtop d,$num_ge) =
(!e. (& 0) < e ==> (?N. !n. n num_ge N ==> (dist d(x n,x0)) < e))
Run time: 0.0s
SEQ =
|- !x x0.
x --> x0 =
(!e. (& 0) < e ==> (?N. !n. n num_ge N ==> (abs((x n) - x0)) < e))
Run time: 0.0s
Intermediate theorems generated: 64
Theorem ABS_0 autoloading from theory `REAL` ...
ABS_0 = |- abs(& 0) = & 0
Run time: 0.0s
Theorem REAL_SUB_REFL autoloading from theory `REAL` ...
REAL_SUB_REFL = |- !x. x - x = & 0
Run time: 0.0s
SEQ_CONST = |- !k. (\x. k) --> k
Run time: 0.0s
Intermediate theorems generated: 58
Theorem DORDER_NGE autoloading from theory `NETS` ...
DORDER_NGE = |- dorder $num_ge
Run time: 0.0s
Theorem NET_ADD autoloading from theory `NETS` ...
NET_ADD =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\ (y tends y0)(mtop mr1,g) ==>
((\n. (x n) + (y n)) tends (x0 + y0))(mtop mr1,g))
Run time: 0.0s
SEQ_ADD =
|- !x x0 y y0.
x --> x0 /\ y --> y0 ==> (\n. (x n) + (y n)) --> (x0 + y0)
Run time: 0.0s
Intermediate theorems generated: 33
Theorem NET_MUL autoloading from theory `NETS` ...
NET_MUL =
|- !g.
dorder g ==>
(!x y x0 y0.
(x tends x0)(mtop mr1,g) /\ (y tends y0)(mtop mr1,g) ==>
((\n. (x n) * (y n)) tends (x0 * y0))(mtop mr1,g))
Run time: 0.0s
SEQ_MUL =
|- !x x0 y y0.
x --> x0 /\ y --> y0 ==> (\n. (x n) * (y n)) --> (x0 * y0)
Run time: 0.0s
Intermediate theorems generated: 33
Theorem NET_NEG autoloading from theory `NETS` ...
NET_NEG =
|- !g.
dorder g ==>
(!x x0.
(x tends x0)(mtop mr1,g) =
((\n. --(x n)) tends (-- x0))(mtop mr1,g))
Run time: 0.0s
SEQ_NEG = |- !x x0. x --> x0 = (\n. --(x n)) --> (-- x0)
Run time: 0.0s
Intermediate theorems generated: 26
Theorem NET_INV autoloading from theory `NETS` ...
NET_INV =
|- !g.
dorder g ==>
(!x x0.
(x tends x0)(mtop mr1,g) /\ ~(x0 = & 0) ==>
((\n. inv(x n)) tends (inv x0))(mtop mr1,g))
Run time: 0.0s
SEQ_INV =
|- !x x0. x --> x0 /\ ~(x0 = & 0) ==> (\n. inv(x n)) --> (inv x0)
Run time: 0.0s
Intermediate theorems generated: 28
Theorem NET_SUB autoloading from theory `NETS` ...
NET_SUB =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\ (y tends y0)(mtop mr1,g) ==>
((\n. (x n) - (y n)) tends (x0 - y0))(mtop mr1,g))
Run time: 0.0s
SEQ_SUB =
|- !x x0 y y0.
x --> x0 /\ y --> y0 ==> (\n. (x n) - (y n)) --> (x0 - y0)
Run time: 0.0s
Intermediate theorems generated: 33
Theorem NET_DIV autoloading from theory `NETS` ...
NET_DIV =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\
(y tends y0)(mtop mr1,g) /\
~(y0 = & 0) ==>
((\n. (x n) / (y n)) tends (x0 / y0))(mtop mr1,g))
Run time: 0.0s
SEQ_DIV =
|- !x x0 y y0.
x --> x0 /\ y --> y0 /\ ~(y0 = & 0) ==>
(\n. (x n) / (y n)) --> (x0 / y0)
Run time: 0.0s
Intermediate theorems generated: 35
Theorem MTOP_TENDS_UNIQ autoloading from theory `NETS` ...
MTOP_TENDS_UNIQ =
|- !g d.
dorder g ==>
(x tends x0)(mtop d,g) /\ (x tends x1)(mtop d,g) ==>
(x0 = x1)
Run time: 0.0s
SEQ_UNIQ = |- !x x1 x2. x --> x1 /\ x --> x2 ==> (x1 = x2)
Run time: 0.0s
Intermediate theorems generated: 28
convergent = |- !f. convergent f = (?l. f --> l)
Run time: 0.0s
Intermediate theorems generated: 2
cauchy =
|- !f.
cauchy f =
(!e.
(& 0) < e ==>
(?N. !m n. m num_ge N /\ n num_ge N ==> (abs((f m) - (f n))) < e))
Run time: 0.0s
Intermediate theorems generated: 2
lim = |- !f. lim f = (@l. f --> l)
Run time: 0.0s
Intermediate theorems generated: 2
SEQ_LIM = |- !f. convergent f = f --> (lim f)
Run time: 0.0s
Intermediate theorems generated: 36
subseq = |- !f. subseq f = (!m n. m num_lt n ==> (f m) num_lt (f n))
Run time: 0.0s
Intermediate theorems generated: 2
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 num_add m = m) /\
(m num_add 0 = m) /\
((SUC m) num_add n = SUC(m num_add n)) /\
(m num_add (SUC n) = SUC(m num_add n))
Run time: 0.0s
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m num_lt n /\ n num_lt p ==> m num_lt p
Run time: 0.0s
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m num_add 1
Run time: 0.0s
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n num_lt m ==> (?p. m = n num_add (p num_add 1))
Run time: 0.0s
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n num_lt (SUC n)
Run time: 0.0s
SUBSEQ_SUC = |- !f. subseq f = (!n. (f n) num_lt (f(SUC n)))
Run time: 0.1s
Intermediate theorems generated: 182
mono =
|- !f.
mono f =
(!m n. m num_le n ==> (f m) <= (f n)) \/
(!m n. m num_le n ==> (f m) >= (f n))
Run time: 0.0s
Intermediate theorems generated: 2
Theorem REAL_LE_TRANS autoloading from theory `REAL` ...
REAL_LE_TRANS = |- !x y z. x <= y /\ y <= z ==> x <= z
Run time: 0.0s
Theorem REAL_LE_REFL autoloading from theory `REAL` ...
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
Theorem LESS_EQUAL_ADD autoloading from theory `arithmetic` ...
LESS_EQUAL_ADD = |- !m n. m num_le n ==> (?p. n = m num_add p)
Run time: 0.0s
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m num_le (SUC m)
Run time: 0.0s
Definition real_ge autoloading from theory `REAL` ...
real_ge = |- !x y. x >= y = y <= x
Run time: 0.0s
Intermediate theorems generated: 1
MONO_SUC =
|- !f. mono f = (!n. (f(SUC n)) >= (f n)) \/ (!n. (f(SUC n)) <= (f n))
Run time: 0.0s
Intermediate theorems generated: 528
Theorem REAL_LT_IMP_LE autoloading from theory `REAL` ...
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
Theorem REAL_LT_ADD1 autoloading from theory `REAL` ...
REAL_LT_ADD1 = |- !x y. x <= y ==> x < (y + (& 1))
Run time: 0.0s
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m num_lt (SUC n) = (m = n) \/ m num_lt n
Run time: 0.1s
Theorem REAL_LET_TOTAL autoloading from theory `REAL` ...
REAL_LET_TOTAL = |- !x y. x <= y \/ y < x
Run time: 0.0s
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n num_lt 0
Run time: 0.0s
MAX_LEMMA = |- !s N. ?k. !n. n num_lt N ==> (abs(s n)) < k
Run time: 0.0s
Intermediate theorems generated: 241
Theorem REAL_LTE_TRANS autoloading from theory `REAL` ...
REAL_LTE_TRANS = |- !x y z. x < y /\ y <= z ==> x < z
Run time: 0.0s
Theorem LESS_CASES autoloading from theory `arithmetic` ...
LESS_CASES = |- !m n. m num_lt n \/ n num_le m
Run time: 0.0s
Theorem REAL_LE_TOTAL autoloading from theory `REAL` ...
REAL_LE_TOTAL = |- !x y. x <= y \/ y <= x
Run time: 0.0s
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m num_le m
Run time: 0.0s
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n num_ge m = m num_le n
Run time: 0.0s
Theorem MR1_BOUNDED autoloading from theory `NETS` ...
MR1_BOUNDED =
|- !g f.
bounded(mr1,g)f = (?k N. g N N /\ (!n. g n N ==> (abs(f n)) < k))
Run time: 0.0s
SEQ_BOUNDED = |- !s. bounded(mr1,$num_ge)s = (?k. !n. (abs(s n)) < k)
Run time: 0.0s
Intermediate theorems generated: 273
Theorem REAL_LE_NEG autoloading from theory `REAL` ...
REAL_LE_NEG = |- !x y. (-- x) <= (-- y) = y <= x
Run time: 0.0s
Theorem REAL_LE_ADDR autoloading from theory `REAL` ...
REAL_LE_ADDR = |- !x y. x <= (x + y) = (& 0) <= y
Run time: 0.0s
Theorem ABS_LE autoloading from theory `REAL` ...
ABS_LE = |- !x. x <= (abs x)
Run time: 0.0s
Theorem ABS_POS autoloading from theory `REAL` ...
ABS_POS = |- !x. (& 0) <= (abs x)
Run time: 0.0s
Theorem REAL_LE_ADDL autoloading from theory `REAL` ...
REAL_LE_ADDL = |- !x y. y <= (x + y) = (& 0) <= x
Run time: 0.0s
Definition abs autoloading from theory `REAL` ...
abs = |- !x. abs x = ((& 0) <= x => x | -- x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_LT_01 autoloading from theory `REAL` ...
REAL_LT_01 = |- (& 0) < (& 1)
Run time: 0.0s
Theorem REAL_LT_ADDR autoloading from theory `REAL` ...
REAL_LT_ADDR = |- !x y. x < (x + y) = (& 0) < y
Run time: 0.0s
Theorem REAL_LET_TRANS autoloading from theory `REAL` ...
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.0s
SEQ_BOUNDED_2 =
|- !f k K. (!n. k <= (f n) /\ (f n) <= K) ==> bounded(mr1,$num_ge)f
Run time: 0.1s
Intermediate theorems generated: 334
Definition bounded autoloading from theory `NETS` ...
bounded =
|- !m g f.
bounded(m,g)f =
(?k x N. g N N /\ (!n. g n N ==> (dist m(f n,x)) < k))
Run time: 0.0s
Intermediate theorems generated: 1
SEQ_CBOUNDED = |- !f. cauchy f ==> bounded(mr1,$num_ge)f
Run time: 0.0s
Intermediate theorems generated: 110
Theorem REAL_LE_RADD autoloading from theory `REAL` ...
REAL_LE_RADD = |- !x y z. (x + z) <= (y + z) = x <= y
Run time: 0.0s
Theorem REAL_ADD_RINV autoloading from theory `REAL` ...
REAL_ADD_RINV = |- !x. x + (-- x) = & 0
Run time: 0.0s
Definition real_sub autoloading from theory `REAL` ...
real_sub = |- !x y. x - y = x + (-- y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_NEG_SUB autoloading from theory `REAL` ...
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
Theorem REAL_NOT_LT autoloading from theory `REAL` ...
REAL_NOT_LT = |- !x y. ~x < y = y <= x
Run time: 0.0s
Theorem REAL_LT_REFL autoloading from theory `REAL` ...
REAL_LT_REFL = |- !x. ~x < x
Run time: 0.0s
Theorem REAL_ADD_SYM autoloading from theory `REAL` ...
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Theorem REAL_LT_SUB_RADD autoloading from theory `REAL` ...
REAL_LT_SUB_RADD = |- !x y z. (x - y) < z = x < (z + y)
Run time: 0.0s
Theorem REAL_SUP autoloading from theory `REAL` ...
REAL_SUP =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x < z) ==>
(!y. (?x. P x /\ y < x) = y < (sup P))
Run time: 0.0s
SEQ_ICONV =
|- !f.
bounded(mr1,$num_ge)f /\ (!m n. m num_ge n ==> (f m) >= (f n)) ==>
convergent f
Run time: 0.0s
Intermediate theorems generated: 910
Theorem REAL_NEGNEG autoloading from theory `REAL` ...
REAL_NEGNEG = |- !x. --(-- x) = x
Run time: 0.1s
SEQ_NEG_CONV = |- !f. convergent f = convergent(\n. --(f n))
Run time: 0.0s
Intermediate theorems generated: 72
Theorem ABS_NEG autoloading from theory `REAL` ...
ABS_NEG = |- !x. abs(-- x) = abs x
Run time: 0.0s
SEQ_NEG_BOUNDED =
|- !f. bounded(mr1,$num_ge)(\n. --(f n)) = bounded(mr1,$num_ge)f
Run time: 0.0s
Intermediate theorems generated: 39
SEQ_BCONV = |- !f. bounded(mr1,$num_ge)f /\ mono f ==> convergent f
Run time: 0.0s
Intermediate theorems generated: 209
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m num_le n /\ n num_le p ==> m num_le p
Run time: 0.0s
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m num_le n = m num_lt n \/ (m = n)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m num_lt n = (SUC m) num_le n
Run time: 0.0s
Theorem REAL_NOT_LE autoloading from theory `REAL` ...
REAL_NOT_LE = |- !x y. ~x <= y = y < x
Run time: 0.0s
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m num_lt n ==> m num_le n
Run time: 0.0s
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Run time: 0.0s
Definition GREATER autoloading from theory `arithmetic` ...
GREATER = |- !m n. m num_gt n = n num_lt m
Run time: 0.0s
Intermediate theorems generated: 1
Theorem num_Axiom autoloading from theory `prim_rec` ...
num_Axiom = |- !e f. ?! fn. (fn 0 = e) /\ (!n. fn(SUC n) = f(fn n)n)
Run time: 0.0s
SEQ_MONOSUB = |- !s. ?f. subseq f /\ mono(\n. s(f n))
Run time: 0.1s
Intermediate theorems generated: 1286
SEQ_SBOUNDED =
|- !s f. bounded(mr1,$num_ge)s ==> bounded(mr1,$num_ge)(\n. s(f n))
Run time: 0.0s
Intermediate theorems generated: 34
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) num_le (SUC m) = n num_le m
Run time: 0.0s
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m num_lt n = n num_le m
Run time: 0.0s
SEQ_SUBLE = |- !f. subseq f ==> (!n. n num_le (f n))
Run time: 0.0s
Intermediate theorems generated: 116
Theorem LESS_EQ_CASES autoloading from theory `arithmetic` ...
LESS_EQ_CASES = |- !m n. m num_le n \/ n num_le m
Run time: 0.0s
SEQ_DIRECT =
|- !f. subseq f ==> (!N1 N2. ?n. n num_ge N1 /\ (f n) num_ge N2)
Run time: 0.0s
Intermediate theorems generated: 118
Theorem REAL_LT_ADD2 autoloading from theory `REAL` ...
REAL_LT_ADD2 = |- !w x y z. w < x /\ y < z ==> (w + y) < (x + z)
Run time: 0.0s
Theorem REAL_HALF_DOUBLE autoloading from theory `REAL` ...
REAL_HALF_DOUBLE = |- !x. (x / (& 2)) + (x / (& 2)) = x
Run time: 0.0s
Theorem ABS_TRIANGLE autoloading from theory `REAL` ...
ABS_TRIANGLE = |- !x y. (abs(x + y)) <= ((abs x) + (abs y))
Run time: 0.0s
Theorem REAL_SUB_TRIANGLE autoloading from theory `REAL` ...
REAL_SUB_TRIANGLE = |- !a b c. (a - b) + (b - c) = a - c
Run time: 0.0s
Theorem REAL_LT_HALF1 autoloading from theory `REAL` ...
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.0s
SEQ_CAUCHY = |- !f. cauchy f = convergent f
Run time: 0.0s
Intermediate theorems generated: 665
Theorem NET_LE autoloading from theory `NETS` ...
NET_LE =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\
(y tends y0)(mtop mr1,g) /\
(?N. g N N /\ (!n. g n N ==> (x n) <= (y n))) ==>
x0 <= y0)
Run time: 0.0s
SEQ_LE =
|- !f g l m.
f --> l /\ g --> m /\ (?N. !n. n num_ge N ==> (f n) <= (g n)) ==>
l <= m
Run time: 0.1s
Intermediate theorems generated: 80
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 num_lt (SUC n)
Run time: 0.0s
SEQ_SUC = |- !f l. f --> l = (\n. f(SUC n)) --> l
Run time: 0.0s
Intermediate theorems generated: 236
Theorem ABS_ABS autoloading from theory `REAL` ...
ABS_ABS = |- !x. abs(abs x) = abs x
Run time: 0.0s
Theorem REAL_SUB_RZERO autoloading from theory `REAL` ...
REAL_SUB_RZERO = |- !x. x - (& 0) = x
Run time: 0.0s
SEQ_ABS = |- !f. (\n. abs(f n)) --> (& 0) = f --> (& 0)
Run time: 0.0s
Intermediate theorems generated: 70
Theorem NET_ABS autoloading from theory `NETS` ...
NET_ABS =
|- !x x0.
(x tends x0)(mtop mr1,g) ==>
((\n. abs(x n)) tends (abs x0))(mtop mr1,g)
Run time: 0.0s
SEQ_ABS_IMP = |- !f l. f --> l ==> (\n. abs(f n)) --> (abs l)
Run time: 0.0s
Intermediate theorems generated: 20
Theorem REAL_LT_INV autoloading from theory `REAL` ...
REAL_LT_INV = |- !x y. (& 0) < x /\ x < y ==> (inv y) < (inv x)
Run time: 0.0s
Theorem REAL_INVINV autoloading from theory `REAL` ...
REAL_INVINV = |- !x. ~(x = & 0) ==> (inv(inv x) = x)
Run time: 0.0s
Theorem ABS_INV autoloading from theory `REAL` ...
ABS_INV = |- !x. ~(x = & 0) ==> (abs(inv x) = inv(abs x))
Run time: 0.0s
Theorem REAL_LT_IMP_NE autoloading from theory `REAL` ...
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
Theorem REAL_LT_TRANS autoloading from theory `REAL` ...
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.1s
Theorem REAL_INV_POS autoloading from theory `REAL` ...
REAL_INV_POS = |- !x. (& 0) < x ==> (& 0) < (inv x)
Run time: 0.0s
Definition real_gt autoloading from theory `REAL` ...
real_gt = |- !x y. x > y = y < x
Run time: 0.0s
Intermediate theorems generated: 1
SEQ_INV0 =
|- !f.
(!y. ?N. !n. n num_ge N ==> (f n) > y) ==> (\n. inv(f n)) --> (& 0)
Run time: 0.0s
Intermediate theorems generated: 423
Theorem POW_0 autoloading from theory `REAL` ...
POW_0 = |- !n. (& 0) pow (SUC n) = & 0
Run time: 0.0s
Theorem REAL_SUB_ADD autoloading from theory `REAL` ...
REAL_SUB_ADD = |- !x y. (x - y) + y = x
Run time: 0.0s
Theorem POW_PLUS1 autoloading from theory `REAL` ...
POW_PLUS1 =
|- !e. (& 0) < e ==> (!n. ((& 1) + ((& n) * e)) <= (((& 1) + e) pow n))
Run time: 0.0s
Theorem REAL_LT_ADDL autoloading from theory `REAL` ...
REAL_LT_ADDL = |- !x y. y < (x + y) = (& 0) < x
Run time: 0.0s
Theorem REAL_LE autoloading from theory `REAL` ...
REAL_LE = |- !m n. (& m) <= (& n) = m num_le n
Run time: 0.0s
Theorem REAL_LE_RMUL autoloading from theory `REAL` ...
REAL_LE_RMUL = |- !x y z. (& 0) < z ==> ((x * z) <= (y * z) = x <= y)
Run time: 0.0s
Theorem REAL_ARCH autoloading from theory `REAL` ...
REAL_ARCH = |- !x. (& 0) < x ==> (!y. ?n. y < ((& n) * x))
Run time: 0.0s
Theorem REAL_INV1 autoloading from theory `REAL` ...
REAL_INV1 = |- inv(& 1) = & 1
Run time: 0.0s
Theorem REAL_ADD_LID autoloading from theory `REAL` ...
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Theorem REAL_LT_SUB_LADD autoloading from theory `REAL` ...
REAL_LT_SUB_LADD = |- !x y z. x < (y - z) = (x + z) < y
Run time: 0.0s
Theorem POW_INV autoloading from theory `REAL` ...
POW_INV = |- !c. ~(c = & 0) ==> (!n. inv(c pow n) = (inv c) pow n)
Run time: 0.0s
Theorem ABS_NZ autoloading from theory `REAL` ...
ABS_NZ = |- !x. ~(x = & 0) = (& 0) < (abs x)
Run time: 0.0s
Theorem POW_NZ autoloading from theory `REAL` ...
POW_NZ = |- !c n. ~(c = & 0) ==> ~(c pow n = & 0)
Run time: 0.0s
Theorem REAL_LE_LT autoloading from theory `REAL` ...
REAL_LE_LT = |- !x y. x <= y = x < y \/ (x = y)
Run time: 0.0s
SEQ_POWER_ABS = |- !c. (abs c) < (& 1) ==> (\n. (abs c) pow n) --> (& 0)
Run time: 0.0s
Intermediate theorems generated: 573
Theorem POW_ABS autoloading from theory `REAL` ...
POW_ABS = |- !c n. (abs c) pow n = abs(c pow n)
Run time: 0.0s
SEQ_POWER = |- !c. (abs c) < (& 1) ==> (\n. c pow n) --> (& 0)
Run time: 0.0s
Intermediate theorems generated: 49
Theorem REAL_LE_LADD autoloading from theory `REAL` ...
REAL_LE_LADD = |- !x y z. (x + y) <= (x + z) = y <= z
Run time: 0.0s
Theorem REAL_SUB_LE autoloading from theory `REAL` ...
REAL_SUB_LE = |- !x y. (& 0) <= (x - y) = y <= x
Run time: 0.0s
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m num_le (m num_add n)
Run time: 0.0s
Theorem REAL_SUB_LT autoloading from theory `REAL` ...
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
NEST_LEMMA =
|- !f g.
(!n. (f(SUC n)) >= (f n)) /\
(!n. (g(SUC n)) <= (g n)) /\
(!n. (f n) <= (g n)) ==>
(?l m.
l <= m /\
((!n. (f n) <= l) /\ f --> l) /\
(!n. m <= (g n)) /\
g --> m)
Run time: 0.2s
Intermediate theorems generated: 2190
Theorem REAL_SUB_0 autoloading from theory `REAL` ...
REAL_SUB_0 = |- !x y. (x - y = & 0) = (x = y)
Run time: 0.0s
NEST_LEMMA_UNIQ =
|- !f g.
(!n. (f(SUC n)) >= (f n)) /\
(!n. (g(SUC n)) <= (g n)) /\
(!n. (f n) <= (g n)) /\
(\n. (f n) - (g n)) --> (& 0) ==>
(?l. ((!n. (f n) <= l) /\ f --> l) /\ (!n. l <= (g n)) /\ g --> l)
Run time: 0.0s
Intermediate theorems generated: 295
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m num_add n = n num_add m
Run time: 0.0s
Theorem REAL_MUL_LINV autoloading from theory `REAL` ...
REAL_MUL_LINV = |- !x. ~(x = & 0) ==> ((inv x) * x = & 1)
Run time: 0.0s
Theorem REAL_LT autoloading from theory `REAL` ...
REAL_LT = |- !m n. (& m) < (& n) = m num_lt n
Run time: 0.0s
Theorem REAL_LT_RMUL autoloading from theory `REAL` ...
REAL_LT_RMUL = |- !x y z. (& 0) < z ==> ((x * z) < (y * z) = x < y)
Run time: 0.0s
Theorem ABS_N autoloading from theory `REAL` ...
ABS_N = |- !n. abs(& n) = & n
Run time: 0.0s
Theorem REAL_MUL_RZERO autoloading from theory `REAL` ...
REAL_MUL_RZERO = |- !x. x * (& 0) = & 0
Run time: 0.0s
Theorem REAL_NEG_0 autoloading from theory `REAL` ...
REAL_NEG_0 = |- --(& 0) = & 0
Run time: 0.0s
Theorem REAL_MUL_RINV autoloading from theory `REAL` ...
REAL_MUL_RINV = |- !x. ~(x = & 0) ==> (x * (inv x) = & 1)
Run time: 0.0s
Theorem REAL_MUL_LID autoloading from theory `REAL` ...
REAL_MUL_LID = |- !x. (& 1) * x = x
Run time: 0.0s
Theorem REAL_INV_MUL autoloading from theory `REAL` ...
REAL_INV_MUL =
|- !x y. ~(x = & 0) /\ ~(y = & 0) ==> (inv(x * y) = (inv x) * (inv y))
Run time: 0.0s
Theorem REAL_MUL_ASSOC autoloading from theory `REAL` ...
REAL_MUL_ASSOC = |- !x y z. x * (y * z) = (x * y) * z
Run time: 0.0s
Theorem REAL_MUL_SYM autoloading from theory `REAL` ...
REAL_MUL_SYM = |- !x y. x * y = y * x
Run time: 0.0s
Theorem REAL_ADD_ASSOC autoloading from theory `REAL` ...
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.0s
Theorem REAL_ADD_LINV autoloading from theory `REAL` ...
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Theorem REAL_ADD_RID autoloading from theory `REAL` ...
REAL_ADD_RID = |- !x. x + (& 0) = x
Run time: 0.0s
Theorem REAL_NEG_ADD autoloading from theory `REAL` ...
REAL_NEG_ADD = |- !x y. --(x + y) = (-- x) + (-- y)
Run time: 0.0s
Theorem REAL_DOUBLE autoloading from theory `REAL` ...
REAL_DOUBLE = |- !x. x + x = (& 2) * x
Run time: 0.0s
Theorem REAL_INJ autoloading from theory `REAL` ...
REAL_INJ = |- !m n. (& m = & n) = (m = n)
Run time: 0.0s
Theorem REAL_DIV_LMUL autoloading from theory `REAL` ...
REAL_DIV_LMUL = |- !x y. ~(y = & 0) ==> (y * (x / y) = x)
Run time: 0.0s
Theorem REAL_SUB_LDISTRIB autoloading from theory `REAL` ...
REAL_SUB_LDISTRIB = |- !x y z. x * (y - z) = (x * y) - (x * z)
Run time: 0.0s
Theorem REAL_EQ_LMUL_IMP autoloading from theory `REAL` ...
REAL_EQ_LMUL_IMP = |- !x y z. ~(x = & 0) /\ (x * y = x * z) ==> (y = z)
Run time: 0.0s
Theorem REAL_MUL_RID autoloading from theory `REAL` ...
REAL_MUL_RID = |- !x. x * (& 1) = x
Run time: 0.0s
Definition real_div autoloading from theory `REAL` ...
real_div = |- !x y. x / y = x * (inv y)
Run time: 0.0s
Intermediate theorems generated: 1
Definition pow autoloading from theory `REAL` ...
pow = |- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_MIDDLE1 autoloading from theory `REAL` ...
REAL_MIDDLE1 = |- !a b. a <= b ==> a <= ((a + b) / (& 2))
Run time: 0.0s
Theorem REAL_MIDDLE2 autoloading from theory `REAL` ...
REAL_MIDDLE2 = |- !a b. a <= b ==> ((a + b) / (& 2)) <= b
Run time: 0.0s
BOLZANO_LEMMA =
|- !P.
(!a b c. a <= b /\ b <= c /\ P(a,b) /\ P(b,c) ==> P(a,c)) /\
(!x.
?d.
(& 0) < d /\ (!a b. a <= x /\ x <= b /\ (b - a) < d ==> P(a,b))) ==>
(!a b. a <= b ==> P(a,b))
Run time: 0.3s
Intermediate theorems generated: 3396
sums = |- !f s. f sums s = (\n. Sum(0,n)f) --> s
Run time: 0.0s
Intermediate theorems generated: 2
summable = |- !f. summable f = (?s. f sums s)
Run time: 0.0s
Intermediate theorems generated: 2
suminf = |- !f. suminf f = (@s. f sums s)
Run time: 0.0s
Intermediate theorems generated: 2
SUM_SUMMABLE = |- !f l. f sums l ==> summable f
Run time: 0.0s
Intermediate theorems generated: 16
SUMMABLE_SUM = |- !f. summable f ==> f sums (suminf f)
Run time: 0.1s
Intermediate theorems generated: 30
SUM_UNIQ = |- !f x. f sums x ==> (x = suminf f)
Run time: 0.0s
Intermediate theorems generated: 69
Theorem SUM_ZERO autoloading from theory `REAL` ...
SUM_ZERO =
|- !f N.
(!n. n num_ge N ==> (f n = & 0)) ==>
(!m n. m num_ge N ==> (Sum(m,n)f = & 0))
Run time: 0.0s
Theorem REAL_ADD_RID_UNIQ autoloading from theory `REAL` ...
REAL_ADD_RID_UNIQ = |- !x y. (x + y = x) = (y = & 0)
Run time: 0.0s
Theorem SUM_TWO autoloading from theory `REAL` ...
SUM_TWO = |- !f n p. (Sum(0,n)f) + (Sum(n,p)f) = Sum(0,n num_add p)f
Run time: 0.0s
Theorem ABS_ZERO autoloading from theory `REAL` ...
ABS_ZERO = |- !x. (abs x = & 0) = (x = & 0)
Run time: 0.0s
SER_0 = |- !f n. (!m. n num_le m ==> (f m = & 0)) ==> f sums (Sum(0,n)f)
Run time: 0.0s
Intermediate theorems generated: 175
Theorem SUM_POS_GEN autoloading from theory `REAL` ...
SUM_POS_GEN =
|- !f m.
(!n. m num_le n ==> (& 0) <= (f n)) ==> (!n. (& 0) <= (Sum(m,n)f))
Run time: 0.0s
SER_POS_LE =
|- !f n.
summable f /\ (!m. n num_le m ==> (& 0) <= (f m)) ==>
(Sum(0,n)f) <= (suminf f)
Run time: 0.1s
Intermediate theorems generated: 220
Theorem Sum autoloading from theory `REAL` ...
Sum =
|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
Run time: 0.0s
SER_POS_LT =
|- !f n.
summable f /\ (!m. n num_le m ==> (& 0) < (f m)) ==>
(Sum(0,n)f) < (suminf f)
Run time: 0.0s
Intermediate theorems generated: 209
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n num_lt n
Run time: 0.0s
Theorem LESS_EQ_0 autoloading from theory `arithmetic` ...
LESS_EQ_0 = |- !n. n num_le 0 = (n = 0)
Run time: 0.0s
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 num_mul m = 0) /\
(m num_mul 0 = 0) /\
(1 num_mul m = m) /\
(m num_mul 1 = m) /\
((SUC m) num_mul n = (m num_mul n) num_add n) /\
(m num_mul (SUC n) = m num_add (m num_mul n))
Run time: 0.0s
Theorem SUM_GROUP autoloading from theory `REAL` ...
SUM_GROUP =
|- !n k f. Sum(0,n)(\m. Sum(m num_mul k,k)f) = Sum(0,n num_mul k)f
Run time: 0.0s
SER_GROUP =
|- !f k.
summable f /\ 0 num_lt k ==>
(\n. Sum(n num_mul k,k)f) sums (suminf f)
Run time: 0.1s
Intermediate theorems generated: 258
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m num_mul n = n num_mul m
Run time: 0.0s
SER_PAIR =
|- !f. summable f ==> (\n. Sum(2 num_mul n,2)f) sums (suminf f)
Run time: 0.0s
Intermediate theorems generated: 34
Theorem SUM_OFFSET autoloading from theory `REAL` ...
SUM_OFFSET =
|- !f n k.
Sum(0,n)(\m. f(m num_add k)) = (Sum(0,n num_add k)f) - (Sum(0,k)f)
Run time: 0.0s
SER_OFFSET =
|- !f.
summable f ==>
(!k. (\n. f(n num_add k)) sums ((suminf f) - (Sum(0,k)f)))
Run time: 0.1s
Intermediate theorems generated: 299
Theorem REAL_EQ_IMP_LE autoloading from theory `REAL` ...
REAL_EQ_IMP_LE = |- !x y. (x = y) ==> x <= y
Run time: 0.0s
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m num_add (n num_add p) = (m num_add n) num_add p
Run time: 0.0s
SER_POS_LT_PAIR =
|- !f n.
summable f /\
(!d.
(& 0) <
((f(n num_add (2 num_mul d))) +
(f(n num_add ((2 num_mul d) num_add 1))))) ==>
(Sum(0,n)f) < (suminf f)
Run time: 0.1s
Intermediate theorems generated: 1204
Theorem SUM_ADD autoloading from theory `REAL` ...
SUM_ADD =
|- !f g m n. Sum(m,n)(\n'. (f n') + (g n')) = (Sum(m,n)f) + (Sum(m,n)g)
Run time: 0.0s
SER_ADD =
|- !x x0 y y0.
x sums x0 /\ y sums y0 ==> (\n. (x n) + (y n)) sums (x0 + y0)
Run time: 0.0s
Intermediate theorems generated: 62
Theorem SUM_CMUL autoloading from theory `REAL` ...
SUM_CMUL = |- !f c m n. Sum(m,n)(\n'. c * (f n')) = c * (Sum(m,n)f)
Run time: 0.0s
SER_CMUL = |- !x x0 c. x sums x0 ==> (\n. c * (x n)) sums (c * x0)
Run time: 0.1s
Intermediate theorems generated: 82
Theorem REAL_NEG_MINUS1 autoloading from theory `REAL` ...
REAL_NEG_MINUS1 = |- !x. -- x = (--(& 1)) * x
Run time: 0.0s
SER_NEG = |- !x x0. x sums x0 ==> (\n. --(x n)) sums (-- x0)
Run time: 0.0s
Intermediate theorems generated: 17
SER_SUB =
|- !x x0 y y0.
x sums x0 /\ y sums y0 ==> (\n. (x n) - (y n)) sums (x0 - y0)
Run time: 0.0s
Intermediate theorems generated: 43
SER_CDIV = |- !x x0 c. x sums x0 ==> (\n. (x n) / c) sums (x0 / c)
Run time: 0.0s
Intermediate theorems generated: 35
Theorem SUM_DIFF autoloading from theory `REAL` ...
SUM_DIFF = |- !f m n. Sum(m,n)f = (Sum(0,m num_add n)f) - (Sum(0,m)f)
Run time: 0.0s
SER_CAUCHY =
|- !f.
summable f =
(!e. (& 0) < e ==> (?N. !m n. m num_ge N ==> (abs(Sum(m,n)f)) < e))
Run time: 0.1s
Intermediate theorems generated: 412
SER_ZERO = |- !f. summable f ==> f --> (& 0)
Run time: 0.0s
Intermediate theorems generated: 121
Theorem SUM_LE autoloading from theory `REAL` ...
SUM_LE =
|- !f g m n.
(!r. m num_le r /\ r num_lt (n num_add m) ==> (f r) <= (g r)) ==>
(Sum(m,n)f) <= (Sum(m,n)g)
Run time: 0.0s
Theorem ABS_SUM autoloading from theory `REAL` ...
ABS_SUM = |- !f m n. (abs(Sum(m,n)f)) <= (Sum(m,n)(\n'. abs(f n')))
Run time: 0.0s
SER_COMPAR =
|- !f g.
(?N. !n. n num_ge N ==> (abs(f n)) <= (g n)) /\ summable g ==>
summable f
Run time: 0.0s
Intermediate theorems generated: 395
SER_COMPARA =
|- !f g.
(?N. !n. n num_ge N ==> (abs(f n)) <= (g n)) /\ summable g ==>
summable(\k. abs(f k))
Run time: 0.0s
Intermediate theorems generated: 41
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 num_le n
Run time: 0.0s
SER_LE =
|- !f g.
(!n. (f n) <= (g n)) /\ summable f /\ summable g ==>
(suminf f) <= (suminf g)
Run time: 0.1s
Intermediate theorems generated: 191
SER_LE2 =
|- !f g.
(!n. (abs(f n)) <= (g n)) /\ summable g ==>
summable f /\ (suminf f) <= (suminf g)
Run time: 0.0s
Intermediate theorems generated: 136
Theorem SUM_ABS autoloading from theory `REAL` ...
SUM_ABS =
|- !f m n. abs(Sum(m,n)(\m. abs(f m))) = Sum(m,n)(\m. abs(f m))
Run time: 0.0s
SER_ACONV = |- !f. summable(\n. abs(f n)) ==> summable f
Run time: 0.0s
Intermediate theorems generated: 126
Theorem SUM_ABS_LE autoloading from theory `REAL` ...
SUM_ABS_LE = |- !f m n. (abs(Sum(m,n)f)) <= (Sum(m,n)(\n'. abs(f n')))
Run time: 0.0s
SER_ABS =
|- !f.
summable(\n. abs(f n)) ==> (abs(suminf f)) <= (suminf(\n. abs(f n)))
Run time: 0.1s
Intermediate theorems generated: 92
Theorem REAL_DIV_RMUL autoloading from theory `REAL` ...
REAL_DIV_RMUL = |- !x y. ~(y = & 0) ==> ((x / y) * y = x)
Run time: 0.0s
Theorem REAL_RDISTRIB autoloading from theory `REAL` ...
REAL_RDISTRIB = |- !x y z. (x + y) * z = (x * z) + (y * z)
Run time: 0.0s
Theorem REAL_EQ_RMUL autoloading from theory `REAL` ...
REAL_EQ_RMUL = |- !x y z. (x * z = y * z) = (z = & 0) \/ (x = y)
Run time: 0.0s
Theorem REAL_DIV_LZERO autoloading from theory `REAL` ...
REAL_DIV_LZERO = |- !x. (& 0) / x = & 0
Run time: 0.0s
GP_FINITE =
|- !x.
~(x = & 1) ==>
(!n. Sum(0,n)(\n'. x pow n') = ((x pow n) - (& 1)) / (x - (& 1)))
Run time: 0.0s
Intermediate theorems generated: 411
Theorem REAL_NEG_INV autoloading from theory `REAL` ...
REAL_NEG_INV = |- !x. ~(x = & 0) ==> (--(inv x) = inv(-- x))
Run time: 0.0s
Theorem REAL_NEG_MUL2 autoloading from theory `REAL` ...
REAL_NEG_MUL2 = |- !x y. (-- x) * (-- y) = x * y
Run time: 0.1s
Theorem REAL_INV_1OVER autoloading from theory `REAL` ...
REAL_INV_1OVER = |- !x. inv x = (& 1) / x
Run time: 0.0s
Theorem ABS_1 autoloading from theory `REAL` ...
ABS_1 = |- abs(& 1) = & 1
Run time: 0.0s
GP = |- !x. (abs x) < (& 1) ==> (\n. x pow n) sums (inv((& 1) - x))
Run time: 0.0s
Intermediate theorems generated: 343
Theorem REAL_NEG_LMUL autoloading from theory `REAL` ...
REAL_NEG_LMUL = |- !x y. --(x * y) = (-- x) * y
Run time: 0.0s
Theorem REAL_LE_MUL autoloading from theory `REAL` ...
REAL_LE_MUL = |- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x * y)
Run time: 0.0s
Theorem REAL_NEG_GE0 autoloading from theory `REAL` ...
REAL_NEG_GE0 = |- !x. (& 0) <= (-- x) = x <= (& 0)
Run time: 0.0s
ABS_NEG_LEMMA =
|- !c. c <= (& 0) ==> (!x y. (abs x) <= (c * (abs y)) ==> (x = & 0))
Run time: 0.0s
Intermediate theorems generated: 114
Theorem REAL_LE_LMUL autoloading from theory `REAL` ...
REAL_LE_LMUL = |- !x y z. (& 0) < x ==> ((x * y) <= (x * z) = y <= z)
Run time: 0.0s
Theorem POW_ADD autoloading from theory `REAL` ...
POW_ADD = |- !c m n. c pow (m num_add n) = (c pow m) * (c pow n)
Run time: 0.0s
Theorem OR_LESS autoloading from theory `arithmetic` ...
OR_LESS = |- !m n. (SUC m) num_le n ==> m num_lt n
Run time: 0.0s
SER_RATIO =
|- !f c N.
c < (& 1) /\
(!n. n num_ge N ==> (abs(f(SUC n))) <= (c * (abs(f n)))) ==>
summable f
Run time: 0.1s
Intermediate theorems generated: 683
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File seq.ml loaded
() : void
Run time: 3.7s
Intermediate theorems generated: 18704
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `lim.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory SEQ loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.1s
real_interface_map =
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 43
() : void
Run time: 0.1s
() : void
Run time: 0.0s
tends_real_real =
|- !f l x0.
(f tends_real_real l)x0 = (f tends l)(mtop mr1,tendsto(mr1,x0))
Run time: 0.0s
Intermediate theorems generated: 2
[] : (string # string) list
Run time: 0.0s
Theorem ABS_SUB autoloading from theory `REAL` ...
ABS_SUB = |- !x y. abs(x - y) = abs(y - x)
Run time: 0.0s
Theorem MR1_DEF autoloading from theory `TOPOLOGY` ...
MR1_DEF = |- !x y. dist mr1(x,y) = abs(y - x)
Run time: 0.0s
Theorem MR1_LIMPT autoloading from theory `TOPOLOGY` ...
MR1_LIMPT = |- !x. limpt(mtop mr1)x re_universe
Run time: 0.0s
Theorem LIM_TENDS2 autoloading from theory `NETS` ...
LIM_TENDS2 =
|- !m1 m2 f x0 y0.
limpt(mtop m1)x0 re_universe ==>
((f tends y0)(mtop m2,tendsto(m1,x0)) =
(!e.
(& 0) < e ==>
(?d.
(& 0) < d /\
(!x.
(& 0) < (dist m1(x,x0)) /\ (dist m1(x,x0)) < d ==>
(dist m2(f x,y0)) < e))))
Run time: 0.0s
LIM =
|- !f y0 x0.
(f --> y0)x0 =
(!e.
(& 0) < e ==>
(?d.
(& 0) < d /\
(!x.
(& 0) < (abs(x - x0)) /\ (abs(x - x0)) < d ==>
(abs((f x) - y0)) < e)))
Run time: 0.0s
Intermediate theorems generated: 102
Theorem REAL_SUB_0 autoloading from theory `REAL` ...
REAL_SUB_0 = |- !x y. (x - y = & 0) = (x = y)
Run time: 0.0s
Theorem ABS_NZ autoloading from theory `REAL` ...
ABS_NZ = |- !x. ~(x = & 0) = (& 0) < (abs x)
Run time: 0.0s
Theorem MTOP_LIMPT autoloading from theory `TOPOLOGY` ...
MTOP_LIMPT =
|- !m x S.
limpt(mtop m)x S =
(!e. (& 0) < e ==> (?y. ~(x = y) /\ S y /\ (dist m(x,y)) < e))
Run time: 0.0s
Theorem REAL_LE_REFL autoloading from theory `REAL` ...
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
Definition tendsto autoloading from theory `NETS` ...
tendsto =
|- !m x y z.
tendsto(m,x)y z =
(& 0) < (dist m(x,y)) /\ (dist m(x,y)) <= (dist m(x,z))
Run time: 0.0s
Intermediate theorems generated: 1
Theorem METRIC_SAME autoloading from theory `TOPOLOGY` ...
METRIC_SAME = |- !m x. dist m(x,x) = & 0
Run time: 0.0s
Theorem MTOP_TENDS autoloading from theory `NETS` ...
MTOP_TENDS =
|- !d g x x0.
(x tends x0)(mtop d,g) =
(!e.
(& 0) < e ==> (?n. g n n /\ (!m. g m n ==> (dist d(x m,x0)) < e)))
Run time: 0.0s
LIM_CONST = |- !k x. ((\x. k) --> k)x
Run time: 0.1s
Intermediate theorems generated: 193
Theorem DORDER_TENDSTO autoloading from theory `NETS` ...
DORDER_TENDSTO = |- !m x. dorder(tendsto(m,x))
Run time: 0.0s
Theorem NET_ADD autoloading from theory `NETS` ...
NET_ADD =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\ (y tends y0)(mtop mr1,g) ==>
((\n. (x n) + (y n)) tends (x0 + y0))(mtop mr1,g))
Run time: 0.0s
LIM_ADD =
|- !f g l m.
(f --> l)x /\ (g --> m)x ==> ((\x. (f x) + (g x)) --> (l + m))x
Run time: 0.0s
Intermediate theorems generated: 40
Theorem NET_MUL autoloading from theory `NETS` ...
NET_MUL =
|- !g.
dorder g ==>
(!x y x0 y0.
(x tends x0)(mtop mr1,g) /\ (y tends y0)(mtop mr1,g) ==>
((\n. (x n) * (y n)) tends (x0 * y0))(mtop mr1,g))
Run time: 0.0s
LIM_MUL =
|- !f g l m.
(f --> l)x /\ (g --> m)x ==> ((\x. (f x) * (g x)) --> (l * m))x
Run time: 0.0s
Intermediate theorems generated: 40
Theorem NET_NEG autoloading from theory `NETS` ...
NET_NEG =
|- !g.
dorder g ==>
(!x x0.
(x tends x0)(mtop mr1,g) =
((\n. --(x n)) tends (-- x0))(mtop mr1,g))
Run time: 0.0s
LIM_NEG = |- !f l. (f --> l)x = ((\x. --(f x)) --> (-- l))x
Run time: 0.0s
Intermediate theorems generated: 33
Theorem NET_INV autoloading from theory `NETS` ...
NET_INV =
|- !g.
dorder g ==>
(!x x0.
(x tends x0)(mtop mr1,g) /\ ~(x0 = & 0) ==>
((\n. inv(x n)) tends (inv x0))(mtop mr1,g))
Run time: 0.0s
LIM_INV =
|- !f l. (f --> l)x /\ ~(l = & 0) ==> ((\x. inv(f x)) --> (inv l))x
Run time: 0.0s
Intermediate theorems generated: 35
Theorem NET_SUB autoloading from theory `NETS` ...
NET_SUB =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\ (y tends y0)(mtop mr1,g) ==>
((\n. (x n) - (y n)) tends (x0 - y0))(mtop mr1,g))
Run time: 0.0s
LIM_SUB =
|- !f g l m.
(f --> l)x /\ (g --> m)x ==> ((\x. (f x) - (g x)) --> (l - m))x
Run time: 0.0s
Intermediate theorems generated: 40
Theorem NET_DIV autoloading from theory `NETS` ...
NET_DIV =
|- !g.
dorder g ==>
(!x x0 y y0.
(x tends x0)(mtop mr1,g) /\
(y tends y0)(mtop mr1,g) /\
~(y0 = & 0) ==>
((\n. (x n) / (y n)) tends (x0 / y0))(mtop mr1,g))
Run time: 0.0s
LIM_DIV =
|- !f g l m.
(f --> l)x /\ (g --> m)x /\ ~(m = & 0) ==>
((\x. (f x) / (g x)) --> (l / m))x
Run time: 0.0s
Intermediate theorems generated: 42
Theorem NET_NULL autoloading from theory `NETS` ...
NET_NULL =
|- !g x x0.
(x tends x0)(mtop mr1,g) =
((\n. (x n) - x0) tends (& 0))(mtop mr1,g)
Run time: 0.0s
LIM_NULL = |- !f l x. (f --> l)x = ((\x. (f x) - l) --> (& 0))x
Run time: 0.0s
Intermediate theorems generated: 23
LIM_X = |- !x0. ((\x. x) --> x0)x0
Run time: 0.1s
Intermediate theorems generated: 52
Theorem MTOP_TENDS_UNIQ autoloading from theory `NETS` ...
MTOP_TENDS_UNIQ =
|- !g d.
dorder g ==>
(x tends x0)(mtop d,g) /\ (x tends x1)(mtop d,g) ==>
(x0 = x1)
Run time: 0.0s
LIM_UNIQ = |- !f l m x. (f --> l)x /\ (f --> m)x ==> (l = m)
Run time: 0.0s
Intermediate theorems generated: 36
LIM_EQUAL =
|- !f g l x0.
(!x. ~(x = x0) ==> (f x = g x)) ==> ((f --> l)x0 = (g --> l)x0)
Run time: 0.0s
Intermediate theorems generated: 171
Theorem REAL_LT_TRANS autoloading from theory `REAL` ...
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_LT_ADD2 autoloading from theory `REAL` ...
REAL_LT_ADD2 = |- !w x y z. w < x /\ y < z ==> (w + y) < (x + z)
Run time: 0.0s
Theorem ABS_TRIANGLE autoloading from theory `REAL` ...
ABS_TRIANGLE = |- !x y. (abs(x + y)) <= ((abs x) + (abs y))
Run time: 0.0s
Theorem REAL_SUB_TRIANGLE autoloading from theory `REAL` ...
REAL_SUB_TRIANGLE = |- !a b c. (a - b) + (b - c) = a - c
Run time: 0.0s
Theorem REAL_LET_TRANS autoloading from theory `REAL` ...
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_HALF_DOUBLE autoloading from theory `REAL` ...
REAL_HALF_DOUBLE = |- !x. (x / (& 2)) + (x / (& 2)) = x
Run time: 0.0s
Theorem REAL_LTE_TRANS autoloading from theory `REAL` ...
REAL_LTE_TRANS = |- !x y z. x < y /\ y <= z ==> x < z
Run time: 0.0s
Theorem REAL_DOWN2 autoloading from theory `REAL` ...
REAL_DOWN2 =
|- !x y. (& 0) < x /\ (& 0) < y ==> (?z. (& 0) < z /\ z < x /\ z < y)
Run time: 0.0s
Theorem REAL_SUB_RZERO autoloading from theory `REAL` ...
REAL_SUB_RZERO = |- !x. x - (& 0) = x
Run time: 0.0s
Theorem REAL_LT_HALF1 autoloading from theory `REAL` ...
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.0s
LIM_TRANSFORM =
|- !f g x0 l.
((\x. (f x) - (g x)) --> (& 0))x0 /\ (g --> l)x0 ==> (f --> l)x0
Run time: 0.1s
Intermediate theorems generated: 473
diffl =
|- !f l x. (f diffl l)x = ((\h. ((f(x + h)) - (f x)) / h) --> l)(& 0)
Run time: 0.0s
Intermediate theorems generated: 2
contl = |- !f x. f contl x = ((\h. f(x + h)) --> (f x))(& 0)
Run time: 0.0s
Intermediate theorems generated: 2
differentiable = |- !f x. f differentiable x = (?l. (f diffl l)x)
Run time: 0.0s
Intermediate theorems generated: 2
DIFF_UNIQ = |- !f l m x. (f diffl l)x /\ (f diffl m)x ==> (l = m)
Run time: 0.0s
Intermediate theorems generated: 26
Theorem REAL_MUL_RZERO autoloading from theory `REAL` ...
REAL_MUL_RZERO = |- !x. x * (& 0) = & 0
Run time: 0.0s
Theorem REAL_DIV_RMUL autoloading from theory `REAL` ...
REAL_DIV_RMUL = |- !x y. ~(y = & 0) ==> ((x / y) * y = x)
Run time: 0.0s
DIFF_CONT = |- !f l x. (f diffl l)x ==> f contl x
Run time: 0.0s
Intermediate theorems generated: 290
Theorem REAL_ADD_SUB autoloading from theory `REAL` ...
REAL_ADD_SUB = |- !x y. (x + y) - x = y
Run time: 0.0s
Theorem REAL_SUB_ADD2 autoloading from theory `REAL` ...
REAL_SUB_ADD2 = |- !x y. y + (x - y) = x
Run time: 0.0s
CONTL_LIM = |- !f x. f contl x = (f --> (f x))x
Run time: 0.0s
Intermediate theorems generated: 275
CONT_CONST = |- !x. (\x. k) contl x
Run time: 0.0s
Intermediate theorems generated: 20
CONT_ADD = |- !x. f contl x /\ g contl x ==> (\x. (f x) + (g x)) contl x
Run time: 0.0s
Intermediate theorems generated: 29
CONT_MUL = |- !x. f contl x /\ g contl x ==> (\x. (f x) * (g x)) contl x
Run time: 0.0s
Intermediate theorems generated: 29
CONT_NEG = |- !x. f contl x ==> (\x. --(f x)) contl x
Run time: 0.1s
Intermediate theorems generated: 43
CONT_INV = |- !x. f contl x /\ ~(f x = & 0) ==> (\x. inv(f x)) contl x
Run time: 0.0s
Intermediate theorems generated: 26
CONT_SUB = |- !x. f contl x /\ g contl x ==> (\x. (f x) - (g x)) contl x
Run time: 0.0s
Intermediate theorems generated: 29
CONT_DIV =
|- !x.
f contl x /\ g contl x /\ ~(g x = & 0) ==>
(\x. (f x) / (g x)) contl x
Run time: 0.0s
Intermediate theorems generated: 31
Theorem REAL_LT_IMP_LE autoloading from theory `REAL` ...
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
Theorem REAL_NOT_LT autoloading from theory `REAL` ...
REAL_NOT_LT = |- !x y. ~x < y = y <= x
Run time: 0.0s
Theorem REAL_SUB_ADD autoloading from theory `REAL` ...
REAL_SUB_ADD = |- !x y. (x - y) + y = x
Run time: 0.0s
Theorem REAL_ADD_SYM autoloading from theory `REAL` ...
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Theorem REAL_LE_RADD autoloading from theory `REAL` ...
REAL_LE_RADD = |- !x y z. (x + z) <= (y + z) = x <= y
Run time: 0.0s
Theorem REAL_LE_NEG autoloading from theory `REAL` ...
REAL_LE_NEG = |- !x y. (-- x) <= (-- y) = y <= x
Run time: 0.0s
Theorem REAL_LE_LADD autoloading from theory `REAL` ...
REAL_LE_LADD = |- !x y z. (x + y) <= (x + z) = y <= z
Run time: 0.0s
Definition real_sub autoloading from theory `REAL` ...
real_sub = |- !x y. x - y = x + (-- y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_NOT_LE autoloading from theory `REAL` ...
REAL_NOT_LE = |- !x y. ~x <= y = y < x
Run time: 0.0s
Theorem REAL_LT_LE autoloading from theory `REAL` ...
REAL_LT_LE = |- !x y. x < y = x <= y /\ ~(x = y)
Run time: 0.0s
Theorem REAL_SUB_LT autoloading from theory `REAL` ...
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
Theorem REAL_SUB_LE autoloading from theory `REAL` ...
REAL_SUB_LE = |- !x y. (& 0) <= (x - y) = y <= x
Run time: 0.0s
Definition abs autoloading from theory `REAL` ...
abs = |- !x. abs x = ((& 0) <= x => x | -- x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_LT_TOTAL autoloading from theory `REAL` ...
REAL_LT_TOTAL = |- !x y. (x = y) \/ x < y \/ y < x
Run time: 0.1s
Theorem REAL_LT_01 autoloading from theory `REAL` ...
REAL_LT_01 = |- (& 0) < (& 1)
Run time: 0.0s
Theorem REAL_LE_TRANS autoloading from theory `REAL` ...
REAL_LE_TRANS = |- !x y z. x <= y /\ y <= z ==> x <= z
Run time: 0.0s
Theorem REAL_LE_TOTAL autoloading from theory `REAL` ...
REAL_LE_TOTAL = |- !x y. x <= y \/ y <= x
Run time: 0.0s
Theorem BOLZANO_LEMMA autoloading from theory `SEQ` ...
BOLZANO_LEMMA =
|- !P.
(!a b c. a <= b /\ b <= c /\ P(a,b) /\ P(b,c) ==> P(a,c)) /\
(!x.
?d.
(& 0) < d /\ (!a b. a <= x /\ x <= b /\ (b - a) < d ==> P(a,b))) ==>
(!a b. a <= b ==> P(a,b))
Run time: 0.0s
IVT =
|- !f a b y.
a <= b /\
((f a) <= y /\ y <= (f b)) /\
(!x. a <= x /\ x <= b ==> f contl x) ==>
(?x. a <= x /\ x <= b /\ (f x = y))
Run time: 0.2s
Intermediate theorems generated: 2647
Theorem REAL_NEGNEG autoloading from theory `REAL` ...
REAL_NEGNEG = |- !x. --(-- x) = x
Run time: 0.0s
Theorem REAL_NEG_EQ autoloading from theory `REAL` ...
REAL_NEG_EQ = |- !x y. (-- x = y) = (x = -- y)
Run time: 0.0s
IVT2 =
|- !f a b y.
a <= b /\
((f b) <= y /\ y <= (f a)) /\
(!x. a <= x /\ x <= b ==> f contl x) ==>
(?x. a <= x /\ x <= b /\ (f x = y))
Run time: 0.1s
Intermediate theorems generated: 158
Theorem REAL_MUL_LZERO autoloading from theory `REAL` ...
REAL_MUL_LZERO = |- !x. (& 0) * x = & 0
Run time: 0.0s
Definition real_div autoloading from theory `REAL` ...
real_div = |- !x y. x / y = x * (inv y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_SUB_REFL autoloading from theory `REAL` ...
REAL_SUB_REFL = |- !x. x - x = & 0
Run time: 0.0s
DIFF_CONST = |- !k x. ((\x. k) diffl (& 0))x
Run time: 0.0s
Intermediate theorems generated: 59
Theorem REAL_RDISTRIB autoloading from theory `REAL` ...
REAL_RDISTRIB = |- !x y z. (x + y) * z = (x * z) + (y * z)
Run time: 0.0s
Theorem REAL_ADD2_SUB2 autoloading from theory `REAL` ...
REAL_ADD2_SUB2 = |- !a b c d. (a + b) - (c + d) = (a - c) + (b - d)
Run time: 0.0s
DIFF_ADD =
|- !f g l m x.
(f diffl l)x /\ (g diffl m)x ==>
((\x. (f x) + (g x)) diffl (l + m))x
Run time: 0.0s
Intermediate theorems generated: 150
Theorem REAL_MUL_SYM autoloading from theory `REAL` ...
REAL_MUL_SYM = |- !x y. x * y = y * x
Run time: 0.0s
Theorem REAL_MUL_ASSOC autoloading from theory `REAL` ...
REAL_MUL_ASSOC = |- !x y z. x * (y * z) = (x * y) * z
Run time: 0.0s
Theorem REAL_SUB_RDISTRIB autoloading from theory `REAL` ...
REAL_SUB_RDISTRIB = |- !x y z. (x - y) * z = (x * z) - (y * z)
Run time: 0.0s
Theorem REAL_SUB_LDISTRIB autoloading from theory `REAL` ...
REAL_SUB_LDISTRIB = |- !x y z. x * (y - z) = (x * y) - (x * z)
Run time: 0.0s
Theorem REAL_ADD_LID autoloading from theory `REAL` ...
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Theorem REAL_ADD_LINV autoloading from theory `REAL` ...
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Theorem REAL_ADD_ASSOC autoloading from theory `REAL` ...
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.1s
DIFF_MUL =
|- !f g l m x.
(f diffl l)x /\ (g diffl m)x ==>
((\x. (f x) * (g x)) diffl ((l * (g x)) + (m * (f x))))x
Run time: 0.0s
Intermediate theorems generated: 567
DIFF_CMUL =
|- !f c l x. (f diffl l)x ==> ((\x. c * (f x)) diffl (c * l))x
Run time: 0.0s
Intermediate theorems generated: 100
Theorem REAL_NEG_MINUS1 autoloading from theory `REAL` ...
REAL_NEG_MINUS1 = |- !x. -- x = (--(& 1)) * x
Run time: 0.0s
DIFF_NEG = |- !f l x. (f diffl l)x ==> ((\x. --(f x)) diffl (-- l))x
Run time: 0.0s
Intermediate theorems generated: 20
DIFF_SUB =
|- !f g l m x.
(f diffl l)x /\ (g diffl m)x ==>
((\x. (f x) - (g x)) diffl (l - m))x
Run time: 0.0s
Intermediate theorems generated: 50
Theorem NET_NULL_MUL autoloading from theory `NETS` ...
NET_NULL_MUL =
|- !g.
dorder g ==>
(!x y.
bounded(mr1,g)x /\ (y tends (& 0))(mtop mr1,g) ==>
((\n. (x n) * (y n)) tends (& 0))(mtop mr1,g))
Run time: 0.0s
LIM_NULL_MUL =
|- !x x0 y.
bounded(mr1,tendsto(mr1,x0))x /\ (y --> (& 0))x0 ==>
((\u. (x u) * (y u)) --> (& 0))x0
Run time: 0.0s
Intermediate theorems generated: 35
Theorem REAL_LT_HALF2 autoloading from theory `REAL` ...
REAL_LT_HALF2 = |- !d. (d / (& 2)) < d = (& 0) < d
Run time: 0.0s
Theorem ABS_REFL autoloading from theory `REAL` ...
ABS_REFL = |- !x. (abs x = x) = (& 0) <= x
Run time: 0.0s
Theorem ABS_LE autoloading from theory `REAL` ...
ABS_LE = |- !x. x <= (abs x)
Run time: 0.0s
Theorem MR1_BOUNDED autoloading from theory `NETS` ...
MR1_BOUNDED =
|- !g f.
bounded(mr1,g)f = (?k N. g N N /\ (!n. g n N ==> (abs(f n)) < k))
Run time: 0.0s
LIM_BOUNDED =
|- bounded(mr1,tendsto(mr1,x0))f =
(?k d.
(& 0) < d /\
(!x. (& 0) < (abs(x - x0)) /\ (abs(x - x0)) < d ==> (abs(f x)) < k))
Run time: 0.1s
Intermediate theorems generated: 362
Theorem REAL_MUL_LID autoloading from theory `REAL` ...
REAL_MUL_LID = |- !x. (& 1) * x = x
Run time: 0.0s
Theorem REAL_MUL_LINV autoloading from theory `REAL` ...
REAL_MUL_LINV = |- !x. ~(x = & 0) ==> ((inv x) * x = & 1)
Run time: 0.0s
CHAIN_LEMMA1 =
|- !f g x h.
((f(g(x + h))) - (f(g x))) / h =
(((f(g(x + h))) - (f(g x))) / ((g(x + h)) - (g x))) *
(((g(x + h)) - (g x)) / h)
Run time: 0.0s
Intermediate theorems generated: 170
Theorem REAL_LT_RADD autoloading from theory `REAL` ...
REAL_LT_RADD = |- !x y z. (x + z) < (y + z) = x < y
Run time: 0.0s
CHAIN_LEMMA2 = |- !x y d. (abs(x - y)) < d ==> (abs x) < ((abs y) + d)
Run time: 0.0s
Intermediate theorems generated: 65
Theorem ABS_POS autoloading from theory `REAL` ...
ABS_POS = |- !x. (& 0) <= (abs x)
Run time: 0.0s
Theorem REAL_LE_ADDL autoloading from theory `REAL` ...
REAL_LE_ADDL = |- !x y. y <= (x + y) = (& 0) <= x
Run time: 0.0s
Theorem ABS_0 autoloading from theory `REAL` ...
ABS_0 = |- abs(& 0) = & 0
Run time: 0.0s
Theorem REAL_LT_REFL autoloading from theory `REAL` ...
REAL_LT_REFL = |- !x. ~x < x
Run time: 0.0s
Theorem ABS_NEG autoloading from theory `REAL` ...
ABS_NEG = |- !x. abs(-- x) = abs x
Run time: 0.0s
Theorem REAL_SUB_LZERO autoloading from theory `REAL` ...
REAL_SUB_LZERO = |- !x. (& 0) - x = -- x
Run time: 0.0s
DIFF_CHAIN =
|- !f g x.
(f diffl l)(g x) /\ (g diffl m)x ==> ((\x. f(g x)) diffl (l * m))x
Run time: 0.3s
Intermediate theorems generated: 2058
Theorem REAL_DIV_REFL autoloading from theory `REAL` ...
REAL_DIV_REFL = |- !x. ~(x = & 0) ==> (x / x = & 1)
Run time: 0.0s
DIFF_X = |- !x. ((\x. x) diffl (& 1))x
Run time: 0.0s
Intermediate theorems generated: 148
Theorem REAL_MUL_RID autoloading from theory `REAL` ...
REAL_MUL_RID = |- !x. x * (& 1) = x
Run time: 0.0s
Theorem POW_ADD autoloading from theory `REAL` ...
POW_ADD = |- !c m n. c pow (m num_add n) = (c pow m) * (c pow n)
Run time: 0.0s
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Run time: 0.1s
Theorem ADD_SUB autoloading from theory `arithmetic` ...
ADD_SUB = |- !a c. (a num_add c) num_sub c = a
Run time: 0.0s
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m num_add 1
Run time: 0.0s
Theorem REAL autoloading from theory `REAL` ...
REAL = |- !n. &(SUC n) = (& n) + (& 1)
Run time: 0.0s
Definition pow autoloading from theory `REAL` ...
pow = |- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
Run time: 0.0s
Intermediate theorems generated: 1
DIFF_POW =
|- !n x. ((\x'. x' pow n) diffl ((& n) * (x pow (n num_sub 1))))x
Run time: 0.0s
Intermediate theorems generated: 335
Theorem REAL_ADD_RID autoloading from theory `REAL` ...
REAL_ADD_RID = |- !x. x + (& 0) = x
Run time: 0.0s
Theorem POW_2 autoloading from theory `REAL` ...
POW_2 = |- !x. x pow 2 = x * x
Run time: 0.0s
Theorem REAL_NEG_SUB autoloading from theory `REAL` ...
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
Theorem REAL_NEG_RMUL autoloading from theory `REAL` ...
REAL_NEG_RMUL = |- !x y. --(x * y) = x * (-- y)
Run time: 0.0s
Theorem REAL_NEG_LMUL autoloading from theory `REAL` ...
REAL_NEG_LMUL = |- !x y. --(x * y) = (-- x) * y
Run time: 0.0s
Theorem REAL_ENTIRE autoloading from theory `REAL` ...
REAL_ENTIRE = |- !x y. (x * y = & 0) = (x = & 0) \/ (y = & 0)
Run time: 0.0s
Theorem REAL_EQ_LMUL autoloading from theory `REAL` ...
REAL_EQ_LMUL = |- !x y z. (x * y = x * z) = (x = & 0) \/ (y = z)
Run time: 0.0s
Theorem REAL_LNEG_UNIQ autoloading from theory `REAL` ...
REAL_LNEG_UNIQ = |- !x y. (x + y = & 0) = (x = -- y)
Run time: 0.0s
Theorem ABS_ZERO autoloading from theory `REAL` ...
ABS_ZERO = |- !x. (abs x = & 0) = (x = & 0)
Run time: 0.0s
DIFF_XM1 =
|- !x. ~(x = & 0) ==> ((\x. inv x) diffl (--((inv x) pow 2)))x
Run time: 0.1s
Intermediate theorems generated: 818
Theorem POW_INV autoloading from theory `REAL` ...
POW_INV = |- !c. ~(c = & 0) ==> (!n. inv(c pow n) = (inv c) pow n)
Run time: 0.0s
DIFF_INV =
|- !f l x.
(f diffl l)x /\ ~(f x = & 0) ==>
((\x. inv(f x)) diffl (--(l / ((f x) pow 2))))x
Run time: 0.0s
Intermediate theorems generated: 106
Theorem REAL_MUL_RINV autoloading from theory `REAL` ...
REAL_MUL_RINV = |- !x. ~(x = & 0) ==> (x * (inv x) = & 1)
Run time: 0.0s
Theorem REAL_INV_MUL autoloading from theory `REAL` ...
REAL_INV_MUL =
|- !x y. ~(x = & 0) /\ ~(y = & 0) ==> (inv(x * y) = (inv x) * (inv y))
Run time: 0.0s
Theorem REAL_LDISTRIB autoloading from theory `REAL` ...
REAL_LDISTRIB = |- !x y z. x * (y + z) = (x * y) + (x * z)
Run time: 0.0s
DIFF_DIV =
|- !f g l m.
(f diffl l)x /\ (g diffl m)x /\ ~(g x = & 0) ==>
((\x. (f x) / (g x)) diffl
(((l * (g x)) - (m * (f x))) / ((g x) pow 2)))
x
Run time: 0.1s
Intermediate theorems generated: 293
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m num_le (m num_add n)
Run time: 0.0s
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n num_lt (SUC n)
Run time: 0.0s
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 num_add m = m) /\
(m num_add 0 = m) /\
((SUC m) num_add n = SUC(m num_add n)) /\
(m num_add (SUC n) = SUC(m num_add n))
Run time: 0.0s
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m num_lt n /\ n num_lt p ==> m num_lt p
Run time: 0.0s
Theorem Sum autoloading from theory `REAL` ...
Sum =
|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
Run time: 0.0s
DIFF_SUM =
|- !f f' m n x.
(!r.
m num_le r /\ r num_lt (m num_add n) ==>
((\x'. f r x') diffl (f' r x))x) ==>
((\x'. Sum(m,n)(\n'. f n' x')) diffl (Sum(m,n)(\r. f' r x)))x
Run time: 0.0s
Intermediate theorems generated: 301
CONT_BOUNDED =
|- !f a b.
a <= b /\ (!x. a <= x /\ x <= b ==> f contl x) ==>
(?M. !x. a <= x /\ x <= b ==> (f x) <= M)
Run time: 0.2s
Intermediate theorems generated: 1866
Theorem REAL_LE_LT autoloading from theory `REAL` ...
REAL_LE_LT = |- !x y. x <= y = x < y \/ (x = y)
Run time: 0.0s
Theorem REAL_SUP_LE autoloading from theory `REAL` ...
REAL_SUP_LE =
|- !P.
(?x. P x) /\ (?z. !x. P x ==> x <= z) ==>
(!y. (?x. P x /\ y < x) = y < (sup P))
Run time: 0.0s
CONT_HASSUP =
|- !f a b.
a <= b /\ (!x. a <= x /\ x <= b ==> f contl x) ==>
(?M.
(!x. a <= x /\ x <= b ==> (f x) <= M) /\
(!N. N < M ==> (?x. a <= x /\ x <= b /\ N < (f x))))
Run time: 0.0s
Intermediate theorems generated: 412
Theorem REAL_LT_SUB_RADD autoloading from theory `REAL` ...
REAL_LT_SUB_RADD = |- !x y z. (x - y) < z = x < (z + y)
Run time: 0.0s
Theorem REAL_LT_SUB_LADD autoloading from theory `REAL` ...
REAL_LT_SUB_LADD = |- !x y z. x < (y - z) = (x + z) < y
Run time: 0.1s
Theorem REAL_INVINV autoloading from theory `REAL` ...
REAL_INVINV = |- !x. ~(x = & 0) ==> (inv(inv x) = x)
Run time: 0.0s
Theorem REAL_LT_INV autoloading from theory `REAL` ...
REAL_LT_INV = |- !x y. (& 0) < x /\ x < y ==> (inv y) < (inv x)
Run time: 0.0s
Theorem REAL_LT_ADDR autoloading from theory `REAL` ...
REAL_LT_ADDR = |- !x y. x < (x + y) = (& 0) < y
Run time: 0.0s
Theorem REAL_INV_POS autoloading from theory `REAL` ...
REAL_INV_POS = |- !x. (& 0) < x ==> (& 0) < (inv x)
Run time: 0.0s
Theorem REAL_LT_IMP_NE autoloading from theory `REAL` ...
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
CONT_ATTAINS =
|- !f a b.
a <= b /\ (!x. a <= x /\ x <= b ==> f contl x) ==>
(?M.
(!x. a <= x /\ x <= b ==> (f x) <= M) /\
(?x. a <= x /\ x <= b /\ (f x = M)))
Run time: 0.1s
Intermediate theorems generated: 1646
CONT_ATTAINS2 =
|- !f a b.
a <= b /\ (!x. a <= x /\ x <= b ==> f contl x) ==>
(?M.
(!x. a <= x /\ x <= b ==> M <= (f x)) /\
(?x. a <= x /\ x <= b /\ (f x = M)))
Run time: 0.1s
Intermediate theorems generated: 177
Theorem ABS_SIGN autoloading from theory `REAL` ...
ABS_SIGN = |- !x y. (abs(x - y)) < y ==> (& 0) < x
Run time: 0.0s
Theorem REAL_LT_RMUL autoloading from theory `REAL` ...
REAL_LT_RMUL = |- !x y z. (& 0) < z ==> ((x * z) < (y * z) = x < y)
Run time: 0.0s
DIFF_LINC =
|- !f x l.
(f diffl l)x /\ (& 0) < l ==>
(?d. (& 0) < d /\ (!h. (& 0) < h /\ h < d ==> (f x) < (f(x + h))))
Run time: 0.0s
Intermediate theorems generated: 270
Theorem REAL_NEG_LE0 autoloading from theory `REAL` ...
REAL_NEG_LE0 = |- !x. (-- x) <= (& 0) = (& 0) <= x
Run time: 0.0s
Theorem ABS_SIGN2 autoloading from theory `REAL` ...
ABS_SIGN2 = |- !x y. (abs(x - y)) < (-- y) ==> x < (& 0)
Run time: 0.0s
Theorem REAL_NEG_INV autoloading from theory `REAL` ...
REAL_NEG_INV = |- !x. ~(x = & 0) ==> (--(inv x) = inv(-- x))
Run time: 0.0s
Theorem REAL_NEG_LT0 autoloading from theory `REAL` ...
REAL_NEG_LT0 = |- !x. (-- x) < (& 0) = (& 0) < x
Run time: 0.0s
DIFF_LDEC =
|- !f x l.
(f diffl l)x /\ l < (& 0) ==>
(?d. (& 0) < d /\ (!h. (& 0) < h /\ h < d ==> (f x) < (f(x - h))))
Run time: 0.1s
Intermediate theorems generated: 469
Theorem REAL_ADD_SUB2 autoloading from theory `REAL` ...
REAL_ADD_SUB2 = |- !x y. x - (x + y) = -- y
Run time: 0.0s
Theorem REAL_SUB_SUB2 autoloading from theory `REAL` ...
REAL_SUB_SUB2 = |- !x y. x - (x - y) = y
Run time: 0.0s
DIFF_LMAX =
|- !f x l.
(f diffl l)x /\
(?d. (& 0) < d /\ (!y. (abs(x - y)) < d ==> (f y) <= (f x))) ==>
(l = & 0)
Run time: 0.1s
Intermediate theorems generated: 572
Theorem REAL_NEG_EQ0 autoloading from theory `REAL` ...
REAL_NEG_EQ0 = |- !x. (-- x = & 0) = (x = & 0)
Run time: 0.0s
DIFF_LMIN =
|- !f x l.
(f diffl l)x /\
(?d. (& 0) < d /\ (!y. (abs(x - y)) < d ==> (f x) <= (f y))) ==>
(l = & 0)
Run time: 0.0s
Intermediate theorems generated: 88
DIFF_LCONST =
|- !f x l.
(f diffl l)x /\
(?d. (& 0) < d /\ (!y. (abs(x - y)) < d ==> (f y = f x))) ==>
(l = & 0)
Run time: 0.1s
Intermediate theorems generated: 96
INTERVAL_LEMMA =
|- !a b x.
a < x /\ x < b ==>
(?d. (& 0) < d /\ (!y. (abs(x - y)) < d ==> a <= y /\ y <= b))
Run time: 0.0s
Intermediate theorems generated: 466
Theorem REAL_MEAN autoloading from theory `REAL` ...
REAL_MEAN = |- !x y. x < y ==> (?z. x < z /\ z < y)
Run time: 0.0s
Theorem REAL_LE_ANTISYM autoloading from theory `REAL` ...
REAL_LE_ANTISYM = |- !x y. x <= y /\ y <= x = (x = y)
Run time: 0.0s
ROLLE =
|- !f a b.
a < b /\
(f a = f b) /\
(!x. a <= x /\ x <= b ==> f contl x) /\
(!x. a < x /\ x < b ==> f differentiable x) ==>
(?z. a < z /\ z < b /\ (f diffl (& 0))z)
Run time: 0.2s
Intermediate theorems generated: 3178
gfn = "\x. (f x) - ((((f b) - (f a)) / (b - a)) * x)" : term
Run time: 0.0s
Theorem REAL_NEG_ADD autoloading from theory `REAL` ...
REAL_NEG_ADD = |- !x y. --(x + y) = (-- x) + (-- y)
Run time: 0.0s
Theorem REAL_EQ_RMUL autoloading from theory `REAL` ...
REAL_EQ_RMUL = |- !x y z. (x * z = y * z) = (z = & 0) \/ (x = y)
Run time: 0.0s
MVT_LEMMA =
|- !f a b.
(\x. (f x) - ((((f b) - (f a)) / (b - a)) * x))a =
(\x. (f x) - ((((f b) - (f a)) / (b - a)) * x))b
Run time: 0.1s
Intermediate theorems generated: 443
Theorem REAL_DIV_LMUL autoloading from theory `REAL` ...
REAL_DIV_LMUL = |- !x y. ~(y = & 0) ==> (y * (x / y) = x)
Run time: 0.0s
MVT =
|- !f a b.
a < b /\
(!x. a <= x /\ x <= b ==> f contl x) /\
(!x. a < x /\ x < b ==> f differentiable x) ==>
(?l z.
a < z /\ z < b /\ (f diffl l)z /\ ((f b) - (f a) = (b - a) * l))
Run time: 0.1s
Intermediate theorems generated: 612
DIFF_ISCONST_END =
|- !f a b.
a < b /\
(!x. a <= x /\ x <= b ==> f contl x) /\
(!x. a < x /\ x < b ==> (f diffl (& 0))x) ==>
(f b = f a)
Run time: 0.0s
Intermediate theorems generated: 253
DIFF_ISCONST =
|- !f a b.
a < b /\
(!x. a <= x /\ x <= b ==> f contl x) /\
(!x. a < x /\ x < b ==> (f diffl (& 0))x) ==>
(!x. a <= x /\ x <= b ==> (f x = f a))
Run time: 0.1s
Intermediate theorems generated: 310
DIFF_ISCONST_ALL = |- !f. (!x. (f diffl (& 0))x) ==> (!x y. f x = f y)
Run time: 0.0s
Intermediate theorems generated: 172
() : void
Run time: 0.1s
Intermediate theorems generated: 1
File lim.ml loaded
() : void
Run time: 4.0s
Intermediate theorems generated: 21608
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `powser.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
Theory SEQ loaded
Theory LIM loaded
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
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EXPAND_TAC = - : (string -> tactic)
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File useful loaded
() : void
Run time: 0.0s
real_interface_map =
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
[(); ()] : void list
Run time: 0.0s
[] : (string # string) list
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 47
() : void
Run time: 0.1s
Definition pow autoloading from theory `REAL` ...
pow = |- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
Run time: 0.0s
Intermediate theorems generated: 1
Definition SUB autoloading from theory `arithmetic` ...
SUB =
|- (!m. 0 num_sub m = 0) /\
(!m n. (SUC m) num_sub n = (m num_lt n => 0 | SUC(m num_sub n)))
Run time: 0.1s
Intermediate theorems generated: 1
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m num_lt n ==> m num_le n
Run time: 0.0s
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m num_le m
Run time: 0.0s
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m num_lt (SUC n) = (m = n) \/ m num_lt n
Run time: 0.0s
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m num_lt n = n num_le m
Run time: 0.0s
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 num_add m = m) /\
(m num_add 0 = m) /\
((SUC m) num_add n = SUC(m num_add n)) /\
(m num_add (SUC n) = SUC(m num_add n))
Run time: 0.0s
Theorem REAL_MUL_ASSOC autoloading from theory `REAL` ...
REAL_MUL_ASSOC = |- !x y z. x * (y * z) = (x * y) * z
Run time: 0.0s
Theorem REAL_MUL_SYM autoloading from theory `REAL` ...
REAL_MUL_SYM = |- !x y. x * y = y * x
Run time: 0.0s
Theorem SUM_SUBST autoloading from theory `REAL` ...
SUM_SUBST =
|- !f g m n.
(!p. m num_le p /\ p num_lt (m num_add n) ==> (f p = g p)) ==>
(Sum(m,n)f = Sum(m,n)g)
Run time: 0.0s
Theorem SUM_CMUL autoloading from theory `REAL` ...
SUM_CMUL = |- !f c m n. Sum(m,n)(\n'. c * (f n')) = c * (Sum(m,n)f)
Run time: 0.0s
POWDIFF_LEMMA =
|- !n x y.
Sum(0,SUC n)(\p. (x pow p) * (y pow ((SUC n) num_sub p))) =
y * (Sum(0,SUC n)(\p. (x pow p) * (y pow (n num_sub p))))
Run time: 0.0s
Intermediate theorems generated: 223
Theorem REAL_ADD_LINV autoloading from theory `REAL` ...
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Theorem REAL_ADD_LID_UNIQ autoloading from theory `REAL` ...
REAL_ADD_LID_UNIQ = |- !x y. (x + y = y) = (x = & 0)
Run time: 0.0s
Theorem REAL_ADD_SYM autoloading from theory `REAL` ...
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Theorem REAL_ADD_ASSOC autoloading from theory `REAL` ...
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.0s
Definition real_sub autoloading from theory `REAL` ...
real_sub = |- !x y. x - y = x + (-- y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_SUB_LDISTRIB autoloading from theory `REAL` ...
REAL_SUB_LDISTRIB = |- !x y z. x * (y - z) = (x * y) - (x * z)
Run time: 0.0s
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c num_sub c = 0
Run time: 0.0s
Theorem REAL_LDISTRIB autoloading from theory `REAL` ...
REAL_LDISTRIB = |- !x y z. x * (y + z) = (x * y) + (x * z)
Run time: 0.0s
Theorem REAL_MUL_RID autoloading from theory `REAL` ...
REAL_MUL_RID = |- !x. x * (& 1) = x
Run time: 0.0s
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 num_sub m = 0) /\ (m num_sub 0 = m)
Run time: 0.0s
Theorem REAL_ADD_LID autoloading from theory `REAL` ...
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Theorem Sum autoloading from theory `REAL` ...
Sum =
|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
Run time: 0.1s
POWDIFF =
|- !n x y.
(x pow (SUC n)) - (y pow (SUC n)) =
(x - y) * (Sum(0,SUC n)(\p. (x pow p) * (y pow (n num_sub p))))
Run time: 0.0s
Intermediate theorems generated: 485
Theorem REAL_NEG_SUB autoloading from theory `REAL` ...
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
Theorem REAL_NEG_LMUL autoloading from theory `REAL` ...
REAL_NEG_LMUL = |- !x y. --(x * y) = (-- x) * y
Run time: 0.0s
Theorem REAL_NEGNEG autoloading from theory `REAL` ...
REAL_NEGNEG = |- !x. --(-- x) = x
Run time: 0.0s
Theorem REAL_SUB_0 autoloading from theory `REAL` ...
REAL_SUB_0 = |- !x y. (x - y = & 0) = (x = y)
Run time: 0.0s
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m num_add n = n num_add m
Run time: 0.0s
Theorem POW_ADD autoloading from theory `REAL` ...
POW_ADD = |- !c m n. c pow (m num_add n) = (c pow m) * (c pow n)
Run time: 0.0s
Theorem REAL_EQ_LMUL2 autoloading from theory `REAL` ...
REAL_EQ_LMUL2 = |- !x y z. ~(x = & 0) ==> ((y = z) = (x * y = x * z))
Run time: 0.0s
POWREV =
|- !n x y.
Sum(0,SUC n)(\p. (x pow p) * (y pow (n num_sub p))) =
Sum(0,SUC n)(\p. (x pow (n num_sub p)) * (y pow p))
Run time: 0.1s
Intermediate theorems generated: 235
Theorem REAL_LT_IMP_NE autoloading from theory `REAL` ...
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
Theorem POW_INV autoloading from theory `REAL` ...
POW_INV = |- !c. ~(c = & 0) ==> (!n. inv(c pow n) = (inv c) pow n)
Run time: 0.0s
Theorem POW_MUL autoloading from theory `REAL` ...
POW_MUL = |- !n x y. (x * y) pow n = (x pow n) * (y pow n)
Run time: 0.0s
Theorem POW_ABS autoloading from theory `REAL` ...
POW_ABS = |- !c n. (abs c) pow n = abs(c pow n)
Run time: 0.0s
Theorem REAL_LT_1 autoloading from theory `REAL` ...
REAL_LT_1 = |- !x y. (& 0) <= x /\ x < y ==> (x / y) < (& 1)
Run time: 0.0s
Theorem REAL_NOT_LT autoloading from theory `REAL` ...
REAL_NOT_LT = |- !x y. ~x < y = y <= x
Run time: 0.0s
Theorem ABS_INV autoloading from theory `REAL` ...
ABS_INV = |- !x. ~(x = & 0) ==> (abs(inv x) = inv(abs x))
Run time: 0.0s
Theorem GP autoloading from theory `SEQ` ...
GP = |- !x. (abs x) < (& 1) ==> (\n. x pow n) sums (inv((& 1) - x))
Run time: 0.0s
Theorem SER_CMUL autoloading from theory `SEQ` ...
SER_CMUL = |- !x x0 c. x sums x0 ==> (\n. c * (x n)) sums (c * x0)
Run time: 0.0s
Definition real_div autoloading from theory `REAL` ...
real_div = |- !x y. x / y = x * (inv y)
Run time: 0.0s
Intermediate theorems generated: 1
Definition summable autoloading from theory `SEQ` ...
summable = |- !f. summable f = (?s. f sums s)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_LT_IMP_LE autoloading from theory `REAL` ...
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
Theorem REAL_LE_RMUL autoloading from theory `REAL` ...
REAL_LE_RMUL = |- !x y z. (& 0) < z ==> ((x * z) <= (y * z) = x <= y)
Run time: 0.1s
Theorem REAL_LE_REFL autoloading from theory `REAL` ...
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
Theorem REAL_MUL_RZERO autoloading from theory `REAL` ...
REAL_MUL_RZERO = |- !x. x * (& 0) = & 0
Run time: 0.0s
Theorem ABS_0 autoloading from theory `REAL` ...
ABS_0 = |- abs(& 0) = & 0
Run time: 0.0s
Theorem ABS_CASES autoloading from theory `REAL` ...
ABS_CASES = |- !x. (x = & 0) \/ (& 0) < (abs x)
Run time: 0.0s
Theorem ABS_ABS autoloading from theory `REAL` ...
ABS_ABS = |- !x. abs(abs x) = abs x
Run time: 0.0s
Theorem ABS_MUL autoloading from theory `REAL` ...
ABS_MUL = |- !x y. abs(x * y) = (abs x) * (abs y)
Run time: 0.0s
Theorem ABS_POS autoloading from theory `REAL` ...
ABS_POS = |- !x. (& 0) <= (abs x)
Run time: 0.0s
Theorem REAL_LET_TRANS autoloading from theory `REAL` ...
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.0s
Theorem POW_NZ autoloading from theory `REAL` ...
POW_NZ = |- !c n. ~(c = & 0) ==> ~(c pow n = & 0)
Run time: 0.0s
Theorem ABS_NZ autoloading from theory `REAL` ...
ABS_NZ = |- !x. ~(x = & 0) = (& 0) < (abs x)
Run time: 0.0s
Theorem REAL_LE_RDIV autoloading from theory `REAL` ...
REAL_LE_RDIV = |- !x y z. (& 0) < x /\ (y * x) <= z ==> y <= (z / x)
Run time: 0.0s
Theorem SER_COMPAR autoloading from theory `SEQ` ...
SER_COMPAR =
|- !f g.
(?N. !n. n num_ge N ==> (abs(f n)) <= (g n)) /\ summable g ==>
summable f
Run time: 0.0s
Theorem SEQ_BOUNDED autoloading from theory `SEQ` ...
SEQ_BOUNDED = |- !s. bounded(mr1,$num_ge)s = (?k. !n. (abs(s n)) < k)
Run time: 0.0s
Theorem SEQ_CBOUNDED autoloading from theory `SEQ` ...
SEQ_CBOUNDED = |- !f. cauchy f ==> bounded(mr1,$num_ge)f
Run time: 0.0s
Theorem SEQ_CAUCHY autoloading from theory `SEQ` ...
SEQ_CAUCHY = |- !f. cauchy f = convergent f
Run time: 0.0s
Theorem SER_ZERO autoloading from theory `SEQ` ...
SER_ZERO = |- !f. summable f ==> f tends_num_real (& 0)
Run time: 0.0s
Definition convergent autoloading from theory `SEQ` ...
convergent = |- !f. convergent f = (?l. f tends_num_real l)
Run time: 0.0s
Intermediate theorems generated: 1
POWSER_INSIDEA =
|- !f x z.
summable(\n. (f n) * (x pow n)) /\ (abs z) < (abs x) ==>
summable(\n. (abs(f n)) * (z pow n))
Run time: 0.1s
Intermediate theorems generated: 753
Theorem SER_ACONV autoloading from theory `SEQ` ...
SER_ACONV = |- !f. summable(\n. abs(f n)) ==> summable f
Run time: 0.0s
POWSER_INSIDE =
|- !f x z.
summable(\n. (f n) * (x pow n)) /\ (abs z) < (abs x) ==>
summable(\n. (f n) * (z pow n))
Run time: 0.0s
Intermediate theorems generated: 67
diffs = |- !c. diffs c = (\n. (&(SUC n)) * (c(SUC n)))
Run time: 0.0s
Intermediate theorems generated: 2
Theorem REAL_NEG_RMUL autoloading from theory `REAL` ...
REAL_NEG_RMUL = |- !x y. --(x * y) = x * (-- y)
Run time: 0.0s
DIFFS_NEG = |- !c. diffs(\n. --(c n)) = (\n. --(diffs c n))
Run time: 0.0s
Intermediate theorems generated: 37
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) num_sub 1 = m
Run time: 0.0s
Theorem REAL_MUL_LZERO autoloading from theory `REAL` ...
REAL_MUL_LZERO = |- !x. (& 0) * x = & 0
Run time: 0.0s
DIFFS_LEMMA =
|- !n c x.
Sum(0,n)(\n'. (diffs c n') * (x pow n')) =
(Sum(0,n)(\n'. (& n') * ((c n') * (x pow (n' num_sub 1))))) +
((& n) * ((c n) * (x pow (n num_sub 1))))
Run time: 0.1s
Intermediate theorems generated: 229
Theorem REAL_EQ_SUB_LADD autoloading from theory `REAL` ...
REAL_EQ_SUB_LADD = |- !x y z. (x = y - z) = (x + z = y)
Run time: 0.0s
DIFFS_LEMMA2 =
|- !n c x.
Sum(0,n)(\n. (& n) * ((c n) * (x pow (n num_sub 1)))) =
(Sum(0,n)(\n. (diffs c n) * (x pow n))) -
((& n) * ((c n) * (x pow (n num_sub 1))))
Run time: 0.0s
Intermediate theorems generated: 34
Theorem REAL_SUB_RZERO autoloading from theory `REAL` ...
REAL_SUB_RZERO = |- !x. x - (& 0) = x
Run time: 0.0s
Theorem SEQ_SUB autoloading from theory `SEQ` ...
SEQ_SUB =
|- !x x0 y y0.
x tends_num_real x0 /\ y tends_num_real y0 ==>
(\n. (x n) - (y n)) tends_num_real (x0 - y0)
Run time: 0.0s
Definition sums autoloading from theory `SEQ` ...
sums = |- !f s. f sums s = (\n. Sum(0,n)f) tends_num_real s
Run time: 0.0s
Intermediate theorems generated: 1
Theorem SUMMABLE_SUM autoloading from theory `SEQ` ...
SUMMABLE_SUM = |- !f. summable f ==> f sums (suminf f)
Run time: 0.0s
Theorem SEQ_SUC autoloading from theory `SEQ` ...
SEQ_SUC = |- !f l. f tends_num_real l = (\n. f(SUC n)) tends_num_real l
Run time: 0.0s
DIFFS_EQUIV =
|- !c x.
summable(\n. (diffs c n) * (x pow n)) ==>
(\n. (& n) * ((c n) * (x pow (n num_sub 1)))) sums
(suminf(\n. (diffs c n) * (x pow n)))
Run time: 0.0s
Intermediate theorems generated: 180
Theorem SUB_ADD autoloading from theory `arithmetic` ...
SUB_ADD = |- !m n. n num_le m ==> ((m num_sub n) num_add n = m)
Run time: 0.0s
TERMDIFF_LEMMA1 =
|- !m z h.
Sum(0,m)(\p. (((z + h) pow (m num_sub p)) * (z pow p)) - (z pow m)) =
Sum
(0,m)
(\p.
(z pow p) * (((z + h) pow (m num_sub p)) - (z pow (m num_sub p))))
Run time: 0.1s
Intermediate theorems generated: 131
Theorem SUB_MONO_EQ autoloading from theory `arithmetic` ...
SUB_MONO_EQ = |- !n m. (SUC n) num_sub (SUC m) = n num_sub m
Run time: 0.0s
Theorem ADD_SUB autoloading from theory `arithmetic` ...
ADD_SUB = |- !a c. (a num_add c) num_sub c = a
Run time: 0.0s
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m num_add 1
Run time: 0.0s
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n num_lt m ==> (?p. m = n num_add (p num_add 1))
Run time: 0.0s
Theorem SUM_NSUB autoloading from theory `REAL` ...
SUM_NSUB =
|- !n f c. (Sum(0,n)f) - ((& n) * c) = Sum(0,n)(\p. (f p) - c)
Run time: 0.0s
Theorem REAL_ADD_RID autoloading from theory `REAL` ...
REAL_ADD_RID = |- !x. x + (& 0) = x
Run time: 0.0s
Theorem REAL_ADD2_SUB2 autoloading from theory `REAL` ...
REAL_ADD2_SUB2 = |- !a b c d. (a + b) - (c + d) = (a - c) + (b - d)
Run time: 0.0s
Theorem REAL_RDISTRIB autoloading from theory `REAL` ...
REAL_RDISTRIB = |- !x y z. (x + y) * z = (x * z) + (y * z)
Run time: 0.0s
Theorem REAL_MUL_LID autoloading from theory `REAL` ...
REAL_MUL_LID = |- !x. (& 1) * x = x
Run time: 0.0s
Theorem REAL autoloading from theory `REAL` ...
REAL = |- !n. &(SUC n) = (& n) + (& 1)
Run time: 0.0s
Theorem REAL_EQ_LMUL autoloading from theory `REAL` ...
REAL_EQ_LMUL = |- !x y z. (x * y = x * z) = (x = & 0) \/ (y = z)
Run time: 0.0s
Theorem REAL_ADD_SUB autoloading from theory `REAL` ...
REAL_ADD_SUB = |- !x y. (x + y) - x = y
Run time: 0.0s
Theorem REAL_SUB_REFL autoloading from theory `REAL` ...
REAL_SUB_REFL = |- !x. x - x = & 0
Run time: 0.0s
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Run time: 0.0s
Theorem REAL_DIV_LMUL autoloading from theory `REAL` ...
REAL_DIV_LMUL = |- !x y. ~(y = & 0) ==> (y * (x / y) = x)
Run time: 0.0s
TERMDIFF_LEMMA2 =
|- !z h.
~(h = & 0) ==>
(((((z + h) pow n) - (z pow n)) / h) -
((& n) * (z pow (n num_sub 1))) =
h *
(Sum
(0,n num_sub 1)
(\p.
(z pow p) *
(Sum
(0,(n num_sub 1) num_sub p)
(\q.
((z + h) pow q) *
(z pow (((n num_sub 2) num_sub p) num_sub q)))))))
Run time: 0.1s
Intermediate theorems generated: 866
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Run time: 0.0s
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n num_lt (SUC n)
Run time: 0.0s
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m num_le (m num_add n)
Run time: 0.0s
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m num_le n /\ n num_le p ==> m num_le p
Run time: 0.0s
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) num_le (SUC m) = n num_le m
Run time: 0.0s
Theorem REAL_LE autoloading from theory `REAL` ...
REAL_LE = |- !m n. (& m) <= (& n) = m num_le n
Run time: 0.0s
Theorem REAL_LE_LT autoloading from theory `REAL` ...
REAL_LE_LT = |- !x y. x <= y = x < y \/ (x = y)
Run time: 0.0s
Theorem POW_POS autoloading from theory `REAL` ...
POW_POS = |- !x. (& 0) <= x ==> (!n. (& 0) <= (x pow n))
Run time: 0.0s
Theorem POW_LE autoloading from theory `REAL` ...
POW_LE = |- !n x y. (& 0) <= x /\ x <= y ==> (x pow n) <= (y pow n)
Run time: 0.0s
Theorem REAL_LE_MUL2 autoloading from theory `REAL` ...
REAL_LE_MUL2 =
|- !x1 x2 y1 y2.
(& 0) <= x1 /\ (& 0) <= y1 /\ x1 <= x2 /\ y1 <= y2 ==>
(x1 * y1) <= (x2 * y2)
Run time: 0.0s
Theorem SUM_BOUND autoloading from theory `REAL` ...
SUM_BOUND =
|- !f K m n.
(!p. m num_le p /\ p num_lt (m num_add n) ==> (f p) <= K) ==>
(Sum(m,n)f) <= ((& n) * K)
Run time: 0.0s
Theorem REAL_LE_LMUL autoloading from theory `REAL` ...
REAL_LE_LMUL = |- !x y z. (& 0) < x ==> ((x * y) <= (x * z) = y <= z)
Run time: 0.0s
Theorem ABS_SUM autoloading from theory `REAL` ...
ABS_SUM = |- !f m n. (abs(Sum(m,n)f)) <= (Sum(m,n)(\n'. abs(f n')))
Run time: 0.0s
Theorem REAL_LE_TRANS autoloading from theory `REAL` ...
REAL_LE_TRANS = |- !x y z. x <= y /\ y <= z ==> x <= z
Run time: 0.0s
TERMDIFF_LEMMA3 =
|- !z h n K.
~(h = & 0) /\ (abs z) <= K /\ (abs(z + h)) <= K ==>
(abs
(((((z + h) pow n) - (z pow n)) / h) -
((& n) * (z pow (n num_sub 1))))) <=
((& n) * ((&(n num_sub 1)) * ((K pow (n num_sub 2)) * (abs h))))
Run time: 0.1s
Intermediate theorems generated: 1294
Theorem REAL_MUL_LINV autoloading from theory `REAL` ...
REAL_MUL_LINV = |- !x. ~(x = & 0) ==> ((inv x) * x = & 1)
Run time: 0.0s
Theorem REAL_LT_RDIV autoloading from theory `REAL` ...
REAL_LT_RDIV = |- !x y z. (& 0) < z ==> ((x / z) < (y / z) = x < y)
Run time: 0.0s
Theorem REAL_LT_LMUL autoloading from theory `REAL` ...
REAL_LT_LMUL = |- !x y z. (& 0) < x ==> ((x * y) < (x * z) = y < z)
Run time: 0.0s
Theorem REAL_LT_TRANS autoloading from theory `REAL` ...
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_DOWN2 autoloading from theory `REAL` ...
REAL_DOWN2 =
|- !x y. (& 0) < x /\ (& 0) < y ==> (?z. (& 0) < z /\ z < x /\ z < y)
Run time: 0.0s
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 num_lt (SUC n)
Run time: 0.0s
Theorem REAL_LT autoloading from theory `REAL` ...
REAL_LT = |- !m n. (& m) < (& n) = m num_lt n
Run time: 0.0s
Theorem REAL_INV_POS autoloading from theory `REAL` ...
REAL_INV_POS = |- !x. (& 0) < x ==> (& 0) < (inv x)
Run time: 0.0s
Theorem REAL_LT_MUL autoloading from theory `REAL` ...
REAL_LT_MUL = |- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x * y)
Run time: 0.0s
Theorem REAL_LE_ANTISYM autoloading from theory `REAL` ...
REAL_LE_ANTISYM = |- !x y. x <= y /\ y <= x = (x = y)
Run time: 0.0s
Theorem REAL_LT_HALF2 autoloading from theory `REAL` ...
REAL_LT_HALF2 = |- !d. (d / (& 2)) < d = (& 0) < d
Run time: 0.0s
Definition abs autoloading from theory `REAL` ...
abs = |- !x. abs x = ((& 0) <= x => x | -- x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_LT_HALF1 autoloading from theory `REAL` ...
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.0s
Theorem LIM autoloading from theory `LIM` ...
LIM =
|- !f y0 x0.
(f tends_real_real y0)x0 =
(!e.
(& 0) < e ==>
(?d.
(& 0) < d /\
(!x.
(& 0) < (abs(x - x0)) /\ (abs(x - x0)) < d ==>
(abs((f x) - y0)) < e)))
Run time: 0.0s
TERMDIFF_LEMMA4 =
|- !f K k.
(& 0) < k /\
(!h. (& 0) < (abs h) /\ (abs h) < k ==> (abs(f h)) <= (K * (abs h))) ==>
(f tends_real_real (& 0))(& 0)
Run time: 0.1s
Intermediate theorems generated: 917
Theorem SER_LE autoloading from theory `SEQ` ...
SER_LE =
|- !f g.
(!n. (f n) <= (g n)) /\ summable f /\ summable g ==>
(suminf f) <= (suminf g)
Run time: 0.0s
Theorem SER_ABS autoloading from theory `SEQ` ...
SER_ABS =
|- !f.
summable(\n. abs(f n)) ==> (abs(suminf f)) <= (suminf(\n. abs(f n)))
Run time: 0.0s
Theorem SUM_SUMMABLE autoloading from theory `SEQ` ...
SUM_SUMMABLE = |- !f l. f sums l ==> summable f
Run time: 0.0s
Theorem SUM_UNIQ autoloading from theory `SEQ` ...
SUM_UNIQ = |- !f x. f sums x ==> (x = suminf f)
Run time: 0.0s
TERMDIFF_LEMMA5 =
|- !f g k.
(& 0) < k /\
summable f /\
(!h.
(& 0) < (abs h) /\ (abs h) < k ==>
(!n. (abs(g h n)) <= ((f n) * (abs h)))) ==>
((\h. suminf(g h)) tends_real_real (& 0))(& 0)
Run time: 0.1s
Intermediate theorems generated: 502
Theorem REAL_LT_SUB_LADD autoloading from theory `REAL` ...
REAL_LT_SUB_LADD = |- !x y z. x < (y - z) = (x + z) < y
Run time: 0.0s
Theorem ABS_TRIANGLE autoloading from theory `REAL` ...
ABS_TRIANGLE = |- !x y. (abs(x + y)) <= ((abs x) + (abs y))
Run time: 0.0s
Theorem REAL_LE_LMUL_IMP autoloading from theory `REAL` ...
REAL_LE_LMUL_IMP =
|- !x y z. (& 0) <= x /\ y <= z ==> (x * y) <= (x * z)
Run time: 0.0s
Theorem REAL_MUL_RINV autoloading from theory `REAL` ...
REAL_MUL_RINV = |- !x. ~(x = & 0) ==> (x * (inv x) = & 1)
Run time: 0.0s
Theorem ABS_LE autoloading from theory `REAL` ...
ABS_LE = |- !x. x <= (abs x)
Run time: 0.0s
Theorem REAL_LTE_TRANS autoloading from theory `REAL` ...
REAL_LTE_TRANS = |- !x y z. x < y /\ y <= z ==> x < z
Run time: 0.0s
Theorem POW_1 autoloading from theory `REAL` ...
POW_1 = |- !x. x pow 1 = x
Run time: 0.0s
Theorem ABS_N autoloading from theory `REAL` ...
ABS_N = |- !n. abs(& n) = & n
Run time: 0.0s
Theorem ABS_REFL autoloading from theory `REAL` ...
ABS_REFL = |- !x. (abs x = x) = (& 0) <= x
Run time: 0.0s
Theorem REAL_MEAN autoloading from theory `REAL` ...
REAL_MEAN = |- !x y. x < y ==> (?z. x < z /\ z < y)
Run time: 0.0s
Theorem REAL_SUB_RDISTRIB autoloading from theory `REAL` ...
REAL_SUB_RDISTRIB = |- !x y z. (x - y) * z = (x * z) - (y * z)
Run time: 0.0s
Theorem LIM_NULL autoloading from theory `LIM` ...
LIM_NULL =
|- !f l x.
(f tends_real_real l)x = ((\x. (f x) - l) tends_real_real (& 0))x
Run time: 0.0s
Theorem SER_CDIV autoloading from theory `SEQ` ...
SER_CDIV = |- !x x0 c. x sums x0 ==> (\n. (x n) / c) sums (x0 / c)
Run time: 0.0s
Theorem SER_SUB autoloading from theory `SEQ` ...
SER_SUB =
|- !x x0 y y0.
x sums x0 /\ y sums y0 ==> (\n. (x n) - (y n)) sums (x0 - y0)
Run time: 0.0s
Theorem ABS_ZERO autoloading from theory `REAL` ...
ABS_ZERO = |- !x. (abs x = & 0) = (x = & 0)
Run time: 0.0s
Theorem ABS_CIRCLE autoloading from theory `REAL` ...
ABS_CIRCLE =
|- !x y h. (abs h) < ((abs y) - (abs x)) ==> (abs(x + h)) < (abs y)
Run time: 0.0s
Theorem REAL_SUB_LT autoloading from theory `REAL` ...
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
Theorem LIM_TRANSFORM autoloading from theory `LIM` ...
LIM_TRANSFORM =
|- !f g x0 l.
((\x. (f x) - (g x)) tends_real_real (& 0))x0 /\
(g tends_real_real l)x0 ==>
(f tends_real_real l)x0
Run time: 0.0s
Definition diffl autoloading from theory `LIM` ...
diffl =
|- !f l x.
(f diffl l)x =
((\h. ((f(x + h)) - (f x)) / h) tends_real_real l)(& 0)
Run time: 0.0s
Intermediate theorems generated: 1
TERMDIFF =
|- !c K.
summable(\n. (c n) * (K pow n)) /\
summable(\n. (diffs c n) * (K pow n)) /\
summable(\n. (diffs(diffs c)n) * (K pow n)) /\
(abs x) < (abs K) ==>
((\x. suminf(\n. (c n) * (x pow n))) diffl
(suminf(\n. (diffs c n) * (x pow n))))
x
Run time: 0.3s
Intermediate theorems generated: 2494
() : void
Run time: 0.0s
Intermediate theorems generated: 1
File powser.ml loaded
() : void
Run time: 2.1s
Intermediate theorems generated: 8507
#\
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `transc.ml`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
() : void
false : bool
Run time: 0.0s
LAND_CONV = - : (conv -> conv)
Run time: 0.0s
TAUT_CONV = - : conv
Run time: 0.0s
AC = - : ((thm # thm) -> conv)
Run time: 0.0s
GEN_PAIR_TAC = - : tactic
Run time: 0.0s
MK_COMB_TAC = - : tactic
Run time: 0.0s
BINOP_TAC = - : tactic
Run time: 0.0s
SYM_CANON_CONV = - : (thm -> ((term # term) -> bool) -> conv)
Run time: 0.0s
IMP_SUBST_TAC = - : thm_tactic
Run time: 0.0s
ABBREV_TAC = - : (term -> tactic)
Run time: 0.0s
EXT_CONV = - : conv
Run time: 0.0s
ABS_TAC = - : tactic
Run time: 0.0s
EQUAL_TAC = - : tactic
Run time: 0.0s
X_BETA_CONV = - : (term -> conv)
Run time: 0.0s
EXACT_CONV = - : (thm list -> conv)
Run time: 0.0s
HABS_CONV = - : conv
Run time: 0.0s
autoload_definitions = - : (string -> void)
Run time: 0.0s
autoload_theorems = - : (string -> void)
Run time: 0.0s
EXPAND_TAC = - : (string -> tactic)
Run time: 0.0s
File useful loaded
() : void
Run time: 0.0s
false : bool
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 1
Theory POWSER loaded
() : void
Run time: 0.2s
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Run time: 0.0s
Theorem DIV_MULT autoloading from theory `arithmetic` ...
DIV_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) DIV n = q)
Run time: 0.0s
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
Run time: 0.0s
MULT_DIV_2 = |- !n. (2 * n) DIV 2 = n
Run time: 0.0s
Intermediate theorems generated: 66
Theorem LEFT_ADD_DISTRIB autoloading from theory `arithmetic` ...
LEFT_ADD_DISTRIB = |- !m n p. p * (m + n) = (p * m) + (p * n)
Run time: 0.0s
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Run time: 0.0s
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
Run time: 0.0s
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
Run time: 0.0s
Theorem ODD_EXISTS autoloading from theory `arithmetic` ...
ODD_EXISTS = |- !n. ODD n = (?m. n = SUC(2 * m))
Run time: 0.0s
Theorem EVEN_ODD autoloading from theory `arithmetic` ...
EVEN_ODD = |- !n. EVEN n = ~ODD n
Run time: 0.0s
EVEN_DIV2 = |- !n. ~EVEN n ==> ((SUC n) DIV 2 = SUC((n - 1) DIV 2))
Run time: 0.0s
Intermediate theorems generated: 152
real_interface_map =
[(`--`, `real_neg`);
(`num_add`, `+`);
(`+`, `real_add`);
(`num_mul`, `*`);
(`*`, `real_mul`);
(`num_sub`, `-`);
(`-`, `real_sub`);
(`num_lt`, `<`);
(`<`, `real_lt`);
(`num_le`, `<=`);
(`<=`, `real_le`);
(`num_gt`, `>`);
(`>`, `real_gt`);
(`num_ge`, `>=`);
(`>=`, `real_ge`);
(`inv`, `real_inv`);
(`&`, `real_of_num`)]
: (string # string) list
Run time: 0.0s
[(); ()] : void list
Run time: 0.0s
[] : (string # string) list
Run time: 0.0s
() : void
Run time: 0.0s
Intermediate theorems generated: 48
() : void
Run time: 0.1s
basic_diffs = [] : thm list
Run time: 0.0s
Theorem DIFF_CHAIN autoloading from theory `LIM` ...
DIFF_CHAIN =
|- !f g x.
(f diffl l)(g x) /\ (g diffl m)x ==> ((\x. f(g x)) diffl (l * m))x
Run time: 0.0s
Theorem DIFF_POW autoloading from theory `LIM` ...
DIFF_POW =
|- !n x. ((\x'. x' pow n) diffl ((& n) * (x pow (n num_sub 1))))x
Run time: 0.0s
Theorem DIFF_X autoloading from theory `LIM` ...
DIFF_X = |- !x. ((\x. x) diffl (& 1))x
Run time: 0.0s
Theorem DIFF_CONST autoloading from theory `LIM` ...
DIFF_CONST = |- !k x. ((\x. k) diffl (& 0))x
Run time: 0.0s
Theorem DIFF_NEG autoloading from theory `LIM` ...
DIFF_NEG = |- !f l x. (f diffl l)x ==> ((\x. --(f x)) diffl (-- l))x
Run time: 0.0s
Theorem DIFF_SUB autoloading from theory `LIM` ...
DIFF_SUB =
|- !f g l m x.
(f diffl l)x /\ (g diffl m)x ==>
((\x. (f x) - (g x)) diffl (l - m))x
Run time: 0.0s
Theorem DIFF_MUL autoloading from theory `LIM` ...
DIFF_MUL =
|- !f g l m x.
(f diffl l)x /\ (g diffl m)x ==>
((\x. (f x) * (g x)) diffl ((l * (g x)) + (m * (f x))))x
Run time: 0.0s
Theorem DIFF_ADD autoloading from theory `LIM` ...
DIFF_ADD =
|- !f g l m x.
(f diffl l)x /\ (g diffl m)x ==>
((\x. (f x) + (g x)) diffl (l + m))x
Run time: 0.0s
Theorem DIFF_DIV autoloading from theory `LIM` ...
DIFF_DIV =
|- !f g l m.
(f diffl l)x /\ (g diffl m)x /\ ~(g x = & 0) ==>
((\x. (f x) / (g x)) diffl
(((l * (g x)) - (m * (f x))) / ((g x) pow 2)))
x
Run time: 0.0s
Theorem DIFF_INV autoloading from theory `LIM` ...
DIFF_INV =
|- !f l x.
(f diffl l)x /\ ~(f x = & 0) ==>
((\x. inv(f x)) diffl (--(l / ((f x) pow 2))))x
Run time: 0.0s
DIFF_CONV = - : conv
Run time: 0.0s
exp_ser = "\n. inv(&(FACT n))" : term
Run time: 0.0s
sin_ser =
"\n.
(EVEN n => & 0 | ((--(& 1)) pow ((n num_sub 1) DIV 2)) / (&(FACT n)))"
: term
Run time: 0.0s
cos_ser =
"\n. (EVEN n => ((--(& 1)) pow (n DIV 2)) / (&(FACT n)) | & 0)"
: term
Run time: 0.0s
exp = |- !x. exp x = suminf(\n. ((\n'. inv(&(FACT n')))n) * (x pow n))
Run time: 0.0s
Intermediate theorems generated: 2
sin =
|- !x.
sin x =
suminf
(\n.
((\n'.
(EVEN n' =>
& 0 |
((--(& 1)) pow ((n' num_sub 1) DIV 2)) / (&(FACT n'))))
n) *
(x pow n))
Run time: 0.0s
Intermediate theorems generated: 2
cos =
|- !x.
cos x =
suminf
(\n.
((\n'.
(EVEN n' => ((--(& 1)) pow (n' DIV 2)) / (&(FACT n')) | & 0))
n) *
(x pow n))
Run time: 0.0s
Intermediate theorems generated: 2
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m num_le (SUC m)
Run time: 0.0s
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m num_le n /\ n num_le p ==> m num_le p
Run time: 0.0s
Theorem REAL_LE_RMUL autoloading from theory `REAL` ...
REAL_LE_RMUL = |- !x y z. (& 0) < z ==> ((x * z) <= (y * z) = x <= y)
Run time: 0.0s
Theorem REAL_LT_IMP_LE autoloading from theory `REAL` ...
REAL_LT_IMP_LE = |- !x y. x < y ==> x <= y
Run time: 0.0s
Theorem REAL_LE_TRANS autoloading from theory `REAL` ...
REAL_LE_TRANS = |- !x y z. x <= y /\ y <= z ==> x <= z
Run time: 0.0s
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 num_le n
Run time: 0.0s
Theorem REAL_LE autoloading from theory `REAL` ...
REAL_LE = |- !m n. (& m) <= (& n) = m num_le n
Run time: 0.0s
Theorem ABS_REFL autoloading from theory `REAL` ...
ABS_REFL = |- !x. (abs x = x) = (& 0) <= x
Run time: 0.0s
Theorem ABS_NZ autoloading from theory `REAL` ...
ABS_NZ = |- !x. ~(x = & 0) = (& 0) < (abs x)
Run time: 0.0s
Theorem REAL_LE_LDIV autoloading from theory `REAL` ...
REAL_LE_LDIV = |- !x y z. (& 0) < x /\ y <= (z * x) ==> (y / x) <= z
Run time: 0.0s
Definition real_div autoloading from theory `REAL` ...
real_div = |- !x y. x / y = x * (inv y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem ABS_INV autoloading from theory `REAL` ...
ABS_INV = |- !x. ~(x = & 0) ==> (abs(inv x) = inv(abs x))
Run time: 0.0s
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 num_lt (SUC n)
Run time: 0.0s
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
Run time: 0.0s
Theorem REAL_INJ autoloading from theory `REAL` ...
REAL_INJ = |- !m n. (& m = & n) = (m = n)
Run time: 0.0s
Theorem REAL_INV_MUL autoloading from theory `REAL` ...
REAL_INV_MUL =
|- !x y. ~(x = & 0) /\ ~(y = & 0) ==> (inv(x * y) = (inv x) * (inv y))
Run time: 0.0s
Theorem REAL_MUL autoloading from theory `REAL` ...
REAL_MUL = |- !m n. (& m) * (& n) = &(m num_mul n)
Run time: 0.0s
Definition FACT autoloading from theory `arithmetic` ...
FACT = |- (FACT 0 = 1) /\ (!n. FACT(SUC n) = (SUC n) num_mul (FACT n))
Run time: 0.0s
Intermediate theorems generated: 1
Theorem ABS_POS autoloading from theory `REAL` ...
ABS_POS = |- !x. (& 0) <= (abs x)
Run time: 0.0s
Theorem REAL_LE_RMUL_IMP autoloading from theory `REAL` ...
REAL_LE_RMUL_IMP =
|- !x y z. (& 0) <= x /\ y <= z ==> (y * x) <= (z * x)
Run time: 0.0s
Theorem REAL_MUL_SYM autoloading from theory `REAL` ...
REAL_MUL_SYM = |- !x y. x * y = y * x
Run time: 0.0s
Theorem POW_1 autoloading from theory `REAL` ...
POW_1 = |- !x. x pow 1 = x
Run time: 0.0s
Theorem REAL_MUL_ASSOC autoloading from theory `REAL` ...
REAL_MUL_ASSOC = |- !x y z. x * (y * z) = (x * y) * z
Run time: 0.0s
Theorem ABS_MUL autoloading from theory `REAL` ...
ABS_MUL = |- !x y. abs(x * y) = (abs x) * (abs y)
Run time: 0.0s
Theorem POW_ADD autoloading from theory `REAL` ...
POW_ADD = |- !c m n. c pow (m num_add n) = (c pow m) * (c pow n)
Run time: 0.0s
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n num_ge m = m num_le n
Run time: 0.1s
Theorem REAL_ARCH autoloading from theory `REAL` ...
REAL_ARCH = |- !x. (& 0) < x ==> (!y. ?n. y < ((& n) * x))
Run time: 0.0s
Theorem REAL_LT_01 autoloading from theory `REAL` ...
REAL_LT_01 = |- (& 0) < (& 1)
Run time: 0.0s
Theorem REAL_DOWN autoloading from theory `REAL` ...
REAL_DOWN = |- !x. (& 0) < x ==> (?y. (& 0) < y /\ y < x)
Run time: 0.0s
Theorem SER_RATIO autoloading from theory `SEQ` ...
SER_RATIO =
|- !f c N.
c < (& 1) /\
(!n. n num_ge N ==> (abs(f(SUC n))) <= (c * (abs(f n)))) ==>
summable f
Run time: 0.0s
Theorem SUMMABLE_SUM autoloading from theory `SEQ` ...
SUMMABLE_SUM = |- !f. summable f ==> f sums (suminf f)
Run time: 0.0s
Theorem FACT_LESS autoloading from theory `arithmetic` ...
FACT_LESS = |- !n. 0 num_lt (FACT n)
Run time: 0.0s
Theorem REAL_LT autoloading from theory `REAL` ...
REAL_LT = |- !m n. (& m) < (& n) = m num_lt n
Run time: 0.0s
Theorem REAL_LT_IMP_NE autoloading from theory `REAL` ...
REAL_LT_IMP_NE = |- !x y. x < y ==> ~(x = y)
Run time: 0.0s
EXP_CONVERGES =
|- !x. (\n. ((\n. inv(&(FACT n)))n) * (x pow n)) sums (exp x)
Run time: 0.1s
Intermediate theorems generated: 628
Theorem REAL_INV_POS autoloading from theory `REAL` ...
REAL_INV_POS = |- !x. (& 0) < x ==> (& 0) < (inv x)
Run time: 0.0s
Theorem REAL_EQ_IMP_LE autoloading from theory `REAL` ...
REAL_EQ_IMP_LE = |- !x y. (x = y) ==> x <= y
Run time: 0.0s
Theorem REAL_MUL_LID autoloading from theory `REAL` ...
REAL_MUL_LID = |- !x. (& 1) * x = x
Run time: 0.0s
Theorem POW_M1 autoloading from theory `REAL` ...
POW_M1 = |- !n. abs((--(& 1)) pow n) = & 1
Run time: 0.0s
Theorem REAL_LE_MUL autoloading from theory `REAL` ...
REAL_LE_MUL = |- !x y. (& 0) <= x /\ (& 0) <= y ==> (& 0) <= (x * y)
Run time: 0.0s
Theorem REAL_MUL_LZERO autoloading from theory `REAL` ...
REAL_MUL_LZERO = |- !x. (& 0) * x = & 0
Run time: 0.0s
Theorem ABS_0 autoloading from theory `REAL` ...
ABS_0 = |- abs(& 0) = & 0
Run time: 0.0s
Theorem POW_ABS autoloading from theory `REAL` ...
POW_ABS = |- !c n. (abs c) pow n = abs(c pow n)
Run time: 0.0s
Theorem SUM_SUMMABLE autoloading from theory `SEQ` ...
SUM_SUMMABLE = |- !f l. f sums l ==> summable f
Run time: 0.0s
Theorem SER_COMPAR autoloading from theory `SEQ` ...
SER_COMPAR =
|- !f g.
(?N. !n. n num_ge N ==> (abs(f n)) <= (g n)) /\ summable g ==>
summable f
Run time: 0.0s
SIN_CONVERGES =
|- !x.
(\n.
((\n.
(EVEN n =>
& 0 |
((--(& 1)) pow ((n num_sub 1) DIV 2)) / (&(FACT n))))
n) *
(x pow n)) sums
(sin x)
Run time: 0.0s
Intermediate theorems generated: 272
COS_CONVERGES =
|- !x.
(\n.
((\n. (EVEN n => ((--(& 1)) pow (n DIV 2)) / (&(FACT n)) | & 0))n) *
(x pow n)) sums
(cos x)
Run time: 0.1s
Intermediate theorems generated: 272
Theorem REAL_MUL_RINV autoloading from theory `REAL` ...
REAL_MUL_RINV = |- !x. ~(x = & 0) ==> (x * (inv x) = & 1)
Run time: 0.0s
Theorem REAL_EQ_RMUL autoloading from theory `REAL` ...
REAL_EQ_RMUL = |- !x y z. (x * z = y * z) = (z = & 0) \/ (x = y)
Run time: 0.0s
Definition diffs autoloading from theory `POWSER` ...
diffs = |- !c. diffs c = (\n. (&(SUC n)) * (c(SUC n)))
Run time: 0.0s
Intermediate theorems generated: 1
EXP_FDIFF = |- diffs(\n. inv(&(FACT n))) = (\n. inv(&(FACT n)))
Run time: 0.0s
Intermediate theorems generated: 193
Theorem REAL_MUL_RZERO autoloading from theory `REAL` ...
REAL_MUL_RZERO = |- !x. x * (& 0) = & 0
Run time: 0.0s
Definition EVEN autoloading from theory `arithmetic` ...
EVEN = |- (EVEN 0 = T) /\ (!n. EVEN(SUC n) = ~EVEN n)
Run time: 0.0s
Intermediate theorems generated: 1
SIN_FDIFF =
|- diffs
(\n.
(EVEN n =>
& 0 |
((--(& 1)) pow ((n num_sub 1) DIV 2)) / (&(FACT n)))) =
(\n. (EVEN n => ((--(& 1)) pow (n DIV 2)) / (&(FACT n)) | & 0))
Run time: 0.0s
Intermediate theorems generated: 361
Theorem REAL_NEG_MINUS1 autoloading from theory `REAL` ...
REAL_NEG_MINUS1 = |- !x. -- x = (--(& 1)) * x
Run time: 0.1s
Definition pow autoloading from theory `REAL` ...
pow = |- (!x. x pow 0 = & 1) /\ (!x n. x pow (SUC n) = x * (x pow n))
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_NEG_LMUL autoloading from theory `REAL` ...
REAL_NEG_LMUL = |- !x y. --(x * y) = (-- x) * y
Run time: 0.0s
Theorem REAL_NEG_0 autoloading from theory `REAL` ...
REAL_NEG_0 = |- --(& 0) = & 0
Run time: 0.0s
COS_FDIFF =
|- diffs(\n. (EVEN n => ((--(& 1)) pow (n DIV 2)) / (&(FACT n)) | & 0)) =
(\n.
--
((\n.
(EVEN n =>
& 0 |
((--(& 1)) pow ((n num_sub 1) DIV 2)) / (&(FACT n))))
n))
Run time: 0.0s
Intermediate theorems generated: 407
Theorem SER_NEG autoloading from theory `SEQ` ...
SER_NEG = |- !x x0. x sums x0 ==> (\n. --(x n)) sums (-- x0)
Run time: 0.0s
Theorem SUM_UNIQ autoloading from theory `SEQ` ...
SUM_UNIQ = |- !f x. f sums x ==> (x = suminf f)
Run time: 0.0s
SIN_NEGLEMMA =
|- !x.
--(sin x) =
suminf
(\n.
--
(((\n.
(EVEN n =>
& 0 |
((--(& 1)) pow ((n num_sub 1) DIV 2)) / (&(FACT n))))
n) *
(x pow n)))
Run time: 0.0s
Intermediate theorems generated: 42
Theorem REAL_LT_ADDR autoloading from theory `REAL` ...
REAL_LT_ADDR = |- !x y. x < (x + y) = (& 0) < y
Run time: 0.0s
Theorem ABS_LE autoloading from theory `REAL` ...
ABS_LE = |- !x. x <= (abs x)
Run time: 0.0s
Theorem REAL_LTE_TRANS autoloading from theory `REAL` ...
REAL_LTE_TRANS = |- !x y z. x < y /\ y <= z ==> x < z
Run time: 0.0s
Theorem TERMDIFF autoloading from theory `POWSER` ...
TERMDIFF =
|- !c K.
summable(\n. (c n) * (K pow n)) /\
summable(\n. (diffs c n) * (K pow n)) /\
summable(\n. (diffs(diffs c)n) * (K pow n)) /\
(abs x) < (abs K) ==>
((\x. suminf(\n. (c n) * (x pow n))) diffl
(suminf(\n. (diffs c n) * (x pow n))))
x
Run time: 0.0s
DIFF_EXP = |- !x. (exp diffl (exp x))x
Run time: 0.1s
Intermediate theorems generated: 144
DIFF_SIN = |- !x. (sin diffl (cos x))x
Run time: 0.0s
Intermediate theorems generated: 200
Theorem DIFFS_NEG autoloading from theory `POWSER` ...
DIFFS_NEG = |- !c. diffs(\n. --(c n)) = (\n. --(diffs c n))
Run time: 0.0s
DIFF_COS = |- !x. (cos diffl (--(sin x)))x
Run time: 0.0s
Intermediate theorems generated: 283
[|- !x. (exp diffl (exp x))x;
|- !x. (sin diffl (cos x))x;
|- !x. (cos diffl (--(sin x)))x]
: thm list
Run time: 0.0s
Theorem POW_0 autoloading from theory `REAL` ...
POW_0 = |- !n. (& 0) pow (SUC n) = & 0
Run time: 0.0s
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n num_lt m ==> (?p. m = n num_add (p num_add 1))
Run time: 0.0s
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m num_lt n = (SUC m) num_le n
Run time: 0.0s
Theorem REAL_INV1 autoloading from theory `REAL` ...
REAL_INV1 = |- inv(& 1) = & 1
Run time: 0.0s
Theorem REAL_MUL_RID autoloading from theory `REAL` ...
REAL_MUL_RID = |- !x. x * (& 1) = x
Run time: 0.0s
Theorem REAL_ADD_LID autoloading from theory `REAL` ...
REAL_ADD_LID = |- !x. (& 0) + x = x
Run time: 0.0s
Theorem Sum autoloading from theory `REAL` ...
Sum =
|- (Sum(n,0)f = & 0) /\ (Sum(n,SUC m)f = (Sum(n,m)f) + (f(n num_add m)))
Run time: 0.0s
Theorem SER_0 autoloading from theory `SEQ` ...
SER_0 = |- !f n. (!m. n num_le m ==> (f m = & 0)) ==> f sums (Sum(0,n)f)
Run time: 0.0s
EXP_0 = |- exp(& 0) = & 1
Run time: 0.0s
Intermediate theorems generated: 274
Theorem REAL_LE_REFL autoloading from theory `REAL` ...
REAL_LE_REFL = |- !x. x <= x
Run time: 0.0s
Theorem REAL_ADD_RID autoloading from theory `REAL` ...
REAL_ADD_RID = |- !x. x + (& 0) = x
Run time: 0.0s
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 num_mul m = 0) /\
(m num_mul 0 = 0) /\
(1 num_mul m = m) /\
(m num_mul 1 = m) /\
((SUC m) num_mul n = (m num_mul n) num_add n) /\
(m num_mul (SUC n) = m num_add (m num_mul n))
Run time: 0.0s
Theorem POW_POS autoloading from theory `REAL` ...
POW_POS = |- !x. (& 0) <= x ==> (!n. (& 0) <= (x pow n))
Run time: 0.0s
Theorem SER_POS_LE autoloading from theory `SEQ` ...
SER_POS_LE =
|- !f n.
summable f /\ (!m. n num_le m ==> (& 0) <= (f m)) ==>
(Sum(0,n)f) <= (suminf f)
Run time: 0.0s
Theorem REAL_LE_LT autoloading from theory `REAL` ...
REAL_LE_LT = |- !x y. x <= y = x < y \/ (x = y)
Run time: 0.0s
EXP_LE_X = |- !x. (& 0) <= x ==> ((& 1) + x) <= (exp x)
Run time: 0.1s
Intermediate theorems generated: 420
EXP_LT_1 = |- !x. (& 0) < x ==> (& 1) < (exp x)
Run time: 0.0s
Intermediate theorems generated: 56
Theorem REAL_SUB_0 autoloading from theory `REAL` ...
REAL_SUB_0 = |- !x y. (x - y = & 0) = (x = y)
Run time: 0.0s
Definition real_sub autoloading from theory `REAL` ...
real_sub = |- !x y. x - y = x + (-- y)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_NEG_RMUL autoloading from theory `REAL` ...
REAL_NEG_RMUL = |- !x y. --(x * y) = x * (-- y)
Run time: 0.0s
Theorem DIFF_ISCONST_ALL autoloading from theory `LIM` ...
DIFF_ISCONST_ALL = |- !f. (!x. (f diffl (& 0))x) ==> (!x y. f x = f y)
Run time: 0.0s
EXP_ADD_MUL = |- !x y. (exp(x + y)) * (exp(-- x)) = exp y
Run time: 0.1s
Intermediate theorems generated: 660
EXP_NEG_MUL = |- !x. (exp x) * (exp(-- x)) = & 1
Run time: 0.0s
Intermediate theorems generated: 19
EXP_NEG_MUL2 = |- !x. (exp(-- x)) * (exp x) = & 1
Run time: 0.0s
Intermediate theorems generated: 16
Theorem REAL_RINV_UNIQ autoloading from theory `REAL` ...
REAL_RINV_UNIQ = |- !x y. (x * y = & 1) ==> (y = inv x)
Run time: 0.0s
EXP_NEG = |- !x. exp(-- x) = inv(exp x)
Run time: 0.0s
Intermediate theorems generated: 13
Theorem EXP_ADD autoloading from theory `arithmetic` ...
EXP_ADD = |- !p q n. n EXP (p num_add q) = (n EXP p) num_mul (n EXP q)
Run time: 0.0s
EXP_ADD = |- !x y. exp(x + y) = (exp x) * (exp y)
Run time: 0.0s
Intermediate theorems generated: 71
Theorem REAL_LE_SQUARE autoloading from theory `REAL` ...
REAL_LE_SQUARE = |- !x. (& 0) <= (x * x)
Run time: 0.0s
Theorem REAL_HALF_DOUBLE autoloading from theory `REAL` ...
REAL_HALF_DOUBLE = |- !x. (x / (& 2)) + (x / (& 2)) = x
Run time: 0.0s
EXP_POS_LE = |- !x. (& 0) <= (exp x)
Run time: 0.0s
Intermediate theorems generated: 27
Theorem REAL_10 autoloading from theory `REAL` ...
REAL_10 = |- ~(& 1 = & 0)
Run time: 0.0s
EXP_NZ = |- !x. ~(exp x = & 0)
Run time: 0.0s
Intermediate theorems generated: 29
Theorem REAL_LT_LE autoloading from theory `REAL` ...
REAL_LT_LE = |- !x y. x < y = x <= y /\ ~(x = y)
Run time: 0.0s
EXP_POS_LT = |- !x. (& 0) < (exp x)
Run time: 0.0s
Intermediate theorems generated: 38
Theorem REAL_RDISTRIB autoloading from theory `REAL` ...
REAL_RDISTRIB = |- !x y z. (x + y) * z = (x * z) + (y * z)
Run time: 0.0s
Theorem REAL_ADD autoloading from theory `REAL` ...
REAL_ADD = |- !m n. (& m) + (& n) = &(m num_add n)
Run time: 0.0s
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m num_add n = n num_add m
Run time: 0.0s
EXP_N = |- !n x. exp((& n) * x) = (exp x) pow n
Run time: 0.0s
Intermediate theorems generated: 152
EXP_SUB = |- !x y. exp(x - y) = (exp x) / (exp y)
Run time: 0.0s
Intermediate theorems generated: 38
Theorem REAL_LT_RMUL autoloading from theory `REAL` ...
REAL_LT_RMUL = |- !x y z. (& 0) < z ==> ((x * z) < (y * z) = x < y)
Run time: 0.0s
Theorem REAL_SUB_LT autoloading from theory `REAL` ...
REAL_SUB_LT = |- !x y. (& 0) < (x - y) = y < x
Run time: 0.0s
EXP_MONO_IMP = |- !x y. x < y ==> (exp x) < (exp y)
Run time: 0.0s
Intermediate theorems generated: 127
Theorem REAL_NOT_LT autoloading from theory `REAL` ...
REAL_NOT_LT = |- !x y. ~x < y = y <= x
Run time: 0.0s
EXP_MONO_LT = |- !x y. (exp x) < (exp y) = x < y
Run time: 0.1s
Intermediate theorems generated: 85
EXP_MONO_LE = |- !x y. (exp x) <= (exp y) = x <= y
Run time: 0.0s
Intermediate theorems generated: 37
Theorem REAL_LE_ANTISYM autoloading from theory `REAL` ...
REAL_LE_ANTISYM = |- !x y. x <= y /\ y <= x = (x = y)
Run time: 0.0s
EXP_INJ = |- !x y. (exp x = exp y) = (x = y)
Run time: 0.0s
Intermediate theorems generated: 39
Theorem DIFF_CONT autoloading from theory `LIM` ...
DIFF_CONT = |- !f l x. (f diffl l)x ==> f contl x
Run time: 0.0s
Theorem REAL_SUB_ADD2 autoloading from theory `REAL` ...
REAL_SUB_ADD2 = |- !x y. y + (x - y) = x
Run time: 0.0s
Theorem REAL_SUB_LE autoloading from theory `REAL` ...
REAL_SUB_LE = |- !x y. (& 0) <= (x - y) = y <= x
Run time: 0.0s
Theorem REAL_LE_SUB_LADD autoloading from theory `REAL` ...
REAL_LE_SUB_LADD = |- !x y z. x <= (y - z) = (x + z) <= y
Run time: 0.0s
Theorem IVT autoloading from theory `LIM` ...
IVT =
|- !f a b y.
a <= b /\
((f a) <= y /\ y <= (f b)) /\
(!x. a <= x /\ x <= b ==> f contl x) ==>
(?x. a <= x /\ x <= b /\ (f x = y))
Run time: 0.0s
EXP_TOTAL_LEMMA =
|- !y.
(& 1) <= y ==> (?x. (& 0) <= x /\ x <= (y - (& 1)) /\ (exp x = y))
Run time: 0.0s
Intermediate theorems generated: 116
Theorem REAL_INVINV autoloading from theory `REAL` ...
REAL_INVINV = |- !x. ~(x = & 0) ==> (inv(inv x) = x)
Run time: 0.0s
Theorem REAL_INV_LT1 autoloading from theory `REAL` ...
REAL_INV_LT1 = |- !x. (& 0) < x /\ x < (& 1) ==> (& 1) < (inv x)
Run time: 0.0s
Theorem REAL_LET_TOTAL autoloading from theory `REAL` ...
REAL_LET_TOTAL = |- !x y. x <= y \/ y < x
Run time: 0.0s
EXP_TOTAL = |- !y. (& 0) < y ==> (?x. exp x = y)
Run time: 0.0s
Intermediate theorems generated: 134
ln = |- !x. ln x = (@u. exp u = x)
Run time: 0.0s
Intermediate theorems generated: 2
LN_EXP = |- !x. ln(exp x) = x
Run time: 0.1s
Intermediate theorems generated: 52
EXP_LN = |- !x. (exp(ln x) = x) = (& 0) < x
Run time: 0.0s
Intermediate theorems generated: 41
Theorem REAL_LT_MUL autoloading from theory `REAL` ...
REAL_LT_MUL = |- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x * y)
Run time: 0.0s
LN_MUL =
|- !x y. (& 0) < x /\ (& 0) < y ==> (ln(x * y) = (ln x) + (ln y))
Run time: 0.0s
Intermediate theorems generated: 113
LN_INJ = |- !x y. (& 0) < x /\ (& 0) < y ==> ((ln x = ln y) = (x = y))
Run time: 0.0s
Intermediate theorems generated: 53
LN_1 = |- ln(& 1) = & 0
Run time: 0.0s
Intermediate theorems generated: 27
Theorem REAL_POS_NZ autoloading from theory `REAL` ...
REAL_POS_NZ = |- !x. (& 0) < x ==> ~(x = & 0)
Run time: 0.0s
Theorem REAL_RNEG_UNIQ autoloading from theory `REAL` ...
REAL_RNEG_UNIQ = |- !x y. (x + y = & 0) = (y = -- x)
Run time: 0.0s
LN_INV = |- !x. (& 0) < x ==> (ln(inv x) = --(ln x))
Run time: 0.0s
Intermediate theorems generated: 81
LN_DIV = |- !x. (& 0) < x /\ (& 0) < y ==> (ln(x / y) = (ln x) - (ln y))
Run time: 0.0s
Intermediate theorems generated: 78
LN_MONO_LT =
|- !x y. (& 0) < x /\ (& 0) < y ==> ((ln x) < (ln y) = x < y)
Run time: 0.0s
Intermediate theorems generated: 53
LN_MONO_LE =
|- !x y. (& 0) < x /\ (& 0) < y ==> ((ln x) <= (ln y) = x <= y)
Run time: 0.0s
Intermediate theorems generated: 53
LN_POW = |- !n x. (& 0) < x ==> (ln(x pow n) = (& n) * (ln x))
Run time: 0.0s
Intermediate theorems generated: 42
root =
|- !n x. root n x = (@u. ((& 0) < x ==> (& 0) < u) /\ (u pow n = x))
Run time: 0.0s
Intermediate theorems generated: 2
sqrt = |- !x. sqrt x = root 2 x
Run time: 0.0s
Intermediate theorems generated: 2
Theorem REAL_MUL_LINV autoloading from theory `REAL` ...
REAL_MUL_LINV = |- !x. ~(x = & 0) ==> ((inv x) * x = & 1)
Run time: 0.0s
ROOT_LT_LEMMA =
|- !n x. (& 0) < x ==> ((exp((ln x) / (&(SUC n)))) pow (SUC n) = x)
Run time: 0.1s
Intermediate theorems generated: 123
ROOT_LN =
|- !n x. (& 0) < x ==> (!n. root(SUC n)x = exp((ln x) / (&(SUC n))))
Run time: 0.0s
Intermediate theorems generated: 282
Theorem REAL_ENTIRE autoloading from theory `REAL` ...
REAL_ENTIRE = |- !x y. (x * y = & 0) = (x = & 0) \/ (y = & 0)
Run time: 0.0s
Theorem REAL_LT_REFL autoloading from theory `REAL` ...
REAL_LT_REFL = |- !x. ~x < x
Run time: 0.0s
ROOT_0 = |- !n. root(SUC n)(& 0) = & 0
Run time: 0.1s
Intermediate theorems generated: 209
Theorem REAL_DIV_LZERO autoloading from theory `REAL` ...
REAL_DIV_LZERO = |- !x. (& 0) / x = & 0
Run time: 0.0s
ROOT_1 = |- !n. root(SUC n)(& 1) = & 1
Run time: 0.0s
Intermediate theorems generated: 28
ROOT_POW_POS = |- !n x. (& 0) <= x ==> ((root(SUC n)x) pow (SUC n) = x)
Run time: 0.0s
Intermediate theorems generated: 66
SQRT_0 = |- sqrt(& 0) = & 0
Run time: 0.0s
Intermediate theorems generated: 20
SQRT_1 = |- sqrt(& 1) = & 1
Run time: 0.0s
Intermediate theorems generated: 20
Theorem REAL_LE_POW2 autoloading from theory `REAL` ...
REAL_LE_POW2 = |- !x. (& 0) <= (x pow 2)
Run time: 0.0s
SQRT_POW2 = |- !x. ((sqrt x) pow 2 = x) = (& 0) <= x
Run time: 0.0s
Intermediate theorems generated: 33
Theorem ODD_EVEN autoloading from theory `arithmetic` ...
ODD_EVEN = |- !n. ODD n = ~EVEN n
Run time: 0.0s
SIN_0 = |- sin(& 0) = & 0
Run time: 0.1s
Intermediate theorems generated: 206
Theorem REAL_DIV_REFL autoloading from theory `REAL` ...
REAL_DIV_REFL = |- !x. ~(x = & 0) ==> (x / x = & 1)
Run time: 0.0s
Theorem DIV_UNIQUE autoloading from theory `arithmetic` ...
DIV_UNIQUE =
|- !n k q.
(?r. (k = (q num_mul n) num_add r) /\ r num_lt n) ==> (k DIV n = q)
Run time: 0.0s
COS_0 = |- cos(& 0) = & 1
Run time: 0.1s
Intermediate theorems generated: 454
SIN_CIRCLE = |- !x. ((sin x) pow 2) + ((cos x) pow 2) = & 1
Run time: 0.0s
Intermediate theorems generated: 690
Theorem REAL_ADD_RINV autoloading from theory `REAL` ...
REAL_ADD_RINV = |- !x. x + (-- x) = & 0
Run time: 0.1s
Theorem REAL_ADD_SYM autoloading from theory `REAL` ...
REAL_ADD_SYM = |- !x y. x + y = y + x
Run time: 0.0s
Theorem REAL_ADD_ASSOC autoloading from theory `REAL` ...
REAL_ADD_ASSOC = |- !x y z. x + (y + z) = (x + y) + z
Run time: 0.0s
Theorem REAL_LTE_ADD autoloading from theory `REAL` ...
REAL_LTE_ADD = |- !x y. (& 0) < x /\ (& 0) <= y ==> (& 0) < (x + y)
Run time: 0.0s
Theorem POW_2 autoloading from theory `REAL` ...
POW_2 = |- !x. x pow 2 = x * x
Run time: 0.0s
Theorem REAL_POW2_ABS autoloading from theory `REAL` ...
REAL_POW2_ABS = |- !x. (abs x) pow 2 = x pow 2
Run time: 0.0s
Theorem REAL_LT1_POW2 autoloading from theory `REAL` ...
REAL_LT1_POW2 = |- !x. (& 1) < x ==> (& 1) < (x pow 2)
Run time: 0.0s
Theorem REAL_NOT_LE autoloading from theory `REAL` ...
REAL_NOT_LE = |- !x y. ~x <= y = y < x
Run time: 0.0s
SIN_BOUND = |- !x. (abs(sin x)) <= (& 1)
Run time: 0.0s
Intermediate theorems generated: 212
Theorem ABS_BOUNDS autoloading from theory `REAL` ...
ABS_BOUNDS = |- !x k. (abs x) <= k = (-- k) <= x /\ x <= k
Run time: 0.0s
SIN_BOUNDS = |- !x. (--(& 1)) <= (sin x) /\ (sin x) <= (& 1)
Run time: 0.0s
Intermediate theorems generated: 24
Theorem REAL_LET_ADD autoloading from theory `REAL` ...
REAL_LET_ADD = |- !x y. (& 0) <= x /\ (& 0) < y ==> (& 0) < (x + y)
Run time: 0.0s
COS_BOUND = |- !x. (abs(cos x)) <= (& 1)
Run time: 0.1s
Intermediate theorems generated: 160
COS_BOUNDS = |- !x. (--(& 1)) <= (cos x) /\ (cos x) <= (& 1)
Run time: 0.0s
Intermediate theorems generated: 24
Theorem REAL_NEGNEG autoloading from theory `REAL` ...
REAL_NEGNEG = |- !x. --(-- x) = x
Run time: 0.0s
Theorem REAL_NEG_ADD autoloading from theory `REAL` ...
REAL_NEG_ADD = |- !x y. --(x + y) = (-- x) + (-- y)
Run time: 0.0s
Theorem REAL_SUB_LZERO autoloading from theory `REAL` ...
REAL_SUB_LZERO = |- !x. (& 0) - x = -- x
Run time: 0.0s
Theorem REAL_EQ_SUB_LADD autoloading from theory `REAL` ...
REAL_EQ_SUB_LADD = |- !x y z. (x = y - z) = (x + z = y)
Run time: 0.0s
Theorem REAL_SUB_REFL autoloading from theory `REAL` ...
REAL_SUB_REFL = |- !x. x - x = & 0
Run time: 0.0s
Theorem REAL_SUB_RZERO autoloading from theory `REAL` ...
REAL_SUB_RZERO = |- !x. x - (& 0) = x
Run time: 0.0s
SIN_COS_ADD =
|- !x y.
(((sin(x + y)) - (((sin x) * (cos y)) + ((cos x) * (sin y)))) pow 2) +
(((cos(x + y)) - (((cos x) * (cos y)) - ((sin x) * (sin y)))) pow 2) =
& 0
Run time: 0.3s
Intermediate theorems generated: 1747
SIN_COS_NEG =
|- !x.
(((sin(-- x)) + (sin x)) pow 2) + (((cos(-- x)) - (cos x)) pow 2) =
& 0
Run time: 0.1s
Intermediate theorems generated: 1099
Theorem REAL_SUMSQ autoloading from theory `REAL` ...
REAL_SUMSQ = |- !x y. ((x * x) + (y * y) = & 0) = (x = & 0) /\ (y = & 0)
Run time: 0.0s
SIN_ADD =
|- !x y. sin(x + y) = ((sin x) * (cos y)) + ((cos x) * (sin y))
Run time: 0.0s
Intermediate theorems generated: 51
COS_ADD =
|- !x y. cos(x + y) = ((cos x) * (cos y)) - ((sin x) * (sin y))
Run time: 0.1s
Intermediate theorems generated: 51
Theorem REAL_LNEG_UNIQ autoloading from theory `REAL` ...
REAL_LNEG_UNIQ = |- !x y. (x + y = & 0) = (x = -- y)
Run time: 0.0s
SIN_NEG = |- !x. sin(-- x) = --(sin x)
Run time: 0.0s
Intermediate theorems generated: 48
COS_NEG = |- !x. cos(-- x) = cos x
Run time: 0.0s
Intermediate theorems generated: 47
Theorem REAL_DOUBLE autoloading from theory `REAL` ...
REAL_DOUBLE = |- !x. x + x = (& 2) * x
Run time: 0.0s
SIN_DOUBLE = |- !x. sin((& 2) * x) = (& 2) * ((sin x) * (cos x))
Run time: 0.0s
Intermediate theorems generated: 29
COS_DOUBLE = |- !x. cos((& 2) * x) = ((cos x) pow 2) - ((sin x) pow 2)
Run time: 0.1s
Intermediate theorems generated: 34
Theorem ODD_DOUBLE autoloading from theory `arithmetic` ...
ODD_DOUBLE = |- !n. ODD(SUC(2 num_mul n))
Run time: 0.0s
Theorem EVEN_DOUBLE autoloading from theory `arithmetic` ...
EVEN_DOUBLE = |- !n. EVEN(2 num_mul n)
Run time: 0.0s
Theorem SUM_2 autoloading from theory `REAL` ...
SUM_2 = |- !f n. Sum(n,2)f = (f n) + (f(n num_add 1))
Run time: 0.0s
Theorem SER_PAIR autoloading from theory `SEQ` ...
SER_PAIR =
|- !f. summable f ==> (\n. Sum(2 num_mul n,2)f) sums (suminf f)
Run time: 0.0s
SIN_PAIRED =
|- !x.
(\n.
(((--(& 1)) pow n) / (&(FACT((2 num_mul n) num_add 1)))) *
(x pow ((2 num_mul n) num_add 1))) sums
(sin x)
Run time: 0.0s
Intermediate theorems generated: 183
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) num_le (SUC m) = n num_le m
Run time: 0.0s
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n num_lt (SUC n)
Run time: 0.0s
Theorem REAL_LT_TRANS autoloading from theory `REAL` ...
REAL_LT_TRANS = |- !x y z. x < y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_LT_MUL2 autoloading from theory `REAL` ...
REAL_LT_MUL2 =
|- !x1 x2 y1 y2.
(& 0) <= x1 /\ (& 0) <= y1 /\ x1 < x2 /\ y1 < y2 ==>
(x1 * y1) < (x2 * y2)
Run time: 0.0s
Theorem REAL_LT_1 autoloading from theory `REAL` ...
REAL_LT_1 = |- !x y. (& 0) <= x /\ x < y ==> (x / y) < (& 1)
Run time: 0.0s
Theorem POW_POS_LT autoloading from theory `REAL` ...
POW_POS_LT = |- !x n. (& 0) < x ==> (& 0) < (x pow (SUC n))
Run time: 0.0s
Theorem REAL_LT_RMUL_IMP autoloading from theory `REAL` ...
REAL_LT_RMUL_IMP = |- !x y z. x < y /\ (& 0) < z ==> (x * z) < (y * z)
Run time: 0.0s
Theorem SER_POS_LT autoloading from theory `SEQ` ...
SER_POS_LT =
|- !f n.
summable f /\ (!m. n num_le m ==> (& 0) < (f m)) ==>
(Sum(0,n)f) < (suminf f)
Run time: 0.0s
Theorem POW_MINUS1 autoloading from theory `REAL` ...
POW_MINUS1 = |- !n. (--(& 1)) pow (2 num_mul n) = & 1
Run time: 0.0s
SIN_POS = |- !x. (& 0) < x /\ x < (& 2) ==> (& 0) < (sin x)
Run time: 0.2s
Intermediate theorems generated: 2052
COS_PAIRED =
|- !x.
(\n.
(((--(& 1)) pow n) / (&(FACT(2 num_mul n)))) *
(x pow (2 num_mul n))) sums
(cos x)
Run time: 0.0s
Intermediate theorems generated: 163
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) num_lt (SUC n) = m num_lt n
Run time: 0.0s
Theorem SER_POS_LT_PAIR autoloading from theory `SEQ` ...
SER_POS_LT_PAIR =
|- !f n.
summable f /\
(!d.
(& 0) <
((f(n num_add (2 num_mul d))) +
(f(n num_add ((2 num_mul d) num_add 1))))) ==>
(Sum(0,n)f) < (suminf f)
Run time: 0.0s
Theorem REAL_ADD_LINV autoloading from theory `REAL` ...
REAL_ADD_LINV = |- !x. (-- x) + x = & 0
Run time: 0.0s
Theorem REAL_EQ_LMUL_IMP autoloading from theory `REAL` ...
REAL_EQ_LMUL_IMP = |- !x y z. ~(x = & 0) /\ (x * y = x * z) ==> (y = z)
Run time: 0.0s
Theorem REAL_NEG_LT0 autoloading from theory `REAL` ...
REAL_NEG_LT0 = |- !x. (-- x) < (& 0) = (& 0) < x
Run time: 0.1s
COS_2 = |- (cos(& 2)) < (& 0)
Run time: 0.4s
Intermediate theorems generated: 3794
Theorem REAL_LET_TRANS autoloading from theory `REAL` ...
REAL_LET_TRANS = |- !x y z. x <= y /\ y < z ==> x < z
Run time: 0.0s
Theorem REAL_NEG_EQ0 autoloading from theory `REAL` ...
REAL_NEG_EQ0 = |- !x. (-- x = & 0) = (x = & 0)
Run time: 0.0s
Theorem DIFF_UNIQ autoloading from theory `LIM` ...
DIFF_UNIQ = |- !f l m x. (f diffl l)x /\ (f diffl m)x ==> (l = m)
Run time: 0.0s
Theorem ROLLE autoloading from theory `LIM` ...
ROLLE =
|- !f a b.
a < b /\
(f a = f b) /\
(!x. a <= x /\ x <= b ==> f contl x) /\
(!x. a < x /\ x < b ==> f differentiable x) ==>
(?z. a < z /\ z < b /\ (f diffl (& 0))z)
Run time: 0.1s
Definition differentiable autoloading from theory `LIM` ...
differentiable = |- !f x. f differentiable x = (?l. (f diffl l)x)
Run time: 0.0s
Intermediate theorems generated: 1
Theorem REAL_LT_TOTAL autoloading from theory `REAL` ...
REAL_LT_TOTAL = |- !x y. (x = y) \/ x < y \/ y < x
Run time: 0.0s
Theorem REAL_LE_01 autoloading from theory `REAL` ...
REAL_LE_01 = |- (& 0) <= (& 1)
Run time: 0.0s
Theorem IVT2 autoloading from theory `LIM` ...
IVT2 =
|- !f a b y.
a <= b /\
((f b) <= y /\ y <= (f a)) /\
(!x. a <= x /\ x <= b ==> f contl x) ==>
(?x. a <= x /\ x <= b /\ (f x = y))
Run time: 0.0s
COS_ISZERO = |- ?! x. (& 0) <= x /\ x <= (& 2) /\ (cos x = & 0)
Run time: 0.0s
Intermediate theorems generated: 775
pi = |- pi = (& 2) * (@x. (& 0) <= x /\ x <= (& 2) /\ (cos x = & 0))
Run time: 0.1s
Intermediate theorems generated: 2
PI2 = |- pi / (& 2) = (@x. (& 0) <= x /\ x <= (& 2) /\ (cos x = & 0))
Run time: 0.0s
Intermediate theorems generated: 117
COS_PI2 = |- cos(pi / (& 2)) = & 0
Run time: 0.0s
Intermediate theorems generated: 42
PI2_BOUNDS = |- (& 0) < (pi / (& 2)) /\ (pi / (& 2)) < (& 2)
Run time: 0.0s
Intermediate theorems generated: 124
Theorem REAL_LT_ADD autoloading from theory `REAL` ...
REAL_LT_ADD = |- !x y. (& 0) < x /\ (& 0) < y ==> (& 0) < (x + y)
Run time: 0.1s
PI_POS = |- (& 0) < pi
Run time: 0.0s
Intermediate theorems generated: 31
Theorem REAL_LT_GT autoloading from theory `REAL` ...
REAL_LT_GT = |- !x y. x < y ==> ~y < x
Run time: 0.0s
Theorem REAL_DIFFSQ autoloading from theory `REAL` ...
REAL_DIFFSQ = |- !x y. (x + y) * (x - y) = (x * x) - (y * y)
Run time: 0.0s
SIN_PI2 = |- sin(pi / (& 2)) = & 1
Run time: 0.0s
Intermediate theorems generated: 212
Theorem REAL_DIV_LMUL autoloading from theory `REAL` ...
REAL_DIV_LMUL = |- !x y. ~(y = & 0) ==> (y * (x / y) = x)
Run time: 0.0s
COS_PI = |- cos pi = --(& 1)
Run time: 0.0s
Intermediate theorems generated: 84
SIN_PI = |- sin pi = & 0
Run time: 0.1s
Intermediate theorems generated: 79
SIN_COS = |- !x. sin x = cos((pi / (& 2)) - x)
Run time: 0.0s
Intermediate theorems generated: 66
COS_SIN = |- !x. cos x = sin((pi / (& 2)) - x)
Run time: 0.0s
Intermediate theorems generated: 56
SIN_PERIODIC_PI = |- !x. sin(x + pi) = --(sin x)
Run time: 0.0s
Intermediate theorems generated: 59
COS_PERIODIC_PI = |- !x. cos(x + pi) = --(cos x)
Run time: 0.1s
Intermediate theorems generated: 59
SIN_PERIODIC = |- !x. sin(x + ((& 2) * pi)) = sin x
Run time: 0.0s
Intermediate theorems generated: 47
COS_PERIODIC = |- !x. cos(x + ((& 2) * pi)) = cos x
Run time: 0.0s
Intermediate theorems generated: 47
COS_NPI = |- !n. cos((& n) * pi) = (--(& 1)) pow n
Run time: 0.0s
Intermediate theorems generated: 134
SIN_NPI = |- !n. sin((& n) * pi) = & 0
Run time: 0.1s
Intermediate theorems generated: 137
SIN_POS_PI2 = |- !x. (& 0) < x /\ x < (pi / (& 2)) ==> (& 0) < (sin x)
Run time: 0.0s
Intermediate theorems generated: 53
COS_POS_PI2 = |- !x. (& 0) < x /\ x < (pi / (& 2)) ==> (& 0) < (cos x)
Run time: 0.0s
Intermediate theorems generated: 450
Theorem REAL_LT_NEG autoloading from theory `REAL` ...
REAL_LT_NEG = |- !x y. (-- x) < (-- y) = y < x
Run time: 0.0s
COS_POS_PI =
|- !x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) ==> (& 0) < (cos x)
Run time: 0.0s
Intermediate theorems generated: 143
Theorem REAL_LT_SUB_RADD autoloading from theory `REAL` ...
REAL_LT_SUB_RADD = |- !x y z. (x - y) < z = x < (z + y)
Run time: 0.0s
Theorem REAL_LT_SUB_LADD autoloading from theory `REAL` ...
REAL_LT_SUB_LADD = |- !x y z. x < (y - z) = (x + z) < y
Run time: 0.0s
Theorem REAL_NEG_SUB autoloading from theory `REAL` ...
REAL_NEG_SUB = |- !x y. --(x - y) = y - x
Run time: 0.0s
SIN_POS_PI = |- !x. (& 0) < x /\ x < pi ==> (& 0) < (sin x)
Run time: 0.0s
Intermediate theorems generated: 96
COS_TOTAL =
|- !y.
(--(& 1)) <= y /\ y <= (& 1) ==>
(?! x. (& 0) <= x /\ x <= pi /\ (cos x = y))
Run time: 0.1s
Intermediate theorems generated: 766
Theorem REAL_EQ_RADD autoloading from theory `REAL` ...
REAL_EQ_RADD = |- !x y z. (x + z = y + z) = (x = y)
Run time: 0.0s
Theorem REAL_SUB_ADD autoloading from theory `REAL` ...
REAL_SUB_ADD = |- !x y. (x - y) + y = x
Run time: 0.0s
Theorem REAL_LE_NEG autoloading from theory `REAL` ...
REAL_LE_NEG = |- !x y. (-- x) <= (-- y) = y <= x
Run time: 0.0s
Theorem REAL_ADD_SUB autoloading from theory `REAL` ...
REAL_ADD_SUB = |- !x y. (x + y) - x = y
Run time: 0.0s
Theorem REAL_EQ_NEG autoloading from theory `REAL` ...
REAL_EQ_NEG = |- !x y. (-- x = -- y) = (x = y)
Run time: 0.0s
Theorem REAL_LE_SUB_RADD autoloading from theory `REAL` ...
REAL_LE_SUB_RADD = |- !x y z. (x - y) <= z = x <= (z + y)
Run time: 0.0s
SIN_TOTAL =
|- !y.
(--(& 1)) <= y /\ y <= (& 1) ==>
(?! x. (--(pi / (& 2))) <= x /\ x <= (pi / (& 2)) /\ (sin x = y))
Run time: 0.1s
Intermediate theorems generated: 431
Theorem REAL_DIV_RMUL autoloading from theory `REAL` ...
REAL_DIV_RMUL = |- !x y. ~(y = & 0) ==> ((x / y) * y = x)
Run time: 0.0s
Theorem REAL_EQ_SUB_RADD autoloading from theory `REAL` ...
REAL_EQ_SUB_RADD = |- !x y z. (x - y = z) = (x = z + y)
Run time: 0.0s
Theorem REAL_LT_HALF2 autoloading from theory `REAL` ...
REAL_LT_HALF2 = |- !d. (d / (& 2)) < d = (& 0) < d
Run time: 0.0s
Theorem REAL_LT_HALF1 autoloading from theory `REAL` ...
REAL_LT_HALF1 = |- !d. (& 0) < (d / (& 2)) = (& 0) < d
Run time: 0.0s
Theorem REAL_NEG_LE0 autoloading from theory `REAL` ...
REAL_NEG_LE0 = |- !x. (-- x) <= (& 0) = (& 0) <= x
Run time: 0.0s
Theorem REAL_ARCH_LEAST autoloading from theory `REAL` ...
REAL_ARCH_LEAST =
|- !y.
(& 0) < y ==>
(!x. (& 0) <= x ==> (?n. ((& n) * y) <= x /\ x < ((&(SUC n)) * y)))
Run time: 0.0s
COS_ZERO_LEMMA =
|- !x.
(& 0) <= x /\ (cos x = & 0) ==>
(?n. ~EVEN n /\ (x = (& n) * (pi / (& 2))))
Run time: 0.1s
Intermediate theorems generated: 675
Theorem REAL_LE_ADDR autoloading from theory `REAL` ...
REAL_LE_ADDR = |- !x y. x <= (x + y) = (& 0) <= y
Run time: 0.0s
SIN_ZERO_LEMMA =
|- !x.
(& 0) <= x /\ (sin x = & 0) ==>
(?n. EVEN n /\ (x = (& n) * (pi / (& 2))))
Run time: 0.0s
Intermediate theorems generated: 305
Theorem REAL_NEG_EQ autoloading from theory `REAL` ...
REAL_NEG_EQ = |- !x y. (-- x = y) = (x = -- y)
Run time: 0.0s
Theorem REAL_LE_TOTAL autoloading from theory `REAL` ...
REAL_LE_TOTAL = |- !x y. x <= y \/ y <= x
Run time: 0.0s
COS_ZERO =
|- !x.
(cos x = & 0) =
(?n. ~EVEN n /\ (x = (& n) * (pi / (& 2)))) \/
(?n. ~EVEN n /\ (x = --((& n) * (pi / (& 2)))))
Run time: 0.1s
Intermediate theorems generated: 630
Theorem EVEN_EXISTS autoloading from theory `arithmetic` ...
EVEN_EXISTS = |- !n. EVEN n = (?m. n = 2 num_mul m)
Run time: 0.0s
Theorem REAL_NEG_GE0 autoloading from theory `REAL` ...
REAL_NEG_GE0 = |- !x. (& 0) <= (-- x) = x <= (& 0)
Run time: 0.0s
SIN_ZERO =
|- !x.
(sin x = & 0) =
(?n. EVEN n /\ (x = (& n) * (pi / (& 2)))) \/
(?n. EVEN n /\ (x = --((& n) * (pi / (& 2)))))
Run time: 0.1s
Intermediate theorems generated: 319
tan = |- !x. tan x = (sin x) / (cos x)
Run time: 0.0s
Intermediate theorems generated: 2
TAN_0 = |- tan(& 0) = & 0
Run time: 0.0s
Intermediate theorems generated: 19
TAN_PI = |- tan pi = & 0
Run time: 0.0s
Intermediate theorems generated: 19
TAN_NPI = |- !n. tan((& n) * pi) = & 0
Run time: 0.1s
Intermediate theorems generated: 24
TAN_NEG = |- !x. tan(-- x) = --(tan x)
Run time: 0.0s
Intermediate theorems generated: 46
TAN_PERIODIC = |- !x. tan(x + ((& 2) * pi)) = tan x
Run time: 0.0s
Intermediate theorems generated: 24
Theorem REAL_LDISTRIB autoloading from theory `REAL` ...
REAL_LDISTRIB = |- !x y z. x * (y + z) = (x * y) + (x * z)
Run time: 0.0s
Theorem REAL_SUB_LDISTRIB autoloading from theory `REAL` ...
REAL_SUB_LDISTRIB = |- !x y z. x * (y - z) = (x * y) - (x * z)
Run time: 0.0s
Theorem REAL_DIV_MUL2 autoloading from theory `REAL` ...
REAL_DIV_MUL2 =
|- !x z. ~(x = & 0) /\ ~(z = & 0) ==> (!y. y / z = (x * y) / (x * z))
Run time: 0.0s
TAN_ADD =
|- !x y.
~(cos x = & 0) /\ ~(cos y = & 0) /\ ~(cos(x + y) = & 0) ==>
(tan(x + y) = ((tan x) + (tan y)) / ((& 1) - ((tan x) * (tan y))))
Run time: 0.1s
Intermediate theorems generated: 869
TAN_DOUBLE =
|- !x.
~(cos x = & 0) /\ ~(cos((& 2) * x) = & 0) ==>
(tan((& 2) * x) = ((& 2) * (tan x)) / ((& 1) - ((tan x) pow 2)))
Run time: 0.1s
Intermediate theorems generated: 68
TAN_POS_PI2 = |- !x. (& 0) < x /\ x < (pi / (& 2)) ==> (& 0) < (tan x)
Run time: 0.0s
Intermediate theorems generated: 78
Theorem REAL_INV_1OVER autoloading from theory `REAL` ...
REAL_INV_1OVER = |- !x. inv x = (& 1) / x
Run time: 0.0s
DIFF_TAN = |- !x. ~(cos x = & 0) ==> (tan diffl (inv((cos x) pow 2)))x
Run time: 0.1s
Intermediate theorems generated: 532
Theorem REAL_LT_INV autoloading from theory `REAL` ...
REAL_LT_INV = |- !x y. (& 0) < x /\ x < y ==> (inv y) < (inv x)
Run time: 0.0s
Theorem ABS_NEG autoloading from theory `REAL` ...
ABS_NEG = |- !x. abs(-- x) = abs x
Run time: 0.0s
Theorem REAL_SUB_SUB autoloading from theory `REAL` ...
REAL_SUB_SUB = |- !x y. (x - y) - x = -- y
Run time: 0.0s
Theorem REAL_DOWN2 autoloading from theory `REAL` ...
REAL_DOWN2 =
|- !x y. (& 0) < x /\ (& 0) < y ==> (?z. (& 0) < z /\ z < x /\ z < y)
Run time: 0.0s
Theorem LIM autoloading from theory `LIM` ...
LIM =
|- !f y0 x0.
(f tends_real_real y0)x0 =
(!e.
(& 0) < e ==>
(?d.
(& 0) < d /\
(!x.
(& 0) < (abs(x - x0)) /\ (abs(x - x0)) < d ==>
(abs((f x) - y0)) < e)))
Run time: 0.0s
Theorem CONTL_LIM autoloading from theory `LIM` ...
CONTL_LIM = |- !f x. f contl x = (f tends_real_real (f x))x
Run time: 0.0s
Theorem LIM_DIV autoloading from theory `LIM` ...
LIM_DIV =
|- !f g l m.
(f tends_real_real l)x /\ (g tends_real_real m)x /\ ~(m = & 0) ==>
((\x. (f x) / (g x)) tends_real_real (l / m))x
Run time: 0.0s
TAN_TOTAL_LEMMA =
|- !y. (& 0) < y ==> (?x. (& 0) < x /\ x < (pi / (& 2)) /\ y < (tan x))
Run time: 0.2s
Intermediate theorems generated: 1046
TAN_TOTAL_POS =
|- !y.
(& 0) <= y ==> (?x. (& 0) <= x /\ x < (pi / (& 2)) /\ (tan x = y))
Run time: 0.0s
Intermediate theorems generated: 372
Theorem POW_NZ autoloading from theory `REAL` ...
POW_NZ = |- !c n. ~(c = & 0) ==> ~(c pow n = & 0)
Run time: 0.0s
Theorem REAL_INV_NZ autoloading from theory `REAL` ...
REAL_INV_NZ = |- !x. ~(x = & 0) ==> ~(inv x = & 0)
Run time: 0.0s
Theorem REAL_LE_NEGL autoloading from theory `REAL` ...
REAL_LE_NEGL = |- !x. (-- x) <= x = (& 0) <= x
Run time: 0.0s
Theorem REAL_LE_NEGTOTAL autoloading from theory `REAL` ...
REAL_LE_NEGTOTAL = |- !x. (& 0) <= x \/ (& 0) <= (-- x)
Run time: 0.0s
TAN_TOTAL =
|- !y. ?! x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) /\ (tan x = y)
Run time: 0.1s
Intermediate theorems generated: 1301
asn =
|- !y.
asn y =
(@x. (--(pi / (& 2))) <= x /\ x <= (pi / (& 2)) /\ (sin x = y))
Run time: 0.0s
Intermediate theorems generated: 2
acs = |- !y. acs y = (@x. (& 0) <= x /\ x <= pi /\ (cos x = y))
Run time: 0.0s
Intermediate theorems generated: 2
atn =
|- !y.
atn y =
(@x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) /\ (tan x = y))
Run time: 0.0s
Intermediate theorems generated: 2
ASN =
|- !y.
(--(& 1)) <= y /\ y <= (& 1) ==>
(--(pi / (& 2))) <= (asn y) /\
(asn y) <= (pi / (& 2)) /\
(sin(asn y) = y)
Run time: 0.0s
Intermediate theorems generated: 79
ASN_SIN = |- !y. (--(& 1)) <= y /\ y <= (& 1) ==> (sin(asn y) = y)
Run time: 0.0s
Intermediate theorems generated: 18
ASN_BOUNDS =
|- !y.
(--(& 1)) <= y /\ y <= (& 1) ==>
(--(pi / (& 2))) <= (asn y) /\ (asn y) <= (pi / (& 2))
Run time: 0.0s
Intermediate theorems generated: 17
SIN_ASN =
|- !x. (--(pi / (& 2))) <= x /\ x <= (pi / (& 2)) ==> (asn(sin x) = x)
Run time: 0.1s
Intermediate theorems generated: 86
ACS =
|- !y.
(--(& 1)) <= y /\ y <= (& 1) ==>
(& 0) <= (acs y) /\ (acs y) <= pi /\ (cos(acs y) = y)
Run time: 0.0s
Intermediate theorems generated: 79
ACS_COS = |- !y. (--(& 1)) <= y /\ y <= (& 1) ==> (cos(acs y) = y)
Run time: 0.0s
Intermediate theorems generated: 18
ACS_BOUNDS =
|- !y.
(--(& 1)) <= y /\ y <= (& 1) ==> (& 0) <= (acs y) /\ (acs y) <= pi
Run time: 0.1s
Intermediate theorems generated: 17
COS_ACS = |- !x. (& 0) <= x /\ x <= pi ==> (acs(cos x) = x)
Run time: 0.0s
Intermediate theorems generated: 86
ATN =
|- !y.
(--(pi / (& 2))) < (atn y) /\
(atn y) < (pi / (& 2)) /\
(tan(atn y) = y)
Run time: 0.0s
Intermediate theorems generated: 76
ATN_TAN = |- !y. tan(atn y) = y
Run time: 0.1s
Intermediate theorems generated: 28
ATN_BOUNDS = |- !y. (--(pi / (& 2))) < (atn y) /\ (atn y) < (pi / (& 2))
Run time: 0.0s
Intermediate theorems generated: 28
TAN_ATN =
|- !x. (--(pi / (& 2))) < x /\ x < (pi / (& 2)) ==> (atn(tan x) = x)
Run time: 0.0s
Intermediate theorems generated: 103
() : void
Run time: 0.1s
Intermediate theorems generated: 1
File transc.ml loaded
() : void
Run time: 6.5s
Intermediate theorems generated: 30503
#make[5]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals/theories'
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/reals'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/window'
rm -f win.th
echo 'set_flag(`abort_when_fail`,true);;' \
'loadt `mk_win_th`;;' \
'quit ();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
|- !a b. a <== b = b ==> a
() : void
File mk_win_th loaded
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `ml_ext`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
le = - : (int -> int -> bool)
() : void
ge = - : (int -> int -> bool)
prefix = - : (* list -> * list -> bool)
suffix = - : (* list -> * list -> bool)
after = - : (* list -> * list -> * list)
before = - : (* list -> * list -> * list)
index = - : ((* -> bool) -> * list -> int)
merge = - : (((* # *) -> bool) -> * list -> * list -> * list)
best = - : (((* # *) -> bool) -> * list -> *)
first = - : (int -> * list -> * list)
last = - : (int -> * list -> * list)
New constructors declared:
POINTER : (((void -> *) # (* -> void) # (void -> void)) -> * pointer)
value = - : (* pointer -> *)
store = - : (* pointer -> * -> void)
dispose = - : (* pointer -> void)
is_nil = - : (* pointer -> bool)
ptrtype = - : (string -> string -> void)
New constructors declared:
SIGNAL : (((* -> void) # (void -> void) # ((* -> void) -> void)) ->
* signal)
signal = - : (* signal -> * -> void)
clear = - : (* signal -> void)
handle = - : (* signal -> (* -> void) -> void)
sigtype = - : (string -> string -> void)
Calling Lisp compiler
File ml_ext compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'compilet `thms`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
PMI_DEF = |- !a b. a <== b = b ==> a
IMP_REFL_THM = |- !x. x ==> x
IMP_TRANS_THM = |- !x y z. (x ==> y) /\ (y ==> z) ==> x ==> z
PMI_REFL_THM = |- !x. x <== x
PMI_TRANS_THM = |- !x y z. x <== y /\ y <== z ==> x <== z
Calling Lisp compiler
File thms compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'compilet `hol_ext`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
.....() : void
goal_frees = - : (goal -> term list)
term_mem = - : (term -> term list -> bool)
term_subset = - : (term list -> term list -> bool)
term_setify = - : (term list -> term list)
term_intersect = - : (term list -> term list -> term list)
term_union = - : (term list -> term list -> term list)
better_thm = - : (thm -> thm -> bool)
better_goal = - : (goal -> goal -> bool)
thm_subset = - : (thm list -> thm list -> bool)
thm_set_equal = - : (thm list -> thm list -> bool)
goal_subset = - : (goal list -> goal list -> bool)
goal_set_equal = - : (goal list -> goal list -> bool)
thm_setify = - : (thm list -> thm list)
goal_setify = - : (goal list -> goal list)
is_fun = - : (term -> bool)
dom = - : (term -> type)
ran = - : (term -> type)
is_trueimp = - : (term -> bool)
is_pmi = - : (term -> bool)
dest_pmi = - : (term -> (term # term))
IMP_PMI_CONV = - : conv
IMP_PMI = - : (thm -> thm)
PMI_IMP_CONV = - : conv
PMI_IMP = - : (thm -> thm)
IMP_REFL = - : conv
PMI_REFL = - : conv
PMI_TRANS = - : (thm -> thm -> thm)
EXISTS_PMI = - : (term -> thm -> thm)
DNEG_THM = |- !t. ~~t = t
NOT_DISJ_THM = |- !t1 t2. ~(t1 \/ t2) = ~t1 /\ ~t2
NOT_IMP_THM = |- !t1 t2. ~(t1 ==> t2) = t1 /\ ~t2
NOT_PMI_THM = |- !t1 t2. ~t1 <== t2 = ~t1 /\ t2
COND_F_THM = |- !t1 t2. (t1 => t2 | F) = t1 /\ t2
SMASH = - : (thm -> thm list)
- : (thm -> thm list)
SMASH = - : (thm -> thm list)
smash = - : (term -> term list)
prove_hyp = - : (goal -> goal -> goal)
true_tm = "T" : term
false_tm = "F" : term
imp_tm = "$==>" : term
pmi_tm = "$<==" : term
equiv_tm = "$=" : term
Calling Lisp compiler
File hol_ext compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'compilet `tables`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
.....() : void
.......................................() : void
FAST_MATCH_MP = - : (thm -> thm -> thm)
refl_ptr = - : conv
add_refl = - : (thm -> void)
reflexive = - : conv
trans_ptr = - : (thm -> thm)
add_trans = - : (thm -> void)
transitive = - : (thm -> thm)
known_relation = - : (term -> bool)
weakenings = [] : thm list
weak_table = [] : (term # term list) list
check_weak_thm = - : (thm -> (term # term))
MATCH_IMP_TRANS = - : (thm -> thm -> thm)
stronger = - : ((term # term) -> bool)
weaker = - : ((term # term) -> bool)
match_type = - : (term -> term -> (type # type) list)
rel_str = - : (term -> term list)
add_weak = - : (thm -> void)
weaken = - : (term -> thm -> thm)
relative_strengths = - : (term -> term list)
add_relation = - : ((thm # thm) -> void)
() : void
() : void
() : void
((-), (-), (-), (-), (-), -)
: (((thm # thm) -> void) #
conv #
(thm -> thm) #
(thm -> void) #
(term -> thm -> thm) #
(term -> term list))
add_relation = - : ((thm # thm) -> void)
reflexive = - : conv
transitive = - : (thm -> thm)
add_weak = - : (thm -> void)
weaken = - : (term -> thm -> thm)
relative_strengths = - : (term -> term list)
New constructors declared:
RATOR : path_elt
RAND : path_elt
BODY : path_elt
type path defined
traverse = - : (path -> term -> term)
New constructors declared:
FOCUS_PATH : (path -> win_path)
CONTEXT_PATH : ((term # path) -> win_path)
type window_rule defined
New constructors declared:
TREE : ((((* list # **) -> void) #
(* list -> (* list # **) list) #
(void -> void)) ->
(*,**) tree)
plant = - : ((*,**) tree -> (* list # **) -> void)
harvest = - : ((*,**) tree -> * list -> (* list # **) list)
purge = - : ((*,**) tree -> void -> void)
newtree =
-
: (void ->
(path_elt,((term -> bool) #
(term -> term -> term) #
(term -> term -> term) #
(term -> thm list -> thm list) #
(term -> term list) #
(term -> thm -> thm)))
tree)
rule_tree =
TREE((-), (-), -)
: (path_elt,((term -> bool) #
(term -> term -> term) #
(term -> term -> term) #
(term -> thm list -> thm list) #
(term -> term list) #
(term -> thm -> thm)))
tree
store_rule = - : (window_rule -> void)
search_rule = - : (path -> window_rule list)
empty_rules = - : (void -> void)
((-), (-), -)
: ((window_rule -> void) # (path -> window_rule list) # (void -> void))
store_rule = - : (window_rule -> void)
search_rule = - : (path -> window_rule list)
empty_rules = - : (void -> void)
Calling Lisp compiler
File tables compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'compilet `basic_close`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
RATOR_CLOSE = - : (term -> thm -> thm)
RAND_CLOSE = - : (term -> thm -> thm)
BODY_CLOSE = - : (term -> thm -> thm)
COND1_THM =
|- !R A B C D.
(!x. R x x) ==> (A ==> R D B) ==> R(A => D | C)(A => B | C)
COND1_CLOSE = - : (term -> thm -> thm)
COND2_THM =
|- !R A B C D.
(!x. R x x) ==> (~A ==> R D C) ==> R(A => B | D)(A => B | C)
COND2_CLOSE = - : (term -> thm -> thm)
BODY2_THM = |- !c f g r. (!v. (v = c) ==> r(f v)(g v)) ==> r(f c)(g c)
BODY2_CLOSE = - : (term -> thm -> thm)
LET_THM =
|- !c f g r. (!v. (v = c) ==> r(f v)(g v)) ==> r(LET f c)(LET g c)
LET_CLOSE = - : (term -> thm -> thm)
() : void
() : void
() : void
() : void
() : void
() : void
() : void
Section basic_close ended
Calling Lisp compiler
File basic_close compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'compilet `eq_close`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
CONJ1_THM = |- !A B C. (B ==> (C = A)) ==> (C /\ B = A /\ B)
CONJ1_CLOSE = - : (term -> thm -> thm)
CONJ2_THM = |- !A B C. (A ==> (C = B)) ==> (A /\ C = A /\ B)
CONJ2_CLOSE = - : (term -> thm -> thm)
IMP1_THM = |- !A B C. (~B ==> (C = A)) ==> (C ==> B = A ==> B)
IMP1_CLOSE = - : (term -> thm -> thm)
IMP2_THM = |- !A B C. (A ==> (C = B)) ==> (A ==> C = A ==> B)
IMP2_CLOSE = - : (term -> thm -> thm)
PMI1_THM = |- !A B C. (B ==> (C = A)) ==> (C <== B = A <== B)
PMI1_CLOSE = - : (term -> thm -> thm)
PMI2_THM = |- !A B C. (~A ==> (C = B)) ==> (A <== C = A <== B)
PMI2_CLOSE = - : (term -> thm -> thm)
DISJ1_THM = |- !A B C. (~B ==> (C = A)) ==> (C \/ B = A \/ B)
DISJ1_CLOSE = - : (term -> thm -> thm)
DISJ2_THM = |- !A B C. (~A ==> (C = B)) ==> (A \/ C = A \/ B)
DISJ2_CLOSE = - : (term -> thm -> thm)
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
Section eq_close ended
Calling Lisp compiler
File eq_close compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'compilet `imp_close`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
IMP_CONJ1_THM = |- !A B C. (B ==> C ==> A) ==> C /\ B ==> A /\ B
IMP_CONJ1_CLOSE = - : (term -> thm -> thm)
IMP_CONJ2_THM = |- !A B C. (A ==> C ==> B) ==> A /\ C ==> A /\ B
IMP_CONJ2_CLOSE = - : (term -> thm -> thm)
IMP_IMP1_THM = |- !A B C. (~B ==> C <== A) ==> (C ==> B) ==> A ==> B
IMP_IMP1_CLOSE = - : (term -> thm -> thm)
IMP_IMP2_THM = |- !A B C. (A ==> C ==> B) ==> (A ==> C) ==> A ==> B
IMP_IMP2_CLOSE = - : (term -> thm -> thm)
IMP_PMI1_THM = |- !A B C. (B ==> C ==> A) ==> C <== B ==> A <== B
IMP_PMI1_CLOSE = - : (term -> thm -> thm)
IMP_PMI2_THM = |- !A B C. (~A ==> C <== B) ==> A <== C ==> A <== B
IMP_PMI2_CLOSE = - : (term -> thm -> thm)
IMP_DISJ1_THM = |- !A B C. (~B ==> C ==> A) ==> C \/ B ==> A \/ B
IMP_DISJ1_CLOSE = - : (term -> thm -> thm)
IMP_DISJ2_THM = |- !A B C. (~A ==> C ==> B) ==> A \/ C ==> A \/ B
IMP_DISJ2_CLOSE = - : (term -> thm -> thm)
IMP_NEG_THM = |- !A B. B <== A ==> ~B ==> ~A
IMP_NEG_CLOSE = - : (term -> thm -> thm)
IMP_ALL_CLOSE = - : (term -> thm -> thm)
IMP_EXISTS_CLOSE = - : (term -> thm -> thm)
PMI_CONJ1_THM = |- !A B C. (B ==> C <== A) ==> (C /\ B) <== (A /\ B)
PMI_CONJ1_CLOSE = - : (term -> thm -> thm)
PMI_CONJ2_THM = |- !A B C. (A ==> C <== B) ==> (A /\ C) <== (A /\ B)
PMI_CONJ2_CLOSE = - : (term -> thm -> thm)
PMI_IMP1_THM = |- !A B C. (~B ==> C ==> A) ==> (C ==> B) <== (A ==> B)
PMI_IMP1_CLOSE = - : (term -> thm -> thm)
PMI_IMP2_THM = |- !A B C. (A ==> C <== B) ==> (A ==> C) <== (A ==> B)
PMI_IMP2_CLOSE = - : (term -> thm -> thm)
PMI_PMI1_THM = |- !A B C. (B ==> C <== A) ==> (C <== B) <== (A <== B)
PMI_PMI1_CLOSE = - : (term -> thm -> thm)
PMI_PMI2_THM = |- !A B C. (~A ==> C ==> B) ==> (A <== C) <== (A <== B)
PMI_PMI2_CLOSE = - : (term -> thm -> thm)
PMI_DISJ1_THM = |- !A B C. (~B ==> C <== A) ==> (C \/ B) <== (A \/ B)
PMI_DISJ1_CLOSE = - : (term -> thm -> thm)
PMI_DISJ2_THM = |- !A B C. (~A ==> C <== B) ==> (A \/ C) <== (A \/ B)
PMI_DISJ2_CLOSE = - : (term -> thm -> thm)
PMI_NEG_THM = |- !A B. (B ==> A) ==> (~B) <== (~A)
PMI_NEG_CLOSE = - : (term -> thm -> thm)
PMI_ALL_CLOSE = - : (term -> thm -> thm)
PMI_EXISTS_CLOSE = - : (term -> thm -> thm)
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
() : void
Calling Lisp compiler
File imp_close compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `ml_ext`;;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'compilet `win`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
...................() : void
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
type window defined
win_thm = - : (window -> thm)
relation = - : (window -> term)
focus = - : (window -> term)
origin = - : (window -> term)
bound = - : (window -> term list)
hyp_thms = - : (window -> thm list)
hypotheses = - : (window -> term list)
disp_hypotheses = - : (window -> term list)
all_hypotheses = - : (window -> term list)
used_hypotheses = - : (window -> term list)
lemma_thms = - : (window -> thm list)
suppositions = - : (window -> goal list)
conjectures = - : (window -> term list)
used_conjectures = - : (window -> term list)
lemmas = - : (window -> term list)
context = - : (window -> term list)
make_win =
-
: (term -> goal list -> term list -> thm list -> thm list -> window)
create_win = - : (term -> term list -> thm list -> window)
transform =
-
: (term -> term list -> thm list -> (window -> window) -> thm)
get_thm = - : (term -> window -> thm)
add_suppose = - : (goal -> window -> window)
conjecture = - : (term -> window -> window)
add_theorem = - : (thm -> window -> window)
transform_win = - : (thm -> window -> window)
match_transform_win = - : (thm -> window -> window)
convert_win = - : (conv -> window -> window)
rule_win = - : ((thm -> thm) -> window -> window)
thm_rule_win = - : ((thm -> thm) -> window -> window)
foc_rule_win = - : (conv -> window -> window)
tactic_win = - : (tactic -> window -> window)
gen_rewrite_win =
-
: ((conv -> conv) -> thm list -> thm list -> window -> window)
pure_rewrite_win = - : (thm list -> window -> window)
rewrite_win = - : (thm list -> window -> window)
pure_once_rewrite_win = - : (thm list -> window -> window)
once_rewrite_win = - : (thm list -> window -> window)
pure_asm_rewrite_win = - : (thm list -> window -> window)
asm_rewrite_win = - : (thm list -> window -> window)
pure_once_asm_rewrite_win = - : (thm list -> window -> window)
once_asm_rewrite_win = - : (thm list -> window -> window)
filter_pure_asm_rewrite_win =
-
: ((term -> bool) -> thm list -> window -> window)
filter_asm_rewrite_win =
-
: ((term -> bool) -> thm list -> window -> window)
filter_pure_once_asm_rewrite_win =
-
: ((term -> bool) -> thm list -> window -> window)
filter_once_asm_rewrite_win =
-
: ((term -> bool) -> thm list -> window -> window)
transfer_sups_thms = - : (window -> window -> window)
open_win_basis =
-
: (win_path -> window -> (window # (window -> window -> window)))
open_context_basis =
-
: (win_path -> window -> (window # (window -> window -> window)))
gen_open_basis =
-
: (win_path -> window -> (window # (window -> window -> window)))
establish_basis =
-
: (win_path -> window -> (window # (window -> window -> window)))
open_win = - : (path -> (window -> window) -> window -> window)
open_context =
-
: (term -> path -> (window -> window) -> window -> window)
gen_open_win = - : (win_path -> (window -> window) -> window -> window)
establish = - : (term -> (window -> window) -> window -> window)
Calling Lisp compiler
File win compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `ml_ext`;;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'loadf `win`;;' \
'compilet `inter`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
...................() : void
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
............................................() : void
epoch = - : (int -> * -> * history)
present = - : (* history -> *)
dodo = - : ((* -> *) -> * history -> * history)
undo = - : (* history -> * history)
redo = - : (* history -> * history)
set_max_hist = - : (int -> * history -> * history)
get_max_hist = - : (* history -> int)
create_stack = - : (window -> window_stack)
change_window = - : ((window -> window) -> window_stack -> window_stack)
open_window =
-
: (win_path ->
(win_path -> window -> (window # (window -> window -> window))) ->
window_stack ->
window_stack)
pop_window = - : (window_stack -> window_stack)
close_window = - : (window_stack -> window_stack)
depth_stack = - : (window_stack -> int)
top_window = - : (window_stack -> window)
top_path = - : (window_stack -> win_path)
bad_conjectures = - : (window_stack -> term list)
print_stack = - : (window_stack -> void)
() : void
- : (string signal -> void)
newsig_stk_sig = - : (void -> string signal)
() : void
- : (void signal -> void)
newsig_win_sig = - : (void -> void signal)
beg_stack_sig = (-) : string signal
end_stack_sig = (-) : string signal
set_stack_sig = (-) : string signal
psh_win_sig = (-) : void signal
pop_win_sig = (-) : void signal
cng_win_sig = (-) : void signal
() : void
- : (window_stack history pointer -> void)
new_wshp = - : (void -> window_stack history pointer)
stack_table = [] : (string # window_stack history pointer) list
cur_nam_st_hist =
inr ()
: ((string # window_stack history pointer) + void)
CURRENT_STACK = - : (void -> window_stack)
CURRENT_NAME = - : (void -> string)
CURRENT_SHP = - : (void -> window_stack history pointer)
history_size = 20 : int
EPOCH = - : (window_stack -> void)
DO = - : ((window_stack -> window_stack) -> void)
UNDO = - : (void -> void)
REDO = - : (void -> void)
SET_MAX_HIST = - : (int -> void list)
GET_MAX_HIST = - : (void -> int)
BEGIN_STACK = - : (string -> term -> term list -> thm list -> void)
END_STACK = - : (string -> void)
SET_STACK = - : (string -> void)
GET_STACK = - : (string -> window_stack)
ALL_STACKS = - : (void -> string list)
((-), (-), (-), (-), (-), (-), (-), (-), (-), (-), (-), -)
: ((void -> window_stack) #
(void -> string) #
((window_stack -> window_stack) -> void) #
(void -> void) #
(void -> void) #
(int -> void list) #
(void -> int) #
(string -> term -> term list -> thm list -> void) #
(string -> void) #
(string -> void) #
(string -> window_stack) #
(void -> string list))
CURRENT_STACK = - : (void -> window_stack)
CURRENT_NAME = - : (void -> string)
DO = - : ((window_stack -> window_stack) -> void)
UNDO = - : (void -> void)
REDO = - : (void -> void)
SET_MAX_HIST = - : (int -> void list)
GET_MAX_HIST = - : (void -> int)
BEGIN_STACK = - : (string -> term -> term list -> thm list -> void)
END_STACK = - : (string -> void)
SET_STACK = - : (string -> void)
GET_STACK = - : (string -> window_stack)
ALL_STACKS = - : (void -> string list)
APPLY_OPEN =
-
: (win_path ->
(win_path -> window -> (window # (window -> window -> window))) ->
void)
APPLY_TRANSFORM = - : ((window -> window) -> void)
CLOSE_WIN = - : (void -> void)
UNDO_WIN = - : (void -> void)
GEN_OPEN_WIN = - : (win_path -> void)
OPEN_WIN = - : (path -> void)
OPEN_CONTEXT = - : (term -> path -> void)
ESTABLISH = - : (term -> void)
TOP_WIN = - : (void -> window)
BAD_CONJECTURES = - : (void -> term list)
TRANSFORM_WIN = - : (thm -> void)
MATCH_TRANSFORM_WIN = - : (thm -> void)
CONVERT_WIN = - : (conv -> void)
RULE_WIN = - : ((thm -> thm) -> void)
THM_RULE_WIN = - : ((thm -> thm) -> void)
FOC_RULE_WIN = - : (conv -> void)
TACTIC_WIN = - : (tactic -> void)
ADD_THEOREM = - : (thm -> void)
ADD_SUPPOSE = - : (goal -> void)
CONJECTURE = - : (term -> void)
FOCUS = - : (void -> term)
LEMMA_THMS = - : (void -> thm list)
WIN_THM = - : (void -> thm)
GEN_REWRITE_WIN = - : ((conv -> conv) -> thm list -> thm list -> void)
PURE_REWRITE_WIN = - : (thm list -> void)
REWRITE_WIN = - : (thm list -> void)
PURE_ONCE_REWRITE_WIN = - : (thm list -> void)
ONCE_REWRITE_WIN = - : (thm list -> void)
PURE_ASM_REWRITE_WIN = - : (thm list -> void)
ASM_REWRITE_WIN = - : (thm list -> void)
PURE_ONCE_ASM_REWRITE_WIN = - : (thm list -> void)
ONCE_ASM_REWRITE_WIN = - : (thm list -> void)
FILTER_PURE_ASM_REWRITE_WIN = - : ((term -> bool) -> thm list -> void)
FILTER_ASM_REWRITE_WIN = - : ((term -> bool) -> thm list -> void)
FILTER_PURE_ONCE_ASM_REWRITE_WIN =
-
: ((term -> bool) -> thm list -> void)
FILTER_ONCE_ASM_REWRITE_WIN = - : ((term -> bool) -> thm list -> void)
SAVE_WIN_THM = - : (void -> thm)
PRINT_STACK = - : (void -> void)
() : void
() : void
() : void
() : void
() : void
Calling Lisp compiler
File inter compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'load_theory `win`;;' \
'compilet `load_code`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theory win loaded
() : void
() : void
Calling Lisp compiler
File load_code compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `load_window`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
load_window = - : (void -> void)
Calling Lisp compiler
File load_window compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `window`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Extending help search path
() : void
Extending search path
() : void
Theory win loaded
() : void
() : void
window_version = `Revision: 3.1` : string
window Library (Revision: 3.1) loaded.
Copyright (c) Jim Grundy 1992
() : void
All rights reserved
() : void
Calling Lisp compiler
File window compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `ml_ext`;;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'loadf `win`;;' \
'loadf `inter`;;' \
'compilet `xlabel`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
...................() : void
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
............................................() : void
......................................................() : void
() : void
- : (string pointer -> void)
new_strptr = - : (void -> string pointer)
set_title = - : (string -> void)
label = (-) : string pointer
xset_stack = - : (string -> void)
xbeg_stack = - : (string -> void)
xend_stack = - : (string -> void)
() : void
() : void
() : void
() : void
Calling Lisp compiler
File xlabel compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `ml_ext`;;' \
'load_theory `win`;;' \
'loadf `thms`;;' \
'loadf `hol_ext`;;' \
'loadf `tables`;;' \
'loadf `win`;;' \
'loadf `inter`;;' \
'compilet `tactic`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
...................() : void
Theory win loaded
() : void
.....() : void
.......................................() : void
.....................................() : void
............................................() : void
......................................................() : void
open_TAC = - : (path -> thm list -> (window -> window) -> tactic)
close_table = [] : (string # window # (window -> window -> window)) list
BEGIN_STACK_TAC = - : (string -> path -> thm list -> tactic)
END_STACK_TAC = - : (string -> tactic)
((-), -) : ((string -> path -> thm list -> tactic) # (string -> tactic))
BEGIN_STACK_TAC = - : (string -> path -> thm list -> tactic)
END_STACK_TAC = - : (string -> tactic)
Calling Lisp compiler
File tactic compiled
() : void
#===> library window built
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/window'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/pair'
echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `syn`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
mk_pabs = - : ((term # term) -> term)
mk_pforall = - : ((term # term) -> term)
mk_pexists = - : ((term # term) -> term)
mk_pselect = - : ((term # term) -> term)
dest_pabs = - : (term -> (term # term))
dest_pforall = - : (term -> (term # term))
dest_pexists = - : (term -> (term # term))
dest_pselect = - : (term -> (term # term))
is_pabs = - : (term -> bool)
is_pforall = - : (term -> bool)
is_pexists = - : (term -> bool)
is_pselect = - : (term -> bool)
rip_pair = - : (term -> term list)
is_pvar = - : (term -> bool)
pvariant = - : (term list -> term -> term)
genlike = - : (term -> term)
list_mk_pabs = - : (goal -> term)
list_mk_pforall = - : (goal -> term)
list_mk_pexists = - : (goal -> term)
strip_pabs = - : (term -> goal)
strip_pforall = - : (term -> goal)
strip_pexists = - : (term -> goal)
bndpair = - : (term -> term)
pbody = - : (term -> term)
occs_in = - : (term -> term -> bool)
is_prod = - : (type -> bool)
dest_prod = - : (type -> (type # type))
mk_prod = - : ((type # type) -> type)
Calling Lisp compiler
File syn compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `syn`;;' \
'compilet `basic`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
........................() : void
MK_PAIR = - : ((thm # thm) -> thm)
PABS = - : (term -> thm -> thm)
PABS_CONV = - : (conv -> conv)
PSUB_CONV = - : (conv -> conv)
CURRY_CONV = - : conv
UNCURRY_CONV = - : conv
PBETA_CONV = - : conv
PBETA_RULE = - : (thm -> thm)
PBETA_TAC = - : tactic
RIGHT_PBETA = - : (thm -> thm)
LIST_PBETA_CONV = - : conv
RIGHT_LIST_PBETA = - : (thm -> thm)
LEFT_PBETA = - : (thm -> thm)
LEFT_LIST_PBETA = - : (thm -> thm)
UNPBETA_CONV = - : (term -> conv)
CURRY_UNCURRY_THM = |- !f. CURRY(UNCURRY f) = f
UNCURRY_CURRY_THM = |- !f. UNCURRY(CURRY f) = f
PETA_CONV = - : conv
PALPHA_CONV = - : (term -> conv)
GEN_PALPHA_CONV = - : (term -> conv)
PALPHA = - : (term -> conv)
paconv = - : (term -> term -> bool)
PAIR_CONV = - : (conv -> conv)
CURRY_ONE_ONE_THM = |- (CURRY f = CURRY g) = (f = g)
UNCURRY_ONE_ONE_THM = |- (UNCURRY f = UNCURRY g) = (f = g)
Calling Lisp compiler
File basic compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `syn`;;' \
'loadf `basic`;;' \
'compilet `both1`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
........................() : void
........................() : void
PFORALL_THM = |- !f. (!x y. f x y) = (!(x,y). f x y)
PEXISTS_THM = |- !f. (?x y. f x y) = (?(x,y). f x y)
CURRY_FORALL_CONV = - : conv
CURRY_EXISTS_CONV = - : conv
UNCURRY_FORALL_CONV = - : conv
UNCURRY_EXISTS_CONV = - : conv
Calling Lisp compiler
File both1 compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `syn`;;' \
'loadf `basic`;;' \
'loadf `both1`;;' \
'compilet `all`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
........................() : void
........................() : void
......() : void
PSPEC = - : (term -> thm -> thm)
PSPECL = - : (term list -> thm -> thm)
IPSPEC = - : (term -> thm -> thm)
IPSPECL = - : (term list -> thm -> thm)
PSPEC_PAIR = - : (thm -> (term # thm))
PSPEC_ALL = - : (thm -> thm)
GPSPEC = - : (thm -> thm)
PSPEC_TAC = - : ((term # term) -> tactic)
PGEN = - : (term -> thm -> thm)
PGENL = - : (term list -> thm -> thm)
P_PGEN_TAC = - : (term -> tactic)
PGEN_TAC = - : tactic
FILTER_PGEN_TAC = - : (term -> tactic)
Calling Lisp compiler
File all compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `syn`;;' \
'loadf `basic`;;' \
'loadf `both1`;;' \
'loadf `all`;;' \
'compilet `exi`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
........................() : void
........................() : void
......() : void
.............() : void
PEXISTS_CONV = - : conv
PSELECT_RULE = - : (thm -> thm)
PSELECT_CONV = - : conv
PEXISTS_RULE = - : (thm -> thm)
PSELECT_INTRO = - : (thm -> thm)
PSELECT_ELIM = - : (thm -> (term # thm) -> thm)
PEXISTS = - : ((term # term) -> thm -> thm)
PCHOOSE = - : ((term # thm) -> thm -> thm)
P_PCHOOSE_THEN = - : (term -> thm_tactical)
PCHOOSE_THEN = - : thm_tactical
P_PCHOOSE_TAC = - : (term -> thm_tactic)
PCHOOSE_TAC = - : thm_tactic
PEXISTS_TAC = - : (term -> tactic)
PEXISTENCE = - : (thm -> thm)
PEXISTS_UNIQUE_CONV = - : conv
BABY_P_PSKOLEM_CONV = - : (term -> conv)
P_PSKOLEM_CONV = - : (term -> conv)
- : (term -> conv)
P_PSKOLEM_CONV = - : (term -> conv)
PSKOLEM_CONV = - : conv
Calling Lisp compiler
File exi compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `syn`;;' \
'loadf `basic`;;' \
'loadf `both1`;;' \
'loadf `all`;;' \
'loadf `exi`;;' \
'compilet `both2`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
........................() : void
........................() : void
......() : void
.............() : void
....................() : void
PSTRIP_THM_THEN = - : thm_tactical
PSTRIP_ASSUME_TAC = - : thm_tactic
PSTRUCT_CASES_TAC = - : thm_tactic
PSTRIP_GOAL_THEN = - : (thm_tactic -> tactic)
FILTER_PSTRIP_THEN = - : (thm_tactic -> term -> tactic)
PSTRIP_TAC = - : tactic
FILTER_PSTRIP_TAC = - : (term -> tactic)
PEXT = - : (thm -> thm)
P_FUN_EQ_CONV = - : (term -> conv)
MK_PABS = - : (thm -> thm)
HALF_MK_PABS = - : (thm -> thm)
MK_PFORALL = - : (thm -> thm)
MK_PEXISTS = - : (thm -> thm)
MK_PEXISTS = - : (thm -> thm)
PFORALL_EQ = - : (term -> thm -> thm)
PEXISTS_EQ = - : (term -> thm -> thm)
PSELECT_EQ = - : (term -> thm -> thm)
LIST_MK_PFORALL = - : (term list -> thm -> thm)
LIST_MK_PEXISTS = - : (term list -> thm -> thm)
PEXISTS_IMP = - : (term -> thm -> thm)
SWAP_PFORALL_CONV = - : conv
SWAP_PEXISTS_CONV = - : conv
PART_PMATCH = - : ((term -> term) -> thm -> conv)
PMATCH_MP_TAC = - : thm_tactic
PMATCH_MP = - : (thm -> thm -> thm)
Calling Lisp compiler
File both2 compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'loadf `syn`;;' \
'loadf `basic`;;' \
'compilet `conv`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
........................() : void
........................() : void
NOT_FORALL_THM = |- !f. ~(!x. f x) = (?x. ~f x)
NOT_EXISTS_THM = |- !f. ~(?x. f x) = (!x. ~f x)
NOT_PFORALL_CONV = - : conv
NOT_PEXISTS_CONV = - : conv
PEXISTS_NOT_CONV = - : conv
PFORALL_NOT_CONV = - : conv
FORALL_AND_THM = |- !f g. (!x. f x /\ g x) = (!x. f x) /\ (!x. g x)
PFORALL_AND_CONV = - : conv
EXISTS_OR_THM = |- !f g. (?x. f x \/ g x) = (?x. f x) \/ (?x. g x)
PEXISTS_OR_CONV = - : conv
AND_PFORALL_CONV = - : conv
LEFT_AND_FORALL_THM = |- !Q f. (!x. f x) /\ Q = (!x. f x /\ Q)
LEFT_AND_PFORALL_CONV = - : conv
RIGHT_AND_FORALL_THM = |- !P g. P /\ (!x. g x) = (!x. P /\ g x)
RIGHT_AND_PFORALL_CONV = - : conv
OR_PEXISTS_CONV = - : conv
LEFT_OR_EXISTS_THM = |- !Q f. (?x. f x) \/ Q = (?x. f x \/ Q)
LEFT_OR_PEXISTS_CONV = - : conv
RIGHT_OR_EXISTS_THM = |- !P g. P \/ (?x. g x) = (?x. P \/ g x)
RIGHT_OR_PEXISTS_CONV = - : conv
BOTH_EXISTS_AND_THM = |- !P Q. (?x. P /\ Q) = (?x. P) /\ (?x. Q)
LEFT_EXISTS_AND_THM = |- !Q f. (?x. f x /\ Q) = (?x. f x) /\ Q
RIGHT_EXISTS_AND_THM = |- !P g. (?x. P /\ g x) = P /\ (?x. g x)
PEXISTS_AND_CONV = - : conv
AND_PEXISTS_CONV = - : conv
LEFT_AND_PEXISTS_CONV = - : conv
RIGHT_AND_PEXISTS_CONV = - : conv
BOTH_FORALL_OR_THM = |- !P Q. (!x. P \/ Q) = (!x. P) \/ (!x. Q)
LEFT_FORALL_OR_THM = |- !Q f. (!x. f x \/ Q) = (!x. f x) \/ Q
RIGHT_FORALL_OR_THM = |- !P g. (!x. P \/ g x) = P \/ (!x. g x)
PFORALL_OR_CONV = - : conv
OR_PFORALL_CONV = - : conv
LEFT_OR_PFORALL_CONV = - : conv
RIGHT_OR_PFORALL_CONV = - : conv
BOTH_FORALL_IMP_THM = |- !P Q. (!x. P ==> Q) = (?x. P) ==> (!x. Q)
LEFT_FORALL_IMP_THM = |- !Q f. (!x. f x ==> Q) = (?x. f x) ==> Q
RIGHT_FORALL_IMP_THM = |- !P g. (!x. P ==> g x) = P ==> (!x. g x)
BOTH_EXISTS_IMP_THM = |- !P Q. (?x. P ==> Q) = (!x. P) ==> (?x. Q)
LEFT_EXISTS_IMP_THM = |- !Q f. (?x. f x ==> Q) = (!x. f x) ==> Q
RIGHT_EXISTS_IMP_THM = |- !P g. (?x. P ==> g x) = P ==> (?x. g x)
PFORALL_IMP_CONV = - : conv
LEFT_IMP_PEXISTS_CONV = - : conv
RIGHT_IMP_PFORALL_CONV = - : conv
PEXISTS_IMP_CONV = - : conv
LEFT_IMP_PFORALL_CONV = - : conv
RIGHT_IMP_PEXISTS_CONV = - : conv
((-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
(-),
-)
: (conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv #
conv)
NOT_PFORALL_CONV = - : conv
NOT_PEXISTS_CONV = - : conv
PEXISTS_NOT_CONV = - : conv
PFORALL_NOT_CONV = - : conv
PFORALL_AND_CONV = - : conv
PEXISTS_OR_CONV = - : conv
AND_PFORALL_CONV = - : conv
LEFT_AND_PFORALL_CONV = - : conv
RIGHT_AND_PFORALL_CONV = - : conv
OR_PEXISTS_CONV = - : conv
LEFT_OR_PEXISTS_CONV = - : conv
RIGHT_OR_PEXISTS_CONV = - : conv
PEXISTS_AND_CONV = - : conv
AND_PEXISTS_CONV = - : conv
LEFT_AND_PEXISTS_CONV = - : conv
RIGHT_AND_PEXISTS_CONV = - : conv
PFORALL_OR_CONV = - : conv
OR_PFORALL_CONV = - : conv
LEFT_OR_PFORALL_CONV = - : conv
RIGHT_OR_PFORALL_CONV = - : conv
PFORALL_IMP_CONV = - : conv
LEFT_IMP_PEXISTS_CONV = - : conv
RIGHT_IMP_PFORALL_CONV = - : conv
PEXISTS_IMP_CONV = - : conv
LEFT_IMP_PFORALL_CONV = - : conv
RIGHT_IMP_PEXISTS_CONV = - : conv
Calling Lisp compiler
File conv compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;' \
'compilet `pair`;;' \
'quit();;' | ../../hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Extending help search path
() : void
() : void
pair_version = `Revision: 3.1` : string
pair Library (Revision: 3.1) loaded.
Copyright (c) Jim Grundy 1992
() : void
All rights reserved
() : void
Calling Lisp compiler
File pair compiled
() : void
#===> library pair built
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/pair'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/word'
rm -f word_base.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_word_base`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
LESS_EQ_SPLIT = |- !m n p. (m + n) <= p ==> n <= p /\ m <= p
Theorem SUB_ADD autoloading from theory `arithmetic` ...
SUB_ADD = |- !m n. n <= m ==> ((m - n) + n = m)
Theorem LESS_EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
SUB_GREATER_EQ_ADD = |- !p n m. p >= n ==> ((p - n) >= m = p >= (m + n))
ADD_LESS_EQ_SUB = |- !p n m. n <= p ==> ((m + n) <= p = m <= (p - n))
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
Theorem NOT_SUC_LESS_EQ_0 autoloading from theory `arithmetic` ...
NOT_SUC_LESS_EQ_0 = |- !n. ~(SUC n) <= 0
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
ADD_LESS_EQ_TRANS = |- !m n p q. (m + n) <= p /\ q <= n ==> (m + q) <= p
Theorem LESS_ANTISYM autoloading from theory `arithmetic` ...
LESS_ANTISYM = |- !m n. ~(m < n /\ n < m)
Theorem LESS_IMP_LESS_ADD autoloading from theory `arithmetic` ...
LESS_IMP_LESS_ADD = |- !n m. n < m ==> (!p. n < (m + p))
Definition SUB autoloading from theory `arithmetic` ...
SUB =
|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
Theorem SUB_MONO_EQ autoloading from theory `arithmetic` ...
SUB_MONO_EQ = |- !n m. (SUC n) - (SUC m) = n - m
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
ADD_SUB_LEM = |- !m n p. p < n ==> ((m + n) - p = m + (n - p))
LESS_EQ_0_EQ = |- !m. m <= 0 ==> (m = 0)
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Theorem PRE autoloading from theory `prim_rec` ...
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
Theorem INDUCTION autoloading from theory `num` ...
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
PRE_LESS_REFL = |- !m. 0 < m ==> (PRE m) < m
Theorem DIV_MULT autoloading from theory `arithmetic` ...
DIV_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) DIV n = q)
Definition MULT autoloading from theory `arithmetic` ...
MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
LESS_DIV_EQ_ZERO = |- !r n. r < n ==> (r DIV n = 0)
Theorem ADD_0 autoloading from theory `arithmetic` ...
ADD_0 = |- !m. m + 0 = m
MULT_DIV = |- !n q. 0 < n ==> ((q * n) DIV n = q)
Theorem RIGHT_ADD_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Theorem DA autoloading from theory `arithmetic` ...
DA = |- !k n. 0 < n ==> (?r q. (k = (q * n) + r) /\ r < n)
ADD_DIV_ADD_DIV =
|- !n. 0 < n ==> (!x r. ((x * n) + r) DIV n = x + (r DIV n))
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
NOT_MULT_LESS_0 = |- !m n. 0 < m /\ 0 < n ==> 0 < (m * n)
Theorem MOD_TIMES autoloading from theory `arithmetic` ...
MOD_TIMES = |- !n. 0 < n ==> (!q r. ((q * n) + r) MOD n = r MOD n)
Theorem MULT_ASSOC autoloading from theory `arithmetic` ...
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
Theorem MOD_MULT autoloading from theory `arithmetic` ...
MOD_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) MOD n = r)
MOD_MULT_MOD =
|- !m n. 0 < n /\ 0 < m ==> (!x. (x MOD (n * m)) MOD n = x MOD n)
MULT_RIGHT_1 = |- !m. m * 1 = m
DIV_ONE = |- !q. q DIV (SUC 0) = q
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
Less_lemma = |- !m n. m < n ==> (?p. (n = m + p) /\ 0 < p)
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
Theorem LESS_LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
Less_MULT_lemma = |- !r m p. 0 < p ==> r < m ==> r < (p * m)
Theorem LESS_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
Less_MULT_ADD_lemma =
|- !m n r r'.
0 < m /\ 0 < n /\ r < m /\ r' < n ==> ((r' * m) + r) < (n * m)
Theorem ADD_INV_0_EQ autoloading from theory `arithmetic` ...
ADD_INV_0_EQ = |- !m n. (m + n = m) = (n = 0)
DIV_DIV_DIV_MULT =
|- !m n. 0 < m /\ 0 < n ==> (!x. (x DIV m) DIV n = x DIV (m * n))
File arith_thms loaded
() : void
() : void
Theorem SUB_LESS_EQ autoloading from theory `arithmetic` ...
SUB_LESS_EQ = |- !n m. (n - m) <= n
Theorem SUB_LESS_0 autoloading from theory `arithmetic` ...
SUB_LESS_0 = |- !n m. m < n = 0 < (n - m)
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
Theorem SEG_SEG autoloading from theory `list` ...
SEG_SEG =
|- !n1 m1 n2 m2 l.
(n1 + m1) <= (LENGTH l) /\ (n2 + m2) <= n1 ==>
(SEG n2 m2(SEG n1 m1 l) = SEG n2(m1 + m2)l)
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Theorem LENGTH_SEG autoloading from theory `list` ...
LENGTH_SEG =
|- !n k l. (n + k) <= (LENGTH l) ==> (LENGTH(SEG n k l) = n)
Theorem ELL_SEG autoloading from theory `list` ...
ELL_SEG =
|- !n l. n < (LENGTH l) ==> (ELL n l = HD(SEG 1(PRE((LENGTH l) - n))l))
Theorem LASTN_SEG autoloading from theory `list` ...
LASTN_SEG =
|- !n l. n <= (LENGTH l) ==> (LASTN n l = SEG n((LENGTH l) - n)l)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
ELL_LASTN =
|- !l m j. m <= (LENGTH l) ==> j < m ==> (ELL j(LASTN m l) = ELL j l)
Theorem ELL_SUC_SNOC autoloading from theory `list` ...
ELL_SUC_SNOC = |- !n x l. ELL(SUC n)(SNOC x l) = ELL n l
Definition BUTLASTN autoloading from theory `list` ...
BUTLASTN =
|- (!l. BUTLASTN 0 l = l) /\
(!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
Theorem ADD_EQ_0 autoloading from theory `arithmetic` ...
ADD_EQ_0 = |- !m n. (m + n = 0) = (m = 0) /\ (n = 0)
Theorem LENGTH_SNOC autoloading from theory `list` ...
LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
ELL_BUTLASTN =
|- !l k j. (j + k) <= (LENGTH l) ==> (ELL j(BUTLASTN k l) = ELL(j + k)l)
Theorem SNOC_11 autoloading from theory `list` ...
SNOC_11 = |- !x l x' l'. (SNOC x l = SNOC x' l') = (x = x') /\ (l = l')
Theorem APPEND_SNOC autoloading from theory `list` ...
APPEND_SNOC = |- !l1 x l2. APPEND l1(SNOC x l2) = SNOC x(APPEND l1 l2)
Theorem APPEND_NIL autoloading from theory `list` ...
APPEND_NIL = |- (!l. APPEND l[] = l) /\ (!l. APPEND[]l = l)
Definition LASTN autoloading from theory `list` ...
LASTN =
|- (!l. LASTN 0 l = []) /\
(!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
APPEND_LASTN_LASTN =
|- !l m1 m2.
(m1 + m2) <= (LENGTH l) ==>
(APPEND(LASTN m2(BUTLASTN m1 l))(LASTN m1 l) = LASTN(m1 + m2)l)
Theorem LASTN_BUTLASTN autoloading from theory `list` ...
LASTN_BUTLASTN =
|- !n m l.
(n + m) <= (LENGTH l) ==>
(LASTN n(BUTLASTN m l) = BUTLASTN m(LASTN(n + m)l))
Theorem SUB_SUB autoloading from theory `arithmetic` ...
SUB_SUB = |- !b c. c <= b ==> (!a. a - (b - c) = (a + c) - b)
Theorem SUB_LESS_EQ_ADD autoloading from theory `arithmetic` ...
SUB_LESS_EQ_ADD = |- !m p. m <= p ==> (!n. (p - m) <= n = p <= (m + n))
Theorem LENGTH_BUTLASTN autoloading from theory `list` ...
LENGTH_BUTLASTN =
|- !n l. n <= (LENGTH l) ==> (LENGTH(BUTLASTN n l) = (LENGTH l) - n)
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
Theorem BUTLASTN_APPEND2 autoloading from theory `list` ...
BUTLASTN_APPEND2 =
|- !n l1 l2.
n <= (LENGTH l2) ==>
(BUTLASTN n(APPEND l1 l2) = APPEND l1(BUTLASTN n l2))
Theorem LASTN_APPEND1 autoloading from theory `list` ...
LASTN_APPEND1 =
|- !l2 n.
(LENGTH l2) <= n ==>
(!l1. LASTN n(APPEND l1 l2) = APPEND(LASTN(n - (LENGTH l2))l1)l2)
Theorem LASTN_LENGTH_ID autoloading from theory `list` ...
LASTN_LENGTH_ID = |- !l. LASTN(LENGTH l)l = l
Theorem ADD_SUB autoloading from theory `arithmetic` ...
ADD_SUB = |- !a c. (a + c) - c = a
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c - c = 0
Theorem LESS_EQUAL_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQUAL_ANTISYM = |- !n m. n <= m /\ m <= n ==> (n = m)
Definition APPEND autoloading from theory `list` ...
APPEND =
|- (!l. APPEND[]l = l) /\
(!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
LASTN_BUTLASTN_APPEND =
|- !l1 l2 m k.
(m + k) <= ((LENGTH l1) + (LENGTH l2)) /\
k < (LENGTH l2) /\
(LENGTH l2) <= (m + k) ==>
(LASTN m(BUTLASTN k(APPEND l1 l2)) =
APPEND
(LASTN((m + k) - (LENGTH l2))l1)
(LASTN((LENGTH l2) - k)(BUTLASTN k l2)))
word_Ax = |- !f. ?! fn. !l. fn(WORD l) = f l
WORD_11 = |- !l l'. (WORD l = WORD l') = (l = l')
word_induct = |- !P. (!l. P(WORD l)) ==> (!w. P w)
word_cases = |- !w. ?l. w = WORD l
WORDLEN_DEF = |- !l. WORDLEN(WORD l) = LENGTH l
PWORDLEN_DEF = |- !n l. PWORDLEN n(WORD l) = (n = LENGTH l)
word_CASES_TAC = - : (term -> tactic)
word_INDUCT_TAC = - : tactic
RESQ_WORDLEN_TAC = - : tactic
File word_funs loaded
() : void
PWORDLEN = |- !n w. PWORDLEN n w = (WORDLEN w = n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
PWORDLEN0 = |- !w. PWORDLEN 0 w ==> (w = WORD[])
PWORDLEN1 = |- !x. PWORDLEN 1(WORD[x])
WSEG_DEF = |- !m k l. WSEG m k(WORD l) = WORD(LASTN m(BUTLASTN k l))
WSEG0 = |- !k w. WSEG 0 k w = WORD[]
Theorem LENGTH_LASTN autoloading from theory `list` ...
LENGTH_LASTN = |- !n l. n <= (LENGTH l) ==> (LENGTH(LASTN n l) = n)
WSEG_PWORDLEN =
|- !n. !w :: PWORDLEN n. !m k. (m + k) <= n ==> PWORDLEN m(WSEG m k w)
WSEG_WORDLEN =
|- !n.
!w :: PWORDLEN n. !m k. (m + k) <= n ==> (WORDLEN(WSEG m k w) = m)
WSEG_WORD_LENGTH = |- !n. !w :: PWORDLEN n. WSEG n 0 w = w
BIT_DEF = |- !k l. BIT k(WORD l) = ELL k l
Definition SNOC autoloading from theory `list` ...
SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
Theorem LAST autoloading from theory `list` ...
LAST = |- !x l. LAST(SNOC x l) = x
Definition ELL autoloading from theory `list` ...
ELL =
|- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))
BIT0 = |- !b. BIT 0(WORD[b]) = b
Theorem BUTLAST autoloading from theory `list` ...
BUTLAST = |- !x l. BUTLAST(SNOC x l) = l
WSEG_BIT =
|- !n. !w :: PWORDLEN n. !k. k < n ==> (WSEG 1 k w = WORD[BIT k w])
BIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k j.
(m + k) <= n ==> j < m ==> (BIT j(WSEG m k w) = BIT(j + k)w)
MSB_DEF = |- !l. MSB(WORD l) = HD l
Theorem ELL_PRE_LENGTH autoloading from theory `list` ...
ELL_PRE_LENGTH = |- !l. ~(l = []) ==> (ELL(PRE(LENGTH l))l = HD l)
Theorem NULL_EQ_NIL autoloading from theory `list` ...
NULL_EQ_NIL = |- !l. NULL l = (l = [])
Theorem LENGTH_NOT_NULL autoloading from theory `list` ...
LENGTH_NOT_NULL = |- !l. 0 < (LENGTH l) = ~NULL l
MSB = |- !n. !w :: PWORDLEN n. 0 < n ==> (MSB w = BIT(PRE n)w)
LSB_DEF = |- !l. LSB(WORD l) = LAST l
Theorem ELL_LAST autoloading from theory `list` ...
ELL_LAST = |- !l. ~NULL l ==> (ELL 0 l = LAST l)
LSB = |- !n. !w :: PWORDLEN n. 0 < n ==> (LSB w = BIT 0 w)
WSPLIT_DEF =
|- !m l. WSPLIT m(WORD l) = WORD(BUTLASTN m l),WORD(LASTN m l)
th = |- ?bt. !l. bt(WORD l) = l
word_bits = |- ?bt. (!l. bt(WORD l) = l) /\ (!w. WORD(bt w) = w)
WCAT_lemma =
|- ?WCAT. !l1 l2. WCAT(WORD l1,WORD l2) = WORD(APPEND l1 l2)
WCAT_DEF = |- !l1 l2. WCAT(WORD l1,WORD l2) = WORD(APPEND l1 l2)
Theorem APPEND_BUTLASTN_LASTN autoloading from theory `list` ...
APPEND_BUTLASTN_LASTN =
|- !n l. n <= (LENGTH l) ==> (APPEND(BUTLASTN n l)(LASTN n l) = l)
WCAT_WSPLIT =
|- !n. !w :: PWORDLEN n. !m. m <= n ==> (WCAT(WSPLIT m w) = w)
Theorem LASTN_LENGTH_APPEND autoloading from theory `list` ...
LASTN_LENGTH_APPEND = |- !l1 l2. LASTN(LENGTH l2)(APPEND l1 l2) = l2
Theorem BUTLASTN_LENGTH_APPEND autoloading from theory `list` ...
BUTLASTN_LENGTH_APPEND =
|- !l2 l1. BUTLASTN(LENGTH l2)(APPEND l1 l2) = l1
WSPLIT_WCAT =
|- !n m.
!w1 :: PWORDLEN n. !w2 :: PWORDLEN m. WSPLIT m(WCAT(w1,w2)) = w1,w2
WORD_PARTITION =
|- (!n. !w :: PWORDLEN n. !m. m <= n ==> (WCAT(WSPLIT m w) = w)) /\
(!n m.
!w1 :: PWORDLEN n. !w2 :: PWORDLEN m. WSPLIT m(WCAT(w1,w2)) = w1,w2)
Theorem APPEND_ASSOC autoloading from theory `list` ...
APPEND_ASSOC =
|- !l1 l2 l3. APPEND l1(APPEND l2 l3) = APPEND(APPEND l1 l2)l3
WCAT_ASSOC = |- !w1 w2 w3. WCAT(w1,WCAT(w2,w3)) = WCAT(WCAT(w1,w2),w3)
WCAT0 = |- !w. (WCAT(WORD[],w) = w) /\ (WCAT(w,WORD[]) = w)
Theorem APPEND_LENGTH_EQ autoloading from theory `list` ...
APPEND_LENGTH_EQ =
|- !l1 l1'.
(LENGTH l1 = LENGTH l1') ==>
(!l2 l2'.
(LENGTH l2 = LENGTH l2') ==>
((APPEND l1 l2 = APPEND l1' l2') = (l1 = l1') /\ (l2 = l2')))
WCAT_11 =
|- !m n.
!wm1 wm2 :: PWORDLEN m.
!wn1 wn2 :: PWORDLEN n.
(WCAT(wm1,wn1) = WCAT(wm2,wn2)) = (wm1 = wm2) /\ (wn1 = wn2)
WSPLIT_PWORDLEN =
|- !n.
!w :: PWORDLEN n.
!m.
m <= n ==>
PWORDLEN(n - m)(FST(WSPLIT m w)) /\ PWORDLEN m(SND(WSPLIT m w))
Theorem LENGTH_APPEND autoloading from theory `list` ...
LENGTH_APPEND =
|- !l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)
WCAT_PWORDLEN =
|- !n1.
!w1 :: PWORDLEN n1.
!n2. !w2 :: PWORDLEN n2. PWORDLEN(n1 + n2)(WCAT(w1,w2))
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
WORDLEN_SUC_WCAT =
|- !n w.
PWORDLEN(SUC n)w ==>
(?b :: PWORDLEN 1. ?w' :: PWORDLEN n. w = WCAT(b,w'))
Theorem LASTN_LASTN autoloading from theory `list` ...
LASTN_LASTN =
|- !l n m.
m <= (LENGTH l) ==> n <= m ==> (LASTN n(LASTN m l) = LASTN n l)
Theorem BUTLASTN_BUTLASTN autoloading from theory `list` ...
BUTLASTN_BUTLASTN =
|- !m n l.
(n + m) <= (LENGTH l) ==>
(BUTLASTN n(BUTLASTN m l) = BUTLASTN(n + m)l)
Theorem BUTLASTN_LASTN autoloading from theory `list` ...
BUTLASTN_LASTN =
|- !m n l.
m <= n /\ n <= (LENGTH l) ==>
(BUTLASTN m(LASTN n l) = LASTN(n - m)(BUTLASTN m l))
WSEG_WSEG =
|- !n.
!w :: PWORDLEN n.
!m1 k1 m2 k2.
(m1 + k1) <= n /\ (m2 + k2) <= m1 ==>
(WSEG m2 k2(WSEG m1 k1 w) = WSEG m2(k1 + k2)w)
WSPLIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!k. k <= n ==> (WSPLIT k w = WSEG(n - k)k w,WSEG k 0 w)
WSPLIT_WSEG1 =
|- !n.
!w :: PWORDLEN n. !k. k <= n ==> (FST(WSPLIT k w) = WSEG(n - k)k w)
WSPLIT_WSEG2 =
|- !n. !w :: PWORDLEN n. !k. k <= n ==> (SND(WSPLIT k w) = WSEG k 0 w)
WCAT_WSEG_WSEG =
|- !n.
!w :: PWORDLEN n.
!m1 m2 k.
(m1 + (m2 + k)) <= n ==>
(WCAT(WSEG m2(m1 + k)w,WSEG m1 k w) = WSEG(m1 + m2)k w)
WORD_SPLIT =
|- !n1 n2. !w :: PWORDLEN(n1 + n2). w = WCAT(WSEG n1 n2 w,WSEG n2 0 w)
WORDLEN_SUC_WCAT_WSEG_WSEG =
|- !w :: PWORDLEN(SUC n). w = WCAT(WSEG 1 n w,WSEG n 0 w)
WORDLEN_SUC_WCAT_WSEG_WSEG_RIGHT =
|- !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WSEG 1 0 w)
WORDLEN_SUC_WCAT_BIT_WSEG =
|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WORD[BIT n w],WSEG n 0 w)
WORDLEN_SUC_WCAT_BIT_WSEG_RIGHT =
|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WORD[BIT 0 w])
WSEG_WCAT1 =
|- !n1 n2.
!w1 :: PWORDLEN n1. !w2 :: PWORDLEN n2. WSEG n1 n2(WCAT(w1,w2)) = w1
WSEG_WCAT2 =
|- !n1 n2.
!w1 :: PWORDLEN n1. !w2 :: PWORDLEN n2. WSEG n2 0(WCAT(w1,w2)) = w2
Theorem CONS_APPEND autoloading from theory `list` ...
CONS_APPEND = |- !x l. CONS x l = APPEND[x]l
WORD_CONS_WCAT = |- !x l. WORD(CONS x l) = WCAT(WORD[x],WORD l)
Theorem SNOC_APPEND autoloading from theory `list` ...
SNOC_APPEND = |- !x l. SNOC x l = APPEND l[x]
WORD_SNOC_WCAT = |- !x l. WORD(SNOC x l) = WCAT(WORD l,WORD[x])
Theorem ELL_APPEND1 autoloading from theory `list` ...
ELL_APPEND1 =
|- !l2 n.
(LENGTH l2) <= n ==>
(!l1. ELL n(APPEND l1 l2) = ELL(n - (LENGTH l2))l1)
BIT_WCAT_FST =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!k.
n2 <= k /\ k < (n1 + n2) ==> (BIT k(WCAT(w1,w2)) = BIT(k - n2)w1)
Theorem ELL_APPEND2 autoloading from theory `list` ...
ELL_APPEND2 =
|- !n l2. n < (LENGTH l2) ==> (!l1. ELL n(APPEND l1 l2) = ELL n l2)
BIT_WCAT_SND =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2. !k. k < n2 ==> (BIT k(WCAT(w1,w2)) = BIT k w2)
Theorem ELL_LENGTH_CONS autoloading from theory `list` ...
ELL_LENGTH_CONS = |- !l x. ELL(LENGTH l)(CONS x l) = x
BIT_WCAT1 = |- !n. !w :: PWORDLEN n. !b. BIT n(WCAT(WORD[b],w)) = b
Theorem BUTLASTN_APPEND1 autoloading from theory `list` ...
BUTLASTN_APPEND1 =
|- !l2 n.
(LENGTH l2) <= n ==>
(!l1. BUTLASTN n(APPEND l1 l2) = BUTLASTN(n - (LENGTH l2))l1)
WSEG_WCAT_WSEG1 =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
m <= n1 /\ n2 <= k ==> (WSEG m k(WCAT(w1,w2)) = WSEG m(k - n2)w1)
Theorem LASTN_APPEND2 autoloading from theory `list` ...
LASTN_APPEND2 =
|- !n l2. n <= (LENGTH l2) ==> (!l1. LASTN n(APPEND l1 l2) = LASTN n l2)
WSEG_WCAT_WSEG2 =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k. (m + k) <= n2 ==> (WSEG m k(WCAT(w1,w2)) = WSEG m k w2)
WSEG_WCAT_WSEG =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
(m + k) <= (n1 + n2) /\ k < n2 /\ n2 <= (m + k) ==>
(WSEG m k(WCAT(w1,w2)) =
WCAT(WSEG((m + k) - n2)0 w1,WSEG(n2 - k)k w2))
PWORDLEN_BIT1 = |- !x. PWORDLEN 1(WORD[x])
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
Theorem CONS_11 autoloading from theory `list` ...
CONS_11 = |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
BIT_EQ_IMP_WORD_EQ =
|- !n.
!w1 w2 :: PWORDLEN n.
(!k. k < n ==> (BIT k w1 = BIT k w2)) ==> (w1 = w2)
() : void
File mk_word_base loaded
() : void
#rm -f word_bitop.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_word_bitop`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
.........................................................() : void
Theory word_base loaded
() : void
() : void
() : void
...() : void
Theorem SUB_LESS_EQ autoloading from theory `arithmetic` ...
SUB_LESS_EQ = |- !n m. (n - m) <= n
Theorem SEG_LASTN_BUTLASTN autoloading from theory `list` ...
SEG_LASTN_BUTLASTN =
|- !n m l.
(n + m) <= (LENGTH l) ==>
(SEG n m l = LASTN n(BUTLASTN((LENGTH l) - (n + m))l))
LASTN_BUTLASTN_SEG =
|- !m k l.
(m + k) <= (LENGTH l) ==>
(LASTN m(BUTLASTN k l) = SEG m((LENGTH l) - (m + k))l)
PBITOP_DEF =
|- !op.
PBITOP op =
(!n.
!w :: PWORDLEN n.
PWORDLEN n(op w) /\
(!m k. (m + k) <= n ==> (op(WSEG m k w) = WSEG m k(op w))))
PBITOP_PWORDLEN =
|- !op :: PBITOP. !n. !w :: PWORDLEN n. PWORDLEN n(op w)
PBITOP_WSEG =
|- !op :: PBITOP.
!n.
!w :: PWORDLEN n.
!m k. (m + k) <= n ==> (op(WSEG m k w) = WSEG m k(op w))
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
Theorem WSEG_BIT autoloading from theory `word_base` ...
WSEG_BIT =
|- !n. !w :: PWORDLEN n. !k. k < n ==> (WSEG 1 k w = WORD[BIT k w])
PBITOP_BIT =
|- !op :: PBITOP.
!n.
!w :: PWORDLEN n.
!k. k < n ==> (op(WORD[BIT k w]) = WORD[BIT k(op w)])
Theorem BIT0 autoloading from theory `word_base` ...
BIT0 = |- !b. BIT 0(WORD[b]) = b
BIT_op_EXISTS =
|- !op :: PBITOP.
?op'.
!n. !w :: PWORDLEN n. !k. k < n ==> (BIT k(op w) = op'(BIT k w))
PBITBOP_DEF =
|- !op.
PBITBOP op =
(!n.
!w1 :: PWORDLEN n.
!w2 :: PWORDLEN n.
PWORDLEN n(op w1 w2) /\
(!m k.
(m + k) <= n ==>
(op(WSEG m k w1)(WSEG m k w2) = WSEG m k(op w1 w2))))
PBITBOP_PWORDLEN =
|- !op :: PBITBOP.
!n. !w1 :: PWORDLEN n. !w2 :: PWORDLEN n. PWORDLEN n(op w1 w2)
PBITBOP_WSEG =
|- !op :: PBITBOP.
!n.
!w1 :: PWORDLEN n.
!w2 :: PWORDLEN n.
!m k.
(m + k) <= n ==>
(op(WSEG m k w1)(WSEG m k w2) = WSEG m k(op w1 w2))
Theorem word_Ax autoloading from theory `word_base` ...
word_Ax = |- !f. ?! fn. !l. fn(WORD l) = f l
PBITBOP_EXISTS =
|- !f. ?fn. !l1 l2. fn(WORD l1)(WORD l2) = WORD(MAP2 f l1 l2)
WMAP_DEF = |- !f l. WMAP f(WORD l) = WORD(MAP f l)
Theorem LENGTH_MAP autoloading from theory `list` ...
LENGTH_MAP = |- !l f. LENGTH(MAP f l) = LENGTH l
Definition PWORDLEN_DEF autoloading from theory `word_base` ...
PWORDLEN_DEF = |- !n l. PWORDLEN n(WORD l) = (n = LENGTH l)
WMAP_PWORDLEN = |- !w :: PWORDLEN n. !f. PWORDLEN n(WMAP f w)
Definition MAP autoloading from theory `list` ...
MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
WMAP0 = |- !f. WMAP f(WORD[]) = WORD[]
Theorem ELL_MAP autoloading from theory `list` ...
ELL_MAP = |- !n l f. n < (LENGTH l) ==> (ELL n(MAP f l) = f(ELL n l))
Definition BIT_DEF autoloading from theory `word_base` ...
BIT_DEF = |- !k l. BIT k(WORD l) = ELL k l
WMAP_BIT =
|- !n.
!w :: PWORDLEN n. !k. k < n ==> (!f. BIT k(WMAP f w) = f(BIT k w))
Theorem LENGTH_BUTLASTN autoloading from theory `list` ...
LENGTH_BUTLASTN =
|- !n l. n <= (LENGTH l) ==> (LENGTH(BUTLASTN n l) = (LENGTH l) - n)
Theorem LASTN_MAP autoloading from theory `list` ...
LASTN_MAP =
|- !n l. n <= (LENGTH l) ==> (!f. LASTN n(MAP f l) = MAP f(LASTN n l))
Theorem BUTLASTN_MAP autoloading from theory `list` ...
BUTLASTN_MAP =
|- !n l.
n <= (LENGTH l) ==> (!f. BUTLASTN n(MAP f l) = MAP f(BUTLASTN n l))
Theorem WORD_11 autoloading from theory `word_base` ...
WORD_11 = |- !l l'. (WORD l = WORD l') = (l = l')
Definition WSEG_DEF autoloading from theory `word_base` ...
WSEG_DEF = |- !m k l. WSEG m k(WORD l) = WORD(LASTN m(BUTLASTN k l))
WMAP_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==> (!f. WMAP f(WSEG m k w) = WSEG m k(WMAP f w))
WMAP_PBITOP = |- !f. PBITOP(WMAP f)
Theorem MAP_APPEND autoloading from theory `list` ...
MAP_APPEND =
|- !f l1 l2. MAP f(APPEND l1 l2) = APPEND(MAP f l1)(MAP f l2)
Definition WCAT_DEF autoloading from theory `word_base` ...
WCAT_DEF = |- !l1 l2. WCAT(WORD l1,WORD l2) = WORD(APPEND l1 l2)
WMAP_WCAT = |- !w1 w2 f. WMAP f(WCAT(w1,w2)) = WCAT(WMAP f w1,WMAP f w2)
Theorem MAP_MAP_o autoloading from theory `list` ...
MAP_MAP_o = |- !f g l. MAP f(MAP g l) = MAP(f o g)l
WMAP_o = |- !w f g. WMAP g(WMAP f w) = WMAP(g o f)w
FORALLBITS_DEF = |- !P l. FORALLBITS P(WORD l) = ALL_EL P l
Theorem ELL_CONS autoloading from theory `list` ...
ELL_CONS = |- !n l. n < (LENGTH l) ==> (!x. ELL n(CONS x l) = ELL n l)
Theorem ELL_LENGTH_CONS autoloading from theory `list` ...
ELL_LENGTH_CONS = |- !l x. ELL(LENGTH l)(CONS x l) = x
Definition ALL_EL autoloading from theory `list` ...
ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
FORALLBITS =
|- !n. !w :: PWORDLEN n. !P. FORALLBITS P w = (!k. k < n ==> P(BIT k w))
Theorem ALL_EL_LASTN autoloading from theory `list` ...
ALL_EL_LASTN =
|- !P l. ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(LASTN m l))
Theorem ALL_EL_SNOC autoloading from theory `list` ...
ALL_EL_SNOC = |- !P x l. ALL_EL P(SNOC x l) = ALL_EL P l /\ P x
Theorem LENGTH_SNOC autoloading from theory `list` ...
LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
Definition BUTLASTN autoloading from theory `list` ...
BUTLASTN =
|- (!l. BUTLASTN 0 l = l) /\
(!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
Definition LASTN autoloading from theory `list` ...
LASTN =
|- (!l. LASTN 0 l = []) /\
(!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
Theorem ADD_EQ_0 autoloading from theory `arithmetic` ...
ADD_EQ_0 = |- !m n. (m + n = 0) = (m = 0) /\ (n = 0)
FORALLBITS_WSEG =
|- !n.
!w :: PWORDLEN n.
!P.
FORALLBITS P w ==>
(!m k. (m + k) <= n ==> FORALLBITS P(WSEG m k w))
Theorem ALL_EL_APPEND autoloading from theory `list` ...
ALL_EL_APPEND =
|- !P l1 l2. ALL_EL P(APPEND l1 l2) = ALL_EL P l1 /\ ALL_EL P l2
FORALLBITS_WCAT =
|- !w1 w2 P.
FORALLBITS P(WCAT(w1,w2)) = FORALLBITS P w1 /\ FORALLBITS P w2
EXISTSABIT_DEF = |- !P l. EXISTSABIT P(WORD l) = SOME_EL P l
Theorem NOT_SOME_EL_ALL_EL autoloading from theory `list` ...
NOT_SOME_EL_ALL_EL = |- !P l. ~SOME_EL P l = ALL_EL($~ o P)l
NOT_EXISTSABIT = |- !P w. ~EXISTSABIT P w = FORALLBITS($~ o P)w
Theorem NOT_ALL_EL_SOME_EL autoloading from theory `list` ...
NOT_ALL_EL_SOME_EL = |- !P l. ~ALL_EL P l = SOME_EL($~ o P)l
NOT_FORALLBITS = |- !P w. ~FORALLBITS P w = EXISTSABIT($~ o P)w
Definition SOME_EL autoloading from theory `list` ...
SOME_EL =
|- (!P. SOME_EL P[] = F) /\
(!P x l. SOME_EL P(CONS x l) = P x \/ SOME_EL P l)
EXISTSABIT_BIT =
|- !n. !w :: PWORDLEN n. !P. EXISTSABIT P w = (?k. k < n /\ P(BIT k w))
Theorem SOME_EL_SEG autoloading from theory `list` ...
SOME_EL_SEG =
|- !m k l.
(m + k) <= (LENGTH l) ==> (!P. SOME_EL P(SEG m k l) ==> SOME_EL P l)
EXISTSABIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==> (!P. EXISTSABIT P(WSEG m k w) ==> EXISTSABIT P w)
Theorem SOME_EL_APPEND autoloading from theory `list` ...
SOME_EL_APPEND =
|- !P l1 l2. SOME_EL P(APPEND l1 l2) = SOME_EL P l1 \/ SOME_EL P l2
EXISTSABIT_WCAT =
|- !w1 w2 P.
EXISTSABIT P(WCAT(w1,w2)) = EXISTSABIT P w1 \/ EXISTSABIT P w2
SHR_DEF =
|- !f b w.
SHR f b w =
WCAT
((f => WSEG 1(PRE(WORDLEN w))w | WORD[b]),WSEG(PRE(WORDLEN w))1 w),
BIT 0 w
SHL_DEF =
|- !f w b.
SHL f w b =
BIT(PRE(WORDLEN w))w,
WCAT(WSEG(PRE(WORDLEN w))0 w,(f => WSEG 1 0 w | WORD[b]))
Theorem BIT_WSEG autoloading from theory `word_base` ...
BIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k j.
(m + k) <= n ==> j < m ==> (BIT j(WSEG m k w) = BIT(j + k)w)
Theorem WSEG_WSEG autoloading from theory `word_base` ...
WSEG_WSEG =
|- !n.
!w :: PWORDLEN n.
!m1 k1 m2 k2.
(m1 + k1) <= n /\ (m2 + k2) <= m1 ==>
(WSEG m2 k2(WSEG m1 k1 w) = WSEG m2(k1 + k2)w)
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
Theorem WSEG_WORDLEN autoloading from theory `word_base` ...
WSEG_WORDLEN =
|- !n.
!w :: PWORDLEN n. !m k. (m + k) <= n ==> (WORDLEN(WSEG m k w) = m)
SHR_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==>
0 < m ==>
(!f b.
SHR f b(WSEG m k w) =
(f =>
WCAT(WSEG 1(k + (m - 1))w,WSEG(m - 1)(k + 1)w) |
WCAT(WORD[b],WSEG(m - 1)(k + 1)w)),BIT k w)
SHR_WSEG_1F =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==>
0 < m ==>
(!b.
SHR F b(WSEG m k w) = WCAT(WORD[b],WSEG(m - 1)(k + 1)w),BIT k w)
SHR_WSEG_NF_lem1 = |- 0 < m ==> ((m - 1) + 1 = m)
SHR_WSEG_NF_lem2 = |- 0 < m ==> ((m - 1) + (k + 1) = m + k)
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Theorem WCAT_WSEG_WSEG autoloading from theory `word_base` ...
WCAT_WSEG_WSEG =
|- !n.
!w :: PWORDLEN n.
!m1 m2 k.
(m1 + (m2 + k)) <= n ==>
(WCAT(WSEG m2(m1 + k)w,WSEG m1 k w) = WSEG(m1 + m2)k w)
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
SHR_WSEG_NF =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) < n ==>
0 < m ==>
(SHR F(BIT(m + k)w)(WSEG m k w) = WSEG m(k + 1)w,BIT k w)
SHL_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==>
0 < m ==>
(!f b.
SHL f(WSEG m k w)b =
BIT(k + (m - 1))w,
(f =>
WCAT(WSEG(m - 1)k w,WSEG 1 k w) |
WCAT(WSEG(m - 1)k w,WORD[b])))
SHL_WSEG_1F =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==>
0 < m ==>
(!b.
SHL F(WSEG m k w)b =
BIT(k + (m - 1))w,WCAT(WSEG(m - 1)k w,WORD[b]))
SHL_WSEG_NF =
|- !n.
!w :: PWORDLEN n.
!m k.
(m + k) <= n ==>
0 < m ==>
0 < k ==>
(SHL F(WSEG m k w)(BIT(k - 1)w) =
BIT(k + (m - 1))w,WSEG m(k - 1)w)
Theorem PWORDLEN1 autoloading from theory `word_base` ...
PWORDLEN1 = |- !x. PWORDLEN 1(WORD[x])
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
Theorem WSEG_PWORDLEN autoloading from theory `word_base` ...
WSEG_PWORDLEN =
|- !n. !w :: PWORDLEN n. !m k. (m + k) <= n ==> PWORDLEN m(WSEG m k w)
Theorem WSEG_WCAT_WSEG1 autoloading from theory `word_base` ...
WSEG_WCAT_WSEG1 =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
m <= n1 /\ n2 <= k ==> (WSEG m k(WCAT(w1,w2)) = WSEG m(k - n2)w1)
Theorem PWORDLEN autoloading from theory `word_base` ...
PWORDLEN = |- !n w. PWORDLEN n w = (WORDLEN w = n)
WSEG_SHL =
|- !n.
!w :: PWORDLEN(SUC n).
!m k.
0 < k /\ (m + k) <= (SUC n) ==>
(!b. WSEG m k(SND(SHL f w b)) = WSEG m(k - 1)w)
Theorem WSEG_WORD_LENGTH autoloading from theory `word_base` ...
WSEG_WORD_LENGTH = |- !n. !w :: PWORDLEN n. WSEG n 0 w = w
Theorem WSEG_WCAT_WSEG autoloading from theory `word_base` ...
WSEG_WCAT_WSEG =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
(m + k) <= (n1 + n2) /\ k < n2 /\ n2 <= (m + k) ==>
(WSEG m k(WCAT(w1,w2)) =
WCAT(WSEG((m + k) - n2)0 w1,WSEG(n2 - k)k w2))
WSEG_SHL_0 =
|- !n.
!w :: PWORDLEN(SUC n).
!m b.
0 < m /\ m <= (SUC n) ==>
(WSEG m 0(SND(SHL f w b)) =
WCAT(WSEG(m - 1)0 w,(f => WSEG 1 0 w | WORD[b])))
() : void
File mk_word_bitop loaded
() : void
#rm -f word_num.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_word_num`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
Theory word_base loaded
() : void
[()] : void list
() : void
...() : void
LVAL_DEF = |- !f b l. LVAL f b l = FOLDL(\e x. (b * e) + (f x))0 l
Theorem LEFT_ADD_DISTRIB autoloading from theory `arithmetic` ...
LEFT_ADD_DISTRIB = |- !m n p. p * (m + n) = (p * m) + (p * n)
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
Theorem MULT_ASSOC autoloading from theory `arithmetic` ...
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
Theorem LENGTH_SNOC autoloading from theory `list` ...
LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
Theorem FOLDL_SNOC autoloading from theory `list` ...
FOLDL_SNOC = |- !f e x l. FOLDL f e(SNOC x l) = f(FOLDL f e l)x
Definition EXP autoloading from theory `arithmetic` ...
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
Definition FOLDL autoloading from theory `list` ...
FOLDL =
|- (!f e. FOLDL f e[] = e) /\
(!f e x l. FOLDL f e(CONS x l) = FOLDL f(f e x)l)
LVAL =
|- (!f b. LVAL f b[] = 0) /\
(!l f b x.
LVAL f b(CONS x l) = ((f x) * (b EXP (LENGTH l))) + (LVAL f b l))
Theorem word_Ax autoloading from theory `word_base` ...
word_Ax = |- !f. ?! fn. !l. fn(WORD l) = f l
NVAL_DEF = |- !f b l. NVAL f b(WORD l) = LVAL f b l
Theorem RIGHT_ADD_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
Definition MULT autoloading from theory `arithmetic` ...
MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
Definition SNOC autoloading from theory `list` ...
SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
LVAL_SNOC = |- !l h f b. LVAL f b(SNOC h l) = ((LVAL f b l) * b) + (f h)
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
LESS_SUC_IMP_LESS_EQ = |- !m n. m < (SUC n) = m <= n
Theorem LESS_LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
Theorem LESS_MONO_ADD autoloading from theory `arithmetic` ...
LESS_MONO_ADD = |- !m n p. m < n ==> (m + p) < (n + p)
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
LVAL_MAX_lem = |- !a b c y. (a + b) < (SUC c) /\ y < b ==> (a + y) < c
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Theorem LESS_EQ_LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_LESS_EQ_MONO =
|- !m n p q. m <= p /\ n <= q ==> (m + n) <= (p + q)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Theorem INDUCTION autoloading from theory `num` ...
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
LESS_MULT_PLUS_DIFF = |- !n k l. k < l ==> ((k * n) + n) <= (l * n)
Theorem LESS_EQ_IMP_LESS_SUC autoloading from theory `arithmetic` ...
LESS_EQ_IMP_LESS_SUC = |- !n m. n <= m ==> n < (SUC m)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
LVAL_MAX =
|- !l f b. (!x. (f x) < b) ==> (LVAL f b l) < (b EXP (LENGTH l))
NVAL_MAX =
|- !f b.
(!x. (f x) < b) ==> (!n. !w :: PWORDLEN n. (NVAL f b w) < (b EXP n))
NVAL0 = |- !f b. NVAL f b(WORD[]) = 0
NVAL1 = |- !f b x. NVAL f b(WORD[x]) = f x
Theorem PWORDLEN0 autoloading from theory `word_base` ...
PWORDLEN0 = |- !w. PWORDLEN 0 w ==> (w = WORD[])
NVAL_WORDLEN_0 = |- !w :: PWORDLEN 0. !fv r. NVAL fv r w = 0
Theorem SNOC_APPEND autoloading from theory `list` ...
SNOC_APPEND = |- !x l. SNOC x l = APPEND l[x]
Definition WCAT_DEF autoloading from theory `word_base` ...
WCAT_DEF = |- !l1 l2. WCAT(WORD l1,WORD l2) = WORD(APPEND l1 l2)
NVAL_WCAT1 =
|- !w f b x. NVAL f b(WCAT(w,WORD[x])) = ((NVAL f b w) * b) + (f x)
Theorem CONS_APPEND autoloading from theory `list` ...
CONS_APPEND = |- !x l. CONS x l = APPEND[x]l
NVAL_WCAT2 =
|- !n.
!w :: PWORDLEN n.
!f b x.
NVAL f b(WCAT(WORD[x],w)) = ((f x) * (b EXP n)) + (NVAL f b w)
Theorem EXP_ADD autoloading from theory `arithmetic` ...
EXP_ADD = |- !p q n. n EXP (p + q) = (n EXP p) * (n EXP q)
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
Theorem WCAT_PWORDLEN autoloading from theory `word_base` ...
WCAT_PWORDLEN =
|- !n1.
!w1 :: PWORDLEN n1.
!n2. !w2 :: PWORDLEN n2. PWORDLEN(n1 + n2)(WCAT(w1,w2))
Theorem WCAT_ASSOC autoloading from theory `word_base` ...
WCAT_ASSOC = |- !w1 w2 w3. WCAT(w1,WCAT(w2,w3)) = WCAT(WCAT(w1,w2),w3)
Theorem WORDLEN_SUC_WCAT_BIT_WSEG autoloading from theory `word_base` ...
WORDLEN_SUC_WCAT_BIT_WSEG =
|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WORD[BIT n w],WSEG n 0 w)
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
Theorem WCAT0 autoloading from theory `word_base` ...
WCAT0 = |- !w. (WCAT(WORD[],w) = w) /\ (WCAT(w,WORD[]) = w)
Theorem WSEG_PWORDLEN autoloading from theory `word_base` ...
WSEG_PWORDLEN =
|- !n. !w :: PWORDLEN n. !m k. (m + k) <= n ==> PWORDLEN m(WSEG m k w)
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
Theorem ADD_0 autoloading from theory `arithmetic` ...
ADD_0 = |- !m. m + 0 = m
NVAL_WCAT =
|- !n m.
!w1 :: PWORDLEN n.
!w2 :: PWORDLEN m.
!f b.
NVAL f b(WCAT(w1,w2)) =
((NVAL f b w1) * (b EXP m)) + (NVAL f b w2)
NLIST_DEF =
|- (!frep b m. NLIST 0 frep b m = []) /\
(!n frep b m.
NLIST(SUC n)frep b m = SNOC(frep(m MOD b))(NLIST n frep b(m DIV b)))
NWORD_DEF = |- !n frep b m. NWORD n frep b m = WORD(NLIST n frep b m)
NLIST_LENGTH = |- !n f b m. LENGTH(NLIST n f b m) = n
Definition WORDLEN_DEF autoloading from theory `word_base` ...
WORDLEN_DEF = |- !l. WORDLEN(WORD l) = LENGTH l
NWORD_LENGTH = |- !n f b m. WORDLEN(NWORD n f b m) = n
Definition PWORDLEN_DEF autoloading from theory `word_base` ...
PWORDLEN_DEF = |- !n l. PWORDLEN n(WORD l) = (n = LENGTH l)
NWORD_PWORDLEN = |- !n f b m. PWORDLEN n(NWORD n f b m)
() : void
File mk_word_num loaded
() : void
#rm -f bword_bitop.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_bword_bitop`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
.........................................................() : void
Theory word_bitop loaded
() : void
[(); ()] : void list
() : void
...() : void
Theorem CONS_11 autoloading from theory `list` ...
CONS_11 = |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
Definition MAP2 autoloading from theory `list` ...
MAP2 =
|- (!f. MAP2 f[][] = []) /\
(!f h1 t1 h2 t2.
MAP2 f(CONS h1 t1)(CONS h2 t2) = CONS(f h1 h2)(MAP2 f t1 t2))
Definition SNOC autoloading from theory `list` ...
SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
MAP2_SNOC =
|- !f h1 h2 l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(MAP2 f(SNOC h1 l1)(SNOC h2 l2) = SNOC(f h1 h2)(MAP2 f l1 l2))
Definition BUTLASTN autoloading from theory `list` ...
BUTLASTN =
|- (!l. BUTLASTN 0 l = l) /\
(!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
BUTLASTN_MAP2 =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(!n.
n <= (LENGTH l1) ==>
(!f.
BUTLASTN n(MAP2 f l1 l2) = MAP2 f(BUTLASTN n l1)(BUTLASTN n l2)))
Theorem SNOC_11 autoloading from theory `list` ...
SNOC_11 = |- !x l x' l'. (SNOC x l = SNOC x' l') = (x = x') /\ (l = l')
Theorem LENGTH_LASTN autoloading from theory `list` ...
LENGTH_LASTN = |- !n l. n <= (LENGTH l) ==> (LENGTH(LASTN n l) = n)
Definition LASTN autoloading from theory `list` ...
LASTN =
|- (!l. LASTN 0 l = []) /\
(!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
LASTN_MAP2 =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(!n.
n <= (LENGTH l1) ==>
(!f. LASTN n(MAP2 f l1 l2) = MAP2 f(LASTN n l1)(LASTN n l2)))
Theorem word_Ax autoloading from theory `word_base` ...
word_Ax = |- !f. ?! fn. !l. fn(WORD l) = f l
WNOT_DEF = |- !l. WNOT(WORD l) = WORD(MAP $~ l)
Theorem LENGTH_BUTLASTN autoloading from theory `list` ...
LENGTH_BUTLASTN =
|- !n l. n <= (LENGTH l) ==> (LENGTH(BUTLASTN n l) = (LENGTH l) - n)
Theorem LASTN_MAP autoloading from theory `list` ...
LASTN_MAP =
|- !n l. n <= (LENGTH l) ==> (!f. LASTN n(MAP f l) = MAP f(LASTN n l))
Theorem BUTLASTN_MAP autoloading from theory `list` ...
BUTLASTN_MAP =
|- !n l.
n <= (LENGTH l) ==> (!f. BUTLASTN n(MAP f l) = MAP f(BUTLASTN n l))
Theorem WORD_11 autoloading from theory `word_base` ...
WORD_11 = |- !l l'. (WORD l = WORD l') = (l = l')
Theorem LENGTH_MAP autoloading from theory `list` ...
LENGTH_MAP = |- !l f. LENGTH(MAP f l) = LENGTH l
Definition WSEG_DEF autoloading from theory `word_base` ...
WSEG_DEF = |- !m k l. WSEG m k(WORD l) = WORD(LASTN m(BUTLASTN k l))
Definition PWORDLEN_DEF autoloading from theory `word_base` ...
PWORDLEN_DEF = |- !n l. PWORDLEN n(WORD l) = (n = LENGTH l)
BIT_WNOT_SYM_lemma =
|- !n.
!w :: PWORDLEN n.
PWORDLEN n(WNOT w) /\
(!m k. (m + k) <= n ==> (WNOT(WSEG m k w) = WSEG m k(WNOT w)))
Definition PBITOP_DEF autoloading from theory `word_bitop` ...
PBITOP_DEF =
|- !op.
PBITOP op =
(!n.
!w :: PWORDLEN n.
PWORDLEN n(op w) /\
(!m k. (m + k) <= n ==> (op(WSEG m k w) = WSEG m k(op w))))
PBITOP_WNOT = |- PBITOP WNOT
Definition MAP autoloading from theory `list` ...
MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
WNOT_WNOT = |- !w. WNOT(WNOT w) = w
Theorem MAP_APPEND autoloading from theory `list` ...
MAP_APPEND =
|- !f l1 l2. MAP f(APPEND l1 l2) = APPEND(MAP f l1)(MAP f l2)
Definition WCAT_DEF autoloading from theory `word_base` ...
WCAT_DEF = |- !l1 l2. WCAT(WORD l1,WORD l2) = WORD(APPEND l1 l2)
WCAT_WNOT =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2. WCAT(WNOT w1,WNOT w2) = WNOT(WCAT(w1,w2))
Theorem LENGTH_MAP2 autoloading from theory `list` ...
LENGTH_MAP2 =
|- !l1 l2.
(LENGTH l1 = LENGTH l2) ==>
(!f.
(LENGTH(MAP2 f l1 l2) = LENGTH l1) /\
(LENGTH(MAP2 f l1 l2) = LENGTH l2))
LENGTH_MAP22 =
|- !l1 l2 f.
(LENGTH l1 = LENGTH l2) ==> (LENGTH(MAP2 f l1 l2) = LENGTH l2)
Theorem PBITBOP_EXISTS autoloading from theory `word_bitop` ...
PBITBOP_EXISTS =
|- !f. ?fn. !l1 l2. fn(WORD l1)(WORD l2) = WORD(MAP2 f l1 l2)
WAND_DEF = |- !l1 l2. (WORD l1) WAND (WORD l2) = WORD(MAP2 $/\ l1 l2)
PBITBOP_WAND_lemma =
|- !n.
!w1 w2 :: PWORDLEN n.
PWORDLEN n(w1 WAND w2) /\
(!m k.
(m + k) <= n ==>
((WSEG m k w1) WAND (WSEG m k w2) = WSEG m k(w1 WAND w2)))
Definition PBITBOP_DEF autoloading from theory `word_bitop` ...
PBITBOP_DEF =
|- !op.
PBITBOP op =
(!n.
!w1 :: PWORDLEN n.
!w2 :: PWORDLEN n.
PWORDLEN n(op w1 w2) /\
(!m k.
(m + k) <= n ==>
(op(WSEG m k w1)(WSEG m k w2) = WSEG m k(op w1 w2))))
PBITBOP_WAND = |- PBITBOP $WAND
WOR_DEF = |- !l1 l2. (WORD l1) WOR (WORD l2) = WORD(MAP2 $\/ l1 l2)
PBITBOP_WOR_lemma =
|- !n.
!w1 w2 :: PWORDLEN n.
PWORDLEN n(w1 WOR w2) /\
(!m k.
(m + k) <= n ==>
((WSEG m k w1) WOR (WSEG m k w2) = WSEG m k(w1 WOR w2)))
PBITBOP_WOR = |- PBITBOP $WOR
WXOR_DEF =
|- !l1 l2. (WORD l1) WXOR (WORD l2) = WORD(MAP2(\x y. ~(x = y))l1 l2)
PBITBOP_WXOR_lemma =
|- !n.
!w1 w2 :: PWORDLEN n.
PWORDLEN n(w1 WXOR w2) /\
(!m k.
(m + k) <= n ==>
((WSEG m k w1) WXOR (WSEG m k w2) = WSEG m k(w1 WXOR w2)))
PBITBOP_WXOR = |- PBITBOP $WXOR
() : void
File mk_bword_bitop loaded
() : void
#rm -f bword_num.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_bword_num`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
.........................................................() : void
Theory word_bitop loaded
() : void
() : void
Theory word_num loaded
() : void
[(); (); ()] : void list
...() : void
BV_DEF = |- !b. BV b = (b => SUC 0 | 0)
Theorem word_Ax autoloading from theory `word_base` ...
word_Ax = |- !f. ?! fn. !l. fn(WORD l) = f l
BNVAL_DEF = |- !l. BNVAL(WORD l) = LVAL BV 2 l
BV_LESS_2 = |- !x. (BV x) < 2
Definition NVAL_DEF autoloading from theory `word_num` ...
NVAL_DEF = |- !f b l. NVAL f b(WORD l) = LVAL f b l
BNVAL_NVAL = |- !w. BNVAL w = NVAL BV 2 w
Theorem NVAL0 autoloading from theory `word_num` ...
NVAL0 = |- !f b. NVAL f b(WORD[]) = 0
BNVAL0 = |- BNVAL(WORD[]) = 0
Theorem SUC_LESS autoloading from theory `prim_rec` ...
SUC_LESS = |- !m n. (SUC m) < n ==> m < n
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
Theorem ADD_EQ_0 autoloading from theory `arithmetic` ...
ADD_EQ_0 = |- !m n. (m + n = 0) = (m = 0) /\ (n = 0)
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
BNVAL_11_lem = |- !m n p. m < p /\ n < p ==> ~(p + m = n)
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
Theorem CONS_11 autoloading from theory `list` ...
CONS_11 = |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
Theorem LVAL autoloading from theory `word_num` ...
LVAL =
|- (!f b. LVAL f b[] = 0) /\
(!l f b x.
LVAL f b(CONS x l) = ((f x) * (b EXP (LENGTH l))) + (LVAL f b l))
Theorem WORD_11 autoloading from theory `word_base` ...
WORD_11 = |- !l l'. (WORD l = WORD l') = (l = l')
Definition WORDLEN_DEF autoloading from theory `word_base` ...
WORDLEN_DEF = |- !l. WORDLEN(WORD l) = LENGTH l
Theorem LVAL_MAX autoloading from theory `word_num` ...
LVAL_MAX =
|- !l f b. (!x. (f x) < b) ==> (LVAL f b l) < (b EXP (LENGTH l))
BNVAL_11 =
|- !w1 w2.
(WORDLEN w1 = WORDLEN w2) ==> (BNVAL w1 = BNVAL w2) ==> (w1 = w2)
BNVAL_ONTO = |- !w. ?n. BNVAL w = n
BNVAL_MAX = |- !n. !w :: PWORDLEN n. (BNVAL w) < (2 EXP n)
Theorem LVAL_SNOC autoloading from theory `word_num` ...
LVAL_SNOC = |- !l h f b. LVAL f b(SNOC h l) = ((LVAL f b l) * b) + (f h)
Theorem SNOC_APPEND autoloading from theory `list` ...
SNOC_APPEND = |- !x l. SNOC x l = APPEND l[x]
Definition WCAT_DEF autoloading from theory `word_base` ...
WCAT_DEF = |- !l1 l2. WCAT(WORD l1,WORD l2) = WORD(APPEND l1 l2)
BNVAL_WCAT1 =
|- !n.
!w :: PWORDLEN n.
!x. BNVAL(WCAT(w,WORD[x])) = ((BNVAL w) * 2) + (BV x)
Theorem NVAL_WCAT2 autoloading from theory `word_num` ...
NVAL_WCAT2 =
|- !n.
!w :: PWORDLEN n.
!f b x.
NVAL f b(WCAT(WORD[x],w)) = ((f x) * (b EXP n)) + (NVAL f b w)
BNVAL_WCAT2 =
|- !n.
!w :: PWORDLEN n.
!x. BNVAL(WCAT(WORD[x],w)) = ((BV x) * (2 EXP n)) + (BNVAL w)
Theorem NVAL_WCAT autoloading from theory `word_num` ...
NVAL_WCAT =
|- !n m.
!w1 :: PWORDLEN n.
!w2 :: PWORDLEN m.
!f b.
NVAL f b(WCAT(w1,w2)) =
((NVAL f b w1) * (b EXP m)) + (NVAL f b w2)
BNVAL_WCAT =
|- !n m.
!w1 :: PWORDLEN n.
!w2 :: PWORDLEN m.
BNVAL(WCAT(w1,w2)) = ((BNVAL w1) * (2 EXP m)) + (BNVAL w2)
VB_DEF = |- !n. VB n = ~(n MOD 2 = 0)
NBWORD_DEF = |- !n m. NBWORD n m = WORD(NLIST n VB 2 m)
Definition NLIST_DEF autoloading from theory `word_num` ...
NLIST_DEF =
|- (!frep b m. NLIST 0 frep b m = []) /\
(!n frep b m.
NLIST(SUC n)frep b m = SNOC(frep(m MOD b))(NLIST n frep b(m DIV b)))
NBWORD0 = |- !m. NBWORD 0 m = WORD[]
Theorem LENGTH_SNOC autoloading from theory `list` ...
LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
NLIST_LENGTH = |- !n f b m. LENGTH(NLIST n f b m) = n
WORDLEN_NBWORD = |- !n m. WORDLEN(NBWORD n m) = n
Theorem PWORDLEN autoloading from theory `word_base` ...
PWORDLEN = |- !n w. PWORDLEN n w = (WORDLEN w = n)
PWORDLEN_NBWORD = |- !n m. PWORDLEN n(NBWORD n m)
Theorem WORD_SNOC_WCAT autoloading from theory `word_base` ...
WORD_SNOC_WCAT = |- !x l. WORD(SNOC x l) = WCAT(WORD l,WORD[x])
NBWORD_SUC =
|- !n m. NBWORD(SUC n)m = WCAT(NBWORD n(m DIV 2),WORD[VB(m MOD 2)])
Theorem SUC_ID autoloading from theory `prim_rec` ...
SUC_ID = |- !n. ~(SUC n = n)
Theorem LESS_MOD autoloading from theory `arithmetic` ...
LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
VB_BV = |- !x. VB(BV x) = x
Theorem ZERO_MOD autoloading from theory `arithmetic` ...
ZERO_MOD = |- !n. 0 < n ==> (0 MOD n = 0)
Theorem ZERO_DIV autoloading from theory `arithmetic` ...
ZERO_DIV = |- !n. 0 < n ==> (0 DIV n = 0)
BV_VB = |- !x. x < 2 ==> (BV(VB x) = x)
Theorem MOD_EQ_0 autoloading from theory `arithmetic` ...
MOD_EQ_0 = |- !n. 0 < n ==> (!k. (k * n) MOD n = 0)
Theorem MOD_MOD autoloading from theory `arithmetic` ...
MOD_MOD = |- !n. 0 < n ==> (!k. (k MOD n) MOD n = k MOD n)
Theorem SNOC_11 autoloading from theory `list` ...
SNOC_11 = |- !x l x' l'. (SNOC x l = SNOC x' l') = (x = x') /\ (l = l')
NBWORD_BNVAL = |- !n. !w :: PWORDLEN n. NBWORD n(BNVAL w) = w
Theorem LESS_MULT_MONO autoloading from theory `arithmetic` ...
LESS_MULT_MONO = |- !m i n. ((SUC n) * m) < ((SUC n) * i) = m < i
Theorem ZERO_LESS_EXP autoloading from theory `arithmetic` ...
ZERO_LESS_EXP = |- !m n. 0 < ((SUC n) EXP m)
Definition EXP autoloading from theory `arithmetic` ...
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
Definition DIVISION autoloading from theory `arithmetic` ...
DIVISION =
|- !n.
0 < n ==> (!k. (k = ((k DIV n) * n) + (k MOD n)) /\ (k MOD n) < n)
BNVAL_NBWORD = |- !n m. m < (2 EXP n) ==> (BNVAL(NBWORD n m) = m)
ZERO_WORD_VAL =
|- !n. !w :: PWORDLEN n. (w = NBWORD n 0) = (BNVAL w = 0)
Theorem WCAT_ASSOC autoloading from theory `word_base` ...
WCAT_ASSOC = |- !w1 w2 w3. WCAT(w1,WCAT(w2,w3)) = WCAT(WCAT(w1,w2),w3)
Theorem ADD_SUC autoloading from theory `arithmetic` ...
ADD_SUC = |- !m n. SUC(m + n) = m + (SUC n)
Theorem WCAT0 autoloading from theory `word_base` ...
WCAT0 = |- !w. (WCAT(WORD[],w) = w) /\ (WCAT(w,WORD[]) = w)
WCAT_NBWORD_0 =
|- !n1 n2. WCAT(NBWORD n1 0,NBWORD n2 0) = NBWORD(n1 + n2)0
WSPLIT_NBWORD_0 =
|- !m n. m <= n ==> (WSPLIT m(NBWORD n 0) = NBWORD(n - m)0,NBWORD m 0)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Theorem WSEG_PWORDLEN autoloading from theory `word_base` ...
WSEG_PWORDLEN =
|- !n. !w :: PWORDLEN n. !m k. (m + k) <= n ==> PWORDLEN m(WSEG m k w)
Theorem WCAT_11 autoloading from theory `word_base` ...
WCAT_11 =
|- !m n.
!wm1 wm2 :: PWORDLEN m.
!wn1 wn2 :: PWORDLEN n.
(WCAT(wm1,wn1) = WCAT(wm2,wn2)) = (wm1 = wm2) /\ (wn1 = wn2)
Theorem WSPLIT_WSEG autoloading from theory `word_base` ...
WSPLIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!k. k <= n ==> (WSPLIT k w = WSEG(n - k)k w,WSEG k 0 w)
EQ_NBWORD0_SPLIT =
|- !n.
!w :: PWORDLEN n.
!m.
m <= n ==>
((w = NBWORD n 0) =
(WSEG(n - m)m w = NBWORD(n - m)0) /\ (WSEG m 0 w = NBWORD m 0))
Theorem MULT_0 autoloading from theory `arithmetic` ...
MULT_0 = |- !m. m * 0 = 0
LESS2_DIV2 = |- !r y. 0 < y /\ r < (2 * y) ==> (r DIV 2) < y
less2 = |- 0 < 2
MOD_DIV_lemma =
|- !x y. 0 < y ==> ((x MOD (2 * y)) DIV 2 = (x DIV 2) MOD y)
Definition PWORDLEN_DEF autoloading from theory `word_base` ...
PWORDLEN_DEF = |- !n l. PWORDLEN n(WORD l) = (n = LENGTH l)
NBWORD_MOD = |- !n m. NBWORD n(m MOD (2 EXP n)) = NBWORD n m
Theorem WSEG_WORD_LENGTH autoloading from theory `word_base` ...
WSEG_WORD_LENGTH = |- !n. !w :: PWORDLEN n. WSEG n 0 w = w
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
Theorem PWORDLEN1 autoloading from theory `word_base` ...
PWORDLEN1 = |- !x. PWORDLEN 1(WORD[x])
Theorem WSEG_WCAT_WSEG autoloading from theory `word_base` ...
WSEG_WCAT_WSEG =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
(m + k) <= (n1 + n2) /\ k < n2 /\ n2 <= (m + k) ==>
(WSEG m k(WCAT(w1,w2)) =
WCAT(WSEG((m + k) - n2)0 w1,WSEG(n2 - k)k w2))
Theorem WSEG0 autoloading from theory `word_base` ...
WSEG0 = |- !k w. WSEG 0 k w = WORD[]
WSEG_NBWORD_SUC = |- !n m. WSEG n 0(NBWORD(SUC n)m) = NBWORD n m
Theorem NVAL_MAX autoloading from theory `word_num` ...
NVAL_MAX =
|- !f b.
(!x. (f x) < b) ==> (!n. !w :: PWORDLEN n. (NVAL f b w) < (b EXP n))
Theorem WORDLEN_SUC_WCAT_BIT_WSEG autoloading from theory `word_base` ...
WORDLEN_SUC_WCAT_BIT_WSEG =
|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WORD[BIT n w],WSEG n 0 w)
NBWORD_SUC_WSEG =
|- !n. !w :: PWORDLEN(SUC n). NBWORD n(BNVAL w) = WSEG n 0 w
Theorem TIMES2 autoloading from theory `arithmetic` ...
TIMES2 = |- !n. 2 * n = n + n
Definition SHL_DEF autoloading from theory `word_bitop` ...
SHL_DEF =
|- !f w b.
SHL f w b =
BIT(PRE(WORDLEN w))w,
WCAT(WSEG(PRE(WORDLEN w))0 w,(f => WSEG 1 0 w | WORD[b]))
DOUBLE_EQ_SHL =
|- !n.
0 < n ==>
(!w :: PWORDLEN n.
!b. NBWORD n((BNVAL w) + ((BNVAL w) + (BV b))) = SND(SHL F w b))
Theorem LESS_ADD_SUC autoloading from theory `arithmetic` ...
LESS_ADD_SUC = |- !m n. m < (m + (SUC n))
Theorem BIT_WCAT_FST autoloading from theory `word_base` ...
BIT_WCAT_FST =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!k.
n2 <= k /\ k < (n1 + n2) ==> (BIT k(WCAT(w1,w2)) = BIT(k - n2)w1)
Definition SNOC autoloading from theory `list` ...
SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
Theorem BIT0 autoloading from theory `word_base` ...
BIT0 = |- !b. BIT 0(WORD[b]) = b
MSB_NBWORD =
|- !n m. BIT n(NBWORD(SUC n)m) = VB((m DIV (2 EXP n)) MOD 2)
ZERO_LESS_TWO_EXP = |- !m. 0 < (2 EXP m)
NBWORD_SPLIT =
|- !n1 n2 m.
NBWORD(n1 + n2)m = WCAT(NBWORD n1(m DIV (2 EXP n2)),NBWORD n2 m)
Theorem WSEG_WCAT2 autoloading from theory `word_base` ...
WSEG_WCAT2 =
|- !n1 n2.
!w1 :: PWORDLEN n1. !w2 :: PWORDLEN n2. WSEG n2 0(WCAT(w1,w2)) = w2
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c - c = 0
Theorem WSEG_WCAT_WSEG1 autoloading from theory `word_base` ...
WSEG_WCAT_WSEG1 =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
m <= n1 /\ n2 <= k ==> (WSEG m k(WCAT(w1,w2)) = WSEG m(k - n2)w1)
WSEG_NBWORD =
|- !m k n.
(m + k) <= n ==>
(!l. WSEG m k(NBWORD n l) = NBWORD m(l DIV (2 EXP k)))
NBWORD_SUC_FST =
|- !n m.
NBWORD(SUC n)m = WCAT(WORD[VB((m DIV (2 EXP n)) MOD 2)],NBWORD n m)
Theorem BIT_WSEG autoloading from theory `word_base` ...
BIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k j.
(m + k) <= n ==> j < m ==> (BIT j(WSEG m k w) = BIT(j + k)w)
BIT_NBWORD0 = |- !k n. k < n ==> (BIT k(NBWORD n 0) = F)
add_lem =
|- !m1 m2 n1 n2 p.
((m1 * p) + n1) + ((m2 * p) + n2) =
((m1 * p) + (m2 * p)) + (n1 + n2)
ADD_BNVAL_LEFT =
|- !n.
!w1 w2 :: PWORDLEN(SUC n).
(BNVAL w1) + (BNVAL w2) =
(((BV(BIT n w1)) + (BV(BIT n w2))) * (2 EXP n)) +
((BNVAL(WSEG n 0 w1)) + (BNVAL(WSEG n 0 w2)))
Theorem WORDLEN_SUC_WCAT_BIT_WSEG_RIGHT autoloading from theory `word_base` ...
WORDLEN_SUC_WCAT_BIT_WSEG_RIGHT =
|- !n. !w :: PWORDLEN(SUC n). w = WCAT(WSEG n 1 w,WORD[BIT 0 w])
ADD_BNVAL_RIGHT =
|- !n.
!w1 w2 :: PWORDLEN(SUC n).
(BNVAL w1) + (BNVAL w2) =
(((BNVAL(WSEG n 1 w1)) + (BNVAL(WSEG n 1 w2))) * 2) +
((BV(BIT 0 w1)) + (BV(BIT 0 w2)))
Theorem WCAT_WSEG_WSEG autoloading from theory `word_base` ...
WCAT_WSEG_WSEG =
|- !n.
!w :: PWORDLEN n.
!m1 m2 k.
(m1 + (m2 + k)) <= n ==>
(WCAT(WSEG m2(m1 + k)w,WSEG m1 k w) = WSEG(m1 + m2)k w)
ADD_BNVAL_SPLIT =
|- !n1 n2.
!w1 w2 :: PWORDLEN(n1 + n2).
(BNVAL w1) + (BNVAL w2) =
(((BNVAL(WSEG n1 n2 w1)) + (BNVAL(WSEG n1 n2 w2))) * (2 EXP n2)) +
((BNVAL(WSEG n2 0 w1)) + (BNVAL(WSEG n2 0 w2)))
() : void
File mk_bword_num loaded
() : void
#rm -f bword_arith.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_bword_arith`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
.........................................................() : void
Theory bword_num loaded
() : void
[(); (); ()] : void list
() : void
MULT_LEFT_1 = |- !m. 1 * m = m
ADD_DIV_SUC_DIV = |- !n. 0 < n ==> (!r. (n + r) DIV n = SUC(r DIV n))
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
LESS_IMP_LESS_EQ_PRE = |- !m n. 0 < n ==> (m < n = m <= (PRE n))
LESS_MONO_DIV =
|- !n. 0 < n ==> (!p q. p < q ==> (p DIV n) <= (q DIV n))
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
LESS_EQ_MONO_DIV =
|- !n. 0 < n ==> (!p q. p <= q ==> (p DIV n) <= (q DIV n))
Theorem PRE_SUC_EQ autoloading from theory `arithmetic` ...
PRE_SUC_EQ = |- !m n. 0 < n ==> ((m = PRE n) = (SUC m = n))
SUC_PRE = |- !n. 0 < n ==> (SUC(PRE n) = n)
Theorem TIMES2 autoloading from theory `arithmetic` ...
TIMES2 = |- !n. 2 * n = n + n
Definition EXP autoloading from theory `arithmetic` ...
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
ONE_LESS_TWO_EXP_SUC = |- !n. 1 < (2 EXP (SUC n))
ADD_MONO_EQ = |- !m n p. (p + m = p + n) = (m = n)
ACARRY_DEF =
|- (!w1 w2 cin. ACARRY 0 w1 w2 cin = cin) /\
(!n w1 w2 cin.
ACARRY(SUC n)w1 w2 cin =
VB
(((BV(BIT n w1)) + ((BV(BIT n w2)) + (BV(ACARRY n w1 w2 cin)))) DIV
2))
ICARRY_DEF =
|- (!w1 w2 cin. ICARRY 0 w1 w2 cin = cin) /\
(!n w1 w2 cin.
ICARRY(SUC n)w1 w2 cin =
BIT n w1 /\ BIT n w2 \/
(BIT n w1 \/ BIT n w2) /\ ICARRY n w1 w2 cin)
Theorem ZERO_MOD autoloading from theory `arithmetic` ...
ZERO_MOD = |- !n. 0 < n ==> (0 MOD n = 0)
Theorem ZERO_DIV autoloading from theory `arithmetic` ...
ZERO_DIV = |- !n. 0 < n ==> (0 DIV n = 0)
div_mod_lemmas =
[|- !x. (SUC(SUC x)) DIV 2 = SUC(x DIV 2);
|- (SUC 0) DIV 2 = 0;
|- 0 DIV 2 = 0;
|- (SUC 0) MOD 2 = SUC 0;
|- 0 MOD 2 = 0]
: thm list
Theorem SUC_NOT autoloading from theory `arithmetic` ...
SUC_NOT = |- !n. ~(0 = SUC n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
Definition VB_DEF autoloading from theory `bword_num` ...
VB_DEF = |- !n. VB n = ~(n MOD 2 = 0)
Definition BV_DEF autoloading from theory `bword_num` ...
BV_DEF = |- !b. BV b = (b => SUC 0 | 0)
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
ACARRY_EQ_ICARRY =
|- !n.
!w1 w2 :: PWORDLEN n.
!cin k. k <= n ==> (ACARRY k w1 w2 cin = ICARRY k w1 w2 cin)
Less2 = |- 0 < 2
Less2_SUC0 = |- (SUC 0) < 2
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
BV_LESS_EQ_1 = |- !x. (BV x) <= 1
Theorem LESS_EQ_LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_LESS_EQ_MONO =
|- !m n p q. m <= p /\ n <= q ==> (m + n) <= (p + q)
ADD_BV_LESS_EQ_2 = |- !x1 x2. ((BV x1) + (BV x2)) <= 2
LESS_EQ1_LESS2 = |- n < 2 = n <= 1
Theorem BNVAL_MAX autoloading from theory `bword_num` ...
BNVAL_MAX = |- !n. !w :: PWORDLEN n. (BNVAL w) < (2 EXP n)
Theorem ZERO_LESS_EXP autoloading from theory `arithmetic` ...
ZERO_LESS_EXP = |- !m n. 0 < ((SUC n) EXP m)
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
BNVAL_LESS_EQ = |- !n. !w :: PWORDLEN n. (BNVAL w) <= ((2 EXP n) - 1)
Theorem LESS_MONO_MULT autoloading from theory `arithmetic` ...
LESS_MONO_MULT = |- !m n p. m <= n ==> (m * p) <= (n * p)
Theorem LEFT_SUB_DISTRIB autoloading from theory `arithmetic` ...
LEFT_SUB_DISTRIB = |- !m n p. p * (m - n) = (p * m) - (p * n)
ADD_BNVAL_LESS_EQ =
|- !n.
!w1 w2 :: PWORDLEN n.
!cin.
((BNVAL w1) + ((BNVAL w2) + (BV cin))) <= ((2 EXP (SUC n)) - 1)
ZERO_LESS_TWO_EXP = |- !m. 0 < (2 EXP m)
EXP_SUB1_LESS = |- ((2 EXP n) - 1) < (2 EXP n)
ADD_BNVAL_LESS_EQ1 =
|- !n cin.
!w1 w2 :: PWORDLEN n.
(((BNVAL w1) + ((BNVAL w2) + (BV cin))) DIV (2 EXP n)) <= (SUC 0)
ADD_BV_BNVAL_DIV_LESS_EQ1 =
|- !n x1 x2 cin.
!w1 w2 :: PWORDLEN n.
((((BV x1) + (BV x2)) +
(((BNVAL w1) + ((BNVAL w2) + (BV cin))) DIV (2 EXP n))) DIV
2) <=
1
Theorem SUC_LESS autoloading from theory `prim_rec` ...
SUC_LESS = |- !m n. (SUC m) < n ==> m < n
ADD_BV_BNVAL_LESS_EQ =
|- !n x1 x2 cin.
!w1 w2 :: PWORDLEN n.
(((BV x1) + (BV x2)) + ((BNVAL w1) + ((BNVAL w2) + (BV cin)))) <=
(SUC(2 EXP (SUC n)))
ADD_BV_BNVAL_LESS_EQ1 =
|- !n x1 x2 cin.
!w1 w2 :: PWORDLEN n.
((((BV x1) + (BV x2)) + ((BNVAL w1) + ((BNVAL w2) + (BV cin)))) DIV
(2 EXP (n + 1))) <=
1
Theorem WSEG_PWORDLEN autoloading from theory `word_base` ...
WSEG_PWORDLEN =
|- !n. !w :: PWORDLEN n. !m k. (m + k) <= n ==> PWORDLEN m(WSEG m k w)
seg_pw =
|- !w. PWORDLEN n w ==> (SUC k) <= n ==> PWORDLEN(SUC k)(WSEG(SUC k)0 w)
Theorem BIT_WSEG autoloading from theory `word_base` ...
BIT_WSEG =
|- !n.
!w :: PWORDLEN n.
!m k j.
(m + k) <= n ==> j < m ==> (BIT j(WSEG m k w) = BIT(j + k)w)
bit_thm =
|- !w.
PWORDLEN n w ==> (SUC k) <= n ==> (BIT k(WSEG(SUC k)0 w) = BIT k w)
Theorem WSEG_WSEG autoloading from theory `word_base` ...
WSEG_WSEG =
|- !n.
!w :: PWORDLEN n.
!m1 k1 m2 k2.
(m1 + k1) <= n /\ (m2 + k2) <= m1 ==>
(WSEG m2 k2(WSEG m1 k1 w) = WSEG m2(k1 + k2)w)
seg_thm =
|- !w.
PWORDLEN n w ==>
(SUC k) <= n ==>
(WSEG k 0(WSEG(SUC k)0 w) = WSEG k 0 w)
seg_pw_thm' = |- !w. PWORDLEN n w ==> k <= n ==> PWORDLEN k(WSEG k 0 w)
spec_thm = - : (thm -> thm list)
Theorem ADD_BNVAL_LEFT autoloading from theory `bword_num` ...
ADD_BNVAL_LEFT =
|- !n.
!w1 w2 :: PWORDLEN(SUC n).
(BNVAL w1) + (BNVAL w2) =
(((BV(BIT n w1)) + (BV(BIT n w2))) * (2 EXP n)) +
((BNVAL(WSEG n 0 w1)) + (BNVAL(WSEG n 0 w2)))
add_left =
... |- (BNVAL(WSEG(SUC k)0 w1)) + (BNVAL(WSEG(SUC k)0 w2)) =
(((BV(BIT k w1)) + (BV(BIT k w2))) * (2 EXP k)) +
((BNVAL(WSEG k 0 w1)) + (BNVAL(WSEG k 0 w2)))
less1_lem =
... |- ((((BV(BIT k w1)) + (BV(BIT k w2))) +
(((BNVAL(WSEG k 0 w1)) + ((BNVAL(WSEG k 0 w2)) + (BV cin))) DIV
(2 EXP k))) DIV
2) <=
1
Theorem BV_VB autoloading from theory `bword_num` ...
BV_VB = |- !x. x < 2 ==> (BV(VB x) = x)
Theorem BNVAL0 autoloading from theory `bword_num` ...
BNVAL0 = |- BNVAL(WORD[]) = 0
Theorem WSEG0 autoloading from theory `word_base` ...
WSEG0 = |- !k w. WSEG 0 k w = WORD[]
ACARRY_EQ_ADD_DIV =
|- !n.
!w1 w2 :: PWORDLEN n.
!k.
k < n ==>
(BV(ACARRY k w1 w2 cin) =
((BNVAL(WSEG k 0 w1)) + ((BNVAL(WSEG k 0 w2)) + (BV cin))) DIV
(2 EXP k))
Theorem NBWORD_MOD autoloading from theory `bword_num` ...
NBWORD_MOD = |- !n m. NBWORD n(m MOD (2 EXP n)) = NBWORD n m
Theorem LESS_ADD_NONZERO autoloading from theory `arithmetic` ...
LESS_ADD_NONZERO = |- !m n. ~(n = 0) ==> m < (m + n)
Theorem NBWORD_SPLIT autoloading from theory `bword_num` ...
NBWORD_SPLIT =
|- !n1 n2 m.
NBWORD(n1 + n2)m = WCAT(NBWORD n1(m DIV (2 EXP n2)),NBWORD n2 m)
Theorem WSEG_WORD_LENGTH autoloading from theory `word_base` ...
WSEG_WORD_LENGTH = |- !n. !w :: PWORDLEN n. WSEG n 0 w = w
Theorem WCAT0 autoloading from theory `word_base` ...
WCAT0 = |- !w. (WCAT(WORD[],w) = w) /\ (WCAT(w,WORD[]) = w)
Theorem NBWORD0 autoloading from theory `bword_num` ...
NBWORD0 = |- !m. NBWORD 0 m = WORD[]
Theorem PWORDLEN_NBWORD autoloading from theory `bword_num` ...
PWORDLEN_NBWORD = |- !n m. PWORDLEN n(NBWORD n m)
Theorem WCAT_11 autoloading from theory `word_base` ...
WCAT_11 =
|- !m n.
!wm1 wm2 :: PWORDLEN m.
!wn1 wn2 :: PWORDLEN n.
(WCAT(wm1,wn1) = WCAT(wm2,wn2)) = (wm1 = wm2) /\ (wn1 = wn2)
Theorem ADD_BNVAL_SPLIT autoloading from theory `bword_num` ...
ADD_BNVAL_SPLIT =
|- !n1 n2.
!w1 w2 :: PWORDLEN(n1 + n2).
(BNVAL w1) + (BNVAL w2) =
(((BNVAL(WSEG n1 n2 w1)) + (BNVAL(WSEG n1 n2 w2))) * (2 EXP n2)) +
((BNVAL(WSEG n2 0 w1)) + (BNVAL(WSEG n2 0 w2)))
ADD_WORD_SPLIT =
|- !n1 n2.
!w1 w2 :: PWORDLEN(n1 + n2).
!cin.
NBWORD(n1 + n2)((BNVAL w1) + ((BNVAL w2) + (BV cin))) =
WCAT
(NBWORD
n1
((BNVAL(WSEG n1 n2 w1)) +
((BNVAL(WSEG n1 n2 w2)) + (BV(ACARRY n2 w1 w2 cin)))),
NBWORD
n2
((BNVAL(WSEG n2 0 w1)) + ((BNVAL(WSEG n2 0 w2)) + (BV cin))))
Theorem WSEG_WCAT2 autoloading from theory `word_base` ...
WSEG_WCAT2 =
|- !n1 n2.
!w1 :: PWORDLEN n1. !w2 :: PWORDLEN n2. WSEG n2 0(WCAT(w1,w2)) = w2
Theorem WSEG_WCAT_WSEG1 autoloading from theory `word_base` ...
WSEG_WCAT_WSEG1 =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!m k.
m <= n1 /\ n2 <= k ==> (WSEG m k(WCAT(w1,w2)) = WSEG m(k - n2)w1)
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c - c = 0
WSEG_NBWORD_ADD =
|- !n.
!w1 w2 :: PWORDLEN n.
!m k cin.
(m + k) <= n ==>
(WSEG m k(NBWORD n((BNVAL w1) + ((BNVAL w2) + (BV cin)))) =
NBWORD
m
((BNVAL(WSEG m k w1)) +
((BNVAL(WSEG m k w2)) + (BV(ACARRY k w1 w2 cin)))))
ADD_NBWORD_EQ0_SPLIT =
|- !n1 n2.
!w1 w2 :: PWORDLEN(n1 + n2).
!cin.
(NBWORD(n1 + n2)((BNVAL w1) + ((BNVAL w2) + (BV cin))) =
NBWORD(n1 + n2)0) =
(NBWORD
n1
((BNVAL(WSEG n1 n2 w1)) +
((BNVAL(WSEG n1 n2 w2)) + (BV(ACARRY n2 w1 w2 cin)))) =
NBWORD n1 0) /\
(NBWORD
n2
((BNVAL(WSEG n2 0 w1)) + ((BNVAL(WSEG n2 0 w2)) + (BV cin))) =
NBWORD n2 0)
Theorem MOD_MOD autoloading from theory `arithmetic` ...
MOD_MOD = |- !n. 0 < n ==> (!k. (k MOD n) MOD n = k MOD n)
VB_MOD_2 = |- !n. VB(n MOD 2) = VB n
Theorem NBWORD_SUC_FST autoloading from theory `bword_num` ...
NBWORD_SUC_FST =
|- !n m.
NBWORD(SUC n)m = WCAT(WORD[VB((m DIV (2 EXP n)) MOD 2)],NBWORD n m)
Theorem VB_BV autoloading from theory `bword_num` ...
VB_BV = |- !x. VB(BV x) = x
Theorem BV_LESS_2 autoloading from theory `bword_num` ...
BV_LESS_2 = |- !x. (BV x) < 2
Theorem LESS_MOD autoloading from theory `arithmetic` ...
LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
Theorem NVAL0 autoloading from theory `word_num` ...
NVAL0 = |- !f b. NVAL f b(WORD[]) = 0
Theorem NBWORD_SUC autoloading from theory `bword_num` ...
NBWORD_SUC =
|- !n m. NBWORD(SUC n)m = WCAT(NBWORD n(m DIV 2),WORD[VB(m MOD 2)])
Theorem BNVAL_NVAL autoloading from theory `bword_num` ...
BNVAL_NVAL = |- !w. BNVAL w = NVAL BV 2 w
Theorem PWORDLEN0 autoloading from theory `word_base` ...
PWORDLEN0 = |- !w. PWORDLEN 0 w ==> (w = WORD[])
Theorem BIT_WCAT_FST autoloading from theory `word_base` ...
BIT_WCAT_FST =
|- !n1 n2.
!w1 :: PWORDLEN n1.
!w2 :: PWORDLEN n2.
!k.
n2 <= k /\ k < (n1 + n2) ==> (BIT k(WCAT(w1,w2)) = BIT(k - n2)w1)
Theorem BIT0 autoloading from theory `word_base` ...
BIT0 = |- !b. BIT 0(WORD[b]) = b
Theorem LESS_ADD_SUC autoloading from theory `arithmetic` ...
LESS_ADD_SUC = |- !m n. m < (m + (SUC n))
Theorem PWORDLEN1 autoloading from theory `word_base` ...
PWORDLEN1 = |- !x. PWORDLEN 1(WORD[x])
ACARRY_MSB =
|- !n.
!w1 w2 :: PWORDLEN n.
!cin.
ACARRY n w1 w2 cin =
BIT n(NBWORD(SUC n)((BNVAL w1) + ((BNVAL w2) + (BV cin))))
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
ACARRY_WSEG =
|- !n.
!w1 w2 :: PWORDLEN n.
!cin k m.
k < m /\ m <= n ==>
(ACARRY k(WSEG m 0 w1)(WSEG m 0 w2)cin = ACARRY k w1 w2 cin)
ICARRY_WSEG =
|- !n.
!w1 w2 :: PWORDLEN n.
!cin k m.
k < m /\ m <= n ==>
(ICARRY k(WSEG m 0 w1)(WSEG m 0 w2)cin = ICARRY k w1 w2 cin)
ACARRY_ACARRY_WSEG =
|- !n.
!w1 w2 :: PWORDLEN n.
!cin m k1 k2.
k1 < m /\ k2 < n /\ (m + k2) <= n ==>
(ACARRY k1(WSEG m k2 w1)(WSEG m k2 w2)(ACARRY k2 w1 w2 cin) =
ACARRY(k1 + k2)w1 w2 cin)
() : void
File mk_bword_arith loaded
() : void
#rm -f word.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_word`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
autoload_all = - : (string -> void)
Loading library arith ...
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
.Updating help search path
.......................................................................................................................................................................................................................................................................................
Library arith loaded.
() : void
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
....() : void
File ver_202 loaded
() : void
() : void
Theory bword_bitop loaded
Theory bword_num loaded
Theory bword_arith loaded
[(); (); ()] : void list
() : void
File mk_word loaded
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'load_library`res_quan`;;'\
'load_theory `word`;;'\
'compilet `word_convs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Loading library res_quan ...
Updating search path
Theory res_quan loaded
...............................................................................Updating help search path
.
Library res_quan loaded.
() : void
#Theory word loaded
() : void
word_CASES_TAC = - : (term -> tactic)
word_INDUCT_TAC = - : tactic
RESQ_WORDLEN_TAC = - : tactic
BIT_CONV = - : conv
WSEG_CONV = - : conv
LESS_CONV = - : conv
LESS_EQ_CONV = - : conv
word_inst_thm = - : ((term # term) -> thm -> thm)
WNOT_PWORDLEN = |- !n. !w :: PWORDLEN n. PWORDLEN n(WNOT w)
WAND_PWORDLEN = |- !n. !w1 w2 :: PWORDLEN n. PWORDLEN n(w1 WAND w2)
WOR_PWORDLEN = |- !n. !w1 w2 :: PWORDLEN n. PWORDLEN n(w1 WOR w2)
WXOR_PWORDLEN = |- !n. !w1 w2 :: PWORDLEN n. PWORDLEN n(w1 WXOR w2)
pwordlen_bitop_funs =
[(`WNOT`, |- !n. !w :: PWORDLEN n. PWORDLEN n(WNOT w));
(`WAND`, |- !n. !w1 w2 :: PWORDLEN n. PWORDLEN n(w1 WAND w2));
(`WOR`, |- !n. !w1 w2 :: PWORDLEN n. PWORDLEN n(w1 WOR w2));
(`WXOR`, |- !n. !w1 w2 :: PWORDLEN n. PWORDLEN n(w1 WXOR w2))]
: (string # thm) list
pwordlen_funs =
[(`WORD`, -);
(`WSEG`, -);
(`WNOT`, -);
(`WAND`, -);
(`WOR`, -);
(`WXOR`, -);
(`WCAT`, -)]
: (string # (term list -> term -> term list -> thm)) list
check = - : (string -> term -> term)
pick_fn = - : (string -> (string # *) list -> term -> *)
PWORDLEN_CONV = - : (term list -> conv)
PWORDLEN_bitop_CONV = - : conv
WSEG_WSEG_CONV = - : (term -> conv)
((-), (-), -) : ((term list -> conv) # conv # (term -> conv))
PWORDLEN_CONV = - : (term list -> conv)
PWORDLEN_bitop_CONV = - : conv
WSEG_WSEG_CONV = - : (term -> conv)
PWORDLEN_TAC = - : (term list -> tactic)
Calling Lisp compiler
File word_convs compiled
() : void
#===> library word rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/word'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/record_proof'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `proof_rec`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
New constructors declared:
Hypothesis : justification
Assume : (term -> justification)
Refl : (term -> justification)
Subst : (((int # term) list # term # int) -> justification)
BetaConv : (term -> justification)
Abs : ((term # int) -> justification)
InstType : (((type # type) list # int) -> justification)
Disch : ((term # int) -> justification)
Mp : ((int # int) -> justification)
MkComb : ((int # int) -> justification)
MkAbs : (int -> justification)
Alpha : ((term # term) -> justification)
AddAssum : ((term # int) -> justification)
Sym : (int -> justification)
Trans : ((int # int) -> justification)
ImpTrans : ((int # int) -> justification)
ApTerm : ((term # int) -> justification)
ApThm : ((int # term) -> justification)
EqMp : ((int # int) -> justification)
EqImpRuleR : (int -> justification)
EqImpRuleL : (int -> justification)
Spec : ((term # int) -> justification)
EqtIntro : (int -> justification)
Gen : ((term # int) -> justification)
EtaConv : (term -> justification)
Ext : (int -> justification)
Exists : (((term # term) # int) -> justification)
Choose : (((term # int) # int) -> justification)
ImpAntisymRule : ((int # int) -> justification)
MkExists : (int -> justification)
Subs : ((int list # int) -> justification)
SubsOccs : (((int list # int) list # int) -> justification)
SubstConv : (((int # term) list # term # term) -> justification)
Conj : ((int # int) -> justification)
Conjunct1 : (int -> justification)
Conjunct2 : (int -> justification)
Disj1 : ((int # term) -> justification)
Disj2 : ((term # int) -> justification)
DisjCases : ((int # int # int) -> justification)
NotIntro : (int -> justification)
NotElim : (int -> justification)
Contr : ((term # int) -> justification)
Ccontr : ((term # int) -> justification)
Inst : (((term # term) list # int) -> justification)
StoreDefinition : ((string # term) -> justification)
Definition : ((string # string) -> justification)
DefExistsRule : (term -> justification)
NewAxiom : ((string # term) -> justification)
Axiom : ((string # string) -> justification)
Theorem : ((string # string) -> justification)
NewConstant : ((string # type) -> justification)
NewType : ((int # string) -> justification)
NumConv : (term -> justification)
New constructors declared:
Line : ((int # thm # justification) -> line)
MakeProof = - : (step list -> line list)
output_strings = - : (string -> string list -> void)
write_pair =
-
: (string ->
((string -> * -> **) # (string -> *** -> ****)) ->
(* # ***) ->
void)
write_list = - : (string -> (string -> * -> **) -> * list -> void)
write_type = - : (string -> type -> void)
write_term = - : (string -> term -> void)
write_thm = - : (string -> thm -> void)
write_all_thm = - : (string -> thm -> void)
write_int = - : (string -> int -> void)
write_just = - : (string -> justification -> void)
write_line = - : (string -> line -> void)
write_tyconst = - : (string -> (int # string) -> void)
write_sig = - : (string -> (string # type) -> void)
write_env = - : (string -> void)
write_thm_list = - : (string -> thm list -> void)
((-), (-), -)
: ((string -> line -> void) #
(string -> thm list -> void) #
(string -> void))
write_line = - : (string -> line -> void)
write_thm_list = - : (string -> thm list -> void)
write_env = - : (string -> void)
format_version = `(VERSION PRF FORMAT 1.0 EXTENDED)
` : string
write_proof_add_to =
-
: (string -> string -> thm list -> line list -> void)
write_proof_to = - : (string -> string -> thm list -> line list -> void)
proof_file_name = `` : string
proof_file_port = `` : string
proof_name = `` : string
proof_count = 0 : int
current_goals = [] : thm list
write_last_proof = - : (string -> thm list -> void)
current_proof_file = - : (void -> string)
current_proof = - : (void -> string)
close_proof_file = - : (void -> void)
new_proof_file = - : (string -> void)
begin_proof = - : (string -> void)
end_proof = - : (* -> void)
sanitise = - : (string -> string)
TAC_PROOF = - : ((goal # tactic) -> thm)
PROVE = - : ((term # tactic) -> thm)
prove = - : ((term # tactic) -> thm)
prove_thm = - : ((string # term # tactic) -> thm)
((-), (-), (-), (-), (-), (-), (-), (-), (-), (-), (-), (-), -)
: ((string -> string -> thm list -> line list -> void) #
(string -> string -> thm list -> line list -> void) #
(string -> thm list -> void) #
(void -> string) #
(void -> string) #
(string -> void) #
(void -> void) #
(string -> void) #
(* -> void) #
((goal # tactic) -> thm) #
((term # tactic) -> thm) #
((term # tactic) -> thm) #
((string # term # tactic) -> thm))
write_proof_add_to =
-
: (string -> string -> thm list -> line list -> void)
write_proof_to = - : (string -> string -> thm list -> line list -> void)
write_last_proof = - : (string -> thm list -> void)
current_proof = - : (void -> string)
current_proof_file = - : (void -> string)
new_proof_file = - : (string -> void)
close_proof_file = - : (void -> void)
begin_proof = - : (string -> void)
end_proof = - : (* -> void)
TAC_PROOF = - : ((goal # tactic) -> thm)
PROVE = - : ((term # tactic) -> thm)
prove = - : ((term # tactic) -> thm)
prove_thm = - : ((string # term # tactic) -> thm)
Calling Lisp compiler
File proof_rec compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `dummy_funs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
new_proof_file = - : (string -> void)
close_proof_file = - : (void -> void)
begin_proof = - : (string -> void)
end_proof = - : (void -> void)
current_proof = - : (void -> string)
current_proof_file = - : (void -> string)
write_proof_add_to =
-
: (string -> string -> thm list -> * list -> void)
write_proof_to = - : (string -> string -> thm list -> * list -> void)
write_last_proof = - : (string -> thm list -> void)
Calling Lisp compiler
File dummy_funs compiled
() : void
#===> library record_proof rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/record_proof'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/parser'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `general`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
FIRST_CHARS = [] : string list
CHARS = [] : string list
DEBUG = false : bool
IGNORE = [] : (string # string) list
USEFUL = [] : (string # string) list
push = - : (* -> * list -> * list)
pop = - : (* list -> (* # * list))
write_string = - : (string -> string -> void)
read_char = - : (string -> string)
close_file = - : (string -> void)
open_file = - : (string -> string -> string)
e_w_s = - : (string -> string -> string list -> string)
e_w_s_ok = - : (string -> string -> string list -> string)
determine_lst = - : (* -> * list -> * list -> bool)
get_word2 =
-
: (string ->
string list ->
string ->
string list ->
(string # *) list ->
(string # **) list ->
(string # ***) list ->
(string list # string))
get_word1 =
-
: (string ->
string list ->
string ->
string list ->
string list ->
(string list # string))
complete_separator =
-
: (string ->
string ->
string list ->
(string # string list) list ->
(string # *) list ->
(string # **) list ->
(string # string))
get_word =
-
: (string ->
string list ->
string ->
(string # string list) list ->
string ->
(string # *) list ->
(string # **) list ->
(string # string))
useful_stuff =
-
: (string -> string -> string -> string list -> (string # string))
ignore_stuff = - : (string -> string -> string -> string list -> string)
read_input =
-
: (string ->
string list ->
string list ->
(string # string list) list ->
string ->
(string # string) list ->
(string # string) list ->
string list)
gnt = - : (string list -> string -> string -> (string # string list))
eat_terminal =
-
: (string -> string -> string list -> * -> (string # string list))
chop_off = - : (int -> * list -> * list -> (* list # * list))
debug_return = - : (string -> string -> void)
do_return_1 =
-
: (* list ->
** ->
string ->
** ->
** list ->
** ->
(* # * list # ** # ** list))
do_return =
-
: (* list ->
string ->
string ->
string ->
string list ->
string ->
(* # * list # string # string list))
debug_enter = - : ((string # string # string) -> void)
debug_on = - : (* -> bool)
debug_off = - : (* -> bool)
Calling Lisp compiler
File general compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `parser`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
EXPECTED = [] : string list
pg_failwith = - : (string -> string -> string -> *)
escaped = - : (string -> string -> string)
write_string = - : (string -> string -> void)
read_char = - : (string -> string)
split_filename =
-
: (string list -> string list -> bool -> (string # string))
close_file = - : (string -> void)
bad_read = - : (string -> *)
terminal_read_1 = - : (string -> string list)
terminal_read = - : (* -> string)
make_Makefile = - : (string -> string -> string -> void)
make_makefile = - : (string -> void)
open_file = - : (string -> string -> (string # string))
eat_white_space = - : (string -> string -> string)
e_w_s = - : (string -> string -> string)
e_w_s_ok = - : (string -> string -> string)
write_comments = - : (string -> string -> string -> string -> string)
get_word1 =
-
: (string ->
string list ->
string ->
string ->
string ->
string ->
(string list # string))
first_test = - : (string -> string -> bool)
get_word =
-
: (string -> string -> string -> string -> string -> (string # string))
get_inits1 =
-
: (string -> string list -> string -> (string list # string))
get_inits = - : (string -> string -> string -> string)
get_inits1_specials =
-
: (string -> string list -> string -> (string list # string))
get_inits_specials = - : (string -> string -> string -> string)
separator = - : (string -> string)
MK_word = - : (string -> string list)
MK_start = - : (string -> string list)
EOF = - : (string -> string)
write_conditional = - : (string -> string list list)
write_if = - : (string -> string -> string list list)
finish_terminal = - : (string -> string -> * list)
epsilon_start = - : (string -> string list list)
get_terminal_2 = - : (string -> string -> string -> string list)
is_EOF = - : (string -> string)
get_terminal_1 =
-
: (string ->
string ->
string ->
string ->
* ->
(string list list # string # string # bool))
get_terminal =
-
: (string ->
string ->
string ->
string ->
* ->
(string list list # string # string # bool))
system_function_args = - : (string -> bool)
prdn_errors_args = - : (string -> string -> void)
tmp_var = - : (string -> int -> string)
HOL_term = - : (string -> bool)
top_or_middle = - : (string -> string list)
get_args_prdn =
-
: (string -> * -> string -> string -> (string # string))
finish_arg = - : (string -> string -> string -> string list)
get_argn1 =
-
: (string ->
string ->
string ->
string ->
string ->
bool ->
string list)
get_arg_name =
-
: (string -> string -> string -> string -> bool -> (string # string))
add_new_calls =
-
: (* list -> string -> * list -> * list -> (* list # * list))
require_start =
-
: (string -> string -> string -> (string list # string))
need_to_use_pops = - : (int -> string list)
add_EXPECTED = - : (string -> bool -> string list)
pop_or_reg =
-
: (string -> string -> bool -> (string list # string # string # bool))
mk_lets =
-
: (string ->
int ->
string ->
bool ->
(string list # string # int # string # bool))
comma = - : (bool -> string -> string)
failed_arg = - : (string -> bool)
preprocess_args =
-
: (string ->
string list ->
string list ->
string list ->
string ->
string ->
int ->
string ->
string ->
bool ->
int ->
bool ->
(string list # string # int # string list # int # string # bool))
get_args_act =
-
: (string ->
string ->
string ->
string list list ->
int ->
string ->
string ->
bool ->
(string list list # string list # int # string # string # bool))
write_tabs = - : (int -> string -> void)
then_if = - : (int -> string -> int)
pop_EXPECTED = - : (* -> string)
write_final =
-
: (string -> string list -> int -> string -> (int # string))
write_final_all =
-
: (string list list -> string -> int -> string -> void)
eat_arrow = - : (string -> string -> string -> int -> string)
unwind_parens = - : (int -> string list)
finish_arm =
-
: (* list -> * list -> * -> * list -> * -> * list -> * list)
new_letrefs =
-
: (string -> string -> string -> bool -> string list list)
NT_letrefs = - : (string -> string -> string -> string list list)
ACTION_letrefs = - : (string -> string -> string -> string list list)
MK_failed = - : (bool -> * -> ** -> *** -> string list list)
MK_return = - : (string -> bool -> string -> string list)
system_function = - : (string -> bool)
terminal_errors = - : (string -> string -> string -> void)
prdn_errors = - : (string -> string -> void)
action_errors = - : (string -> string -> void)
final_trap = - : (bool -> * -> string list list)
get_rest_of_prdn =
-
: (string ->
string list list ->
string list list ->
string ->
string ->
int ->
int ->
bool ->
string ->
string ->
bool ->
string list list)
process = - : (string -> string -> string -> string -> string list list)
MK_lambda = - : (string -> string list list -> string list list)
write_decs = - : (string -> string -> string -> void)
make_main_wrapper = - : (string -> void)
emit_firsts = - : (string -> string -> string -> void)
emit_specials = - : (string -> string -> string -> void)
token_failwith = - : (string -> *)
make_tokeniser = - : (string -> bool -> bool -> void)
decls_fail = - : (string -> *)
decls_errors = - : (string -> bool -> bool -> (bool # bool))
make_productions =
-
: (string -> string -> string -> string -> bool -> bool -> void)
get_ty = - : (string list -> bool -> string)
parse = - : (* -> void)
- : (* -> void)
parse = - : (* -> void)
Calling Lisp compiler
File parser compiled
() : void
#===> library parser rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/parser'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/prettyp'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `PP_printer/extents`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
max = - : (int list -> int)
min = - : (int list -> int)
change_assocl = - : ((* # **) list -> (* # **) list -> (* # **) list)
Nat = - : (int -> nat)
Int = - : (nat -> int)
print_nat = - : (nat -> void)
- : (nat -> void)
get_margin = - : (void -> int)
Calling Lisp compiler
File PP_printer/extents compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'compilet `PP_printer/strings`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
substr = - : (int -> int -> string -> string)
strlen = - : (string -> int)
num_of_leading_chars = - : (string list -> string -> int)
trim_leading_chars = - : (string list -> string -> string)
trim_trailing_chars = - : (string list -> string -> string)
trim_enclosing_chars = - : (string list -> string -> string)
string_contains = - : (string -> string -> bool)
strings_contain = - : (string list -> string -> bool)
string_copies = - : (string -> int -> string)
Calling Lisp compiler
File PP_printer/strings compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'compilet `PP_printer/ptree`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
New constructors declared:
Print_node : ((string # print_tree list) -> print_tree)
print_tree_name = - : (print_tree -> string)
print_tree_children = - : (print_tree -> print_tree list)
Calling Lisp compiler
File PP_printer/ptree compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'loadf `PP_printer/ptree`;;'\
'compilet `PP_printer/treematch`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
...() : void
New constructors declared:
No_address : address
Address : (int list -> address)
New constructors declared:
Bound_name : ((string # address) -> metavar_binding)
Bound_names : ((string # address) list -> metavar_binding)
Bound_child : ((print_tree # address) -> metavar_binding)
Bound_children : ((print_tree # address) list -> metavar_binding)
type print_binding defined
type print_test defined
New constructors declared:
Default : loop_limit
Val : (nat -> loop_limit)
New constructors declared:
Const_name : ((string # child_metavar list) -> print_patt_tree)
Var_name : ((string # child_metavar list) -> print_patt_tree)
Wild_name : (child_metavar list -> print_patt_tree)
Var_child : (string -> print_patt_tree)
Wild_child : print_patt_tree
Link_child : (((loop_limit # loop_limit) # string list) ->
print_patt_tree)
Print_label : ((string # print_patt_tree) -> print_patt_tree)
Print_link : ((((loop_limit # loop_limit) # string list) #
print_patt_tree) ->
print_patt_tree)
Print_loop : ((print_patt_tree # print_patt_tree) -> print_patt_tree)
Var_children : (string -> child_metavar)
Wild_children : child_metavar
Patt_child : (print_patt_tree -> child_metavar)
type print_pattern defined
New constructors declared:
No_link : print_loop_link
Link : ((((loop_limit # loop_limit) # string list) #
print_tree #
int list) ->
print_loop_link)
lookup_metavar = - : (print_binding -> string -> metavar_binding)
eq_metavar_bind = - : (metavar_binding -> metavar_binding -> bool)
no_address_meta = - : (metavar_binding -> metavar_binding)
replace = - : ((* # **) list -> (* # **) -> (* # **) list)
replacel = - : ((* # **) list -> (* # **) list -> (* # **) list)
print_merge = - : (print_binding -> print_binding -> print_binding)
print_loop_merge = - : (print_binding -> print_binding -> print_binding)
raise_binding = - : (print_binding -> print_binding)
raise_bindings = - : (print_binding -> print_binding -> print_binding)
correspond_bindings =
-
: (print_binding -> print_binding -> print_binding)
raise_bindings_safe =
-
: (print_binding -> print_binding -> print_binding)
extract_info_from_patt =
-
: (print_patt_tree -> ((string list # string list) # print_loop_link))
extract_info_from_child =
-
: (child_metavar -> ((string list # string list) # print_loop_link))
zero_loop_info = - : (print_patt_tree -> (print_binding # loop_limit))
new_addresses =
-
: (int list -> print_tree list -> (print_tree # int list) list)
split_list = - : ((int # int) -> * list -> (* list # * list # * list))
print_tree_match' =
-
: (print_patt_tree ->
(print_tree # int list) ->
(print_binding # print_loop_link))
children_match =
-
: (child_metavar list ->
(print_tree # int list) list ->
(print_binding # print_loop_link))
print_tree_match =
-
: (print_patt_tree -> print_tree -> (print_binding # print_loop_link))
add_context = - : (string -> (string # int) list -> (string # int) list)
print_pattern_match =
-
: (print_pattern ->
string ->
(string # int) list ->
print_tree ->
print_binding)
((-), -)
: ((string -> (string # int) list -> (string # int) list) #
(print_pattern ->
string ->
(string # int) list ->
print_tree ->
print_binding))
add_context = - : (string -> (string # int) list -> (string # int) list)
print_pattern_match =
-
: (print_pattern ->
string ->
(string # int) list ->
print_tree ->
print_binding)
Calling Lisp compiler
File PP_printer/treematch compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'loadf `PP_printer/ptree`;;'\
'loadf `PP_printer/treematch`;;'\
'compilet `PP_printer/boxes`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
...() : void
.............................() : void
New constructors declared:
N_box : * print_box
A_box : (((nat # string) # *) -> * print_box)
L_box : (((nat # nat # * print_box # * print_box) # *) -> * print_box)
C_box : ((((nat # nat # nat) #
nat #
(int # nat) #
* print_box #
* print_box) #
*) ->
* print_box)
print_box_io = - : (* print_box -> int)
print_box_width = - : (* print_box -> int)
print_box_fo = - : (* print_box -> int)
print_box_height = - : (* print_box -> int)
print_box_sizes = - : (* print_box -> ((int # int # int) # int))
replace_box_label = - : (* -> * print_box -> * print_box)
New constructors declared:
Abs : (int -> print_indent)
Inc : (int -> print_indent)
New constructors declared:
UB_H : (((int -> int -> * print_box) #
(nat # (int -> int -> * print_box)) list) ->
* unbuilt_box)
UB_V : (((int -> int -> * print_box) #
((print_indent # nat) # (int -> int -> * print_box)) list) ->
* unbuilt_box)
UB_HV : (((int -> int -> * print_box) #
((nat # print_indent # nat) # (int -> int -> * print_box))
list) ->
* unbuilt_box)
UB_HoV : (((int -> int -> * print_box) #
((nat # print_indent # nat) # (int -> int -> * print_box))
list) ->
* unbuilt_box)
join_boxes =
-
: (int -> int -> * print_box -> * print_box -> * -> * print_box)
join_H_boxes =
-
: (nat -> * print_box -> * print_box -> * -> * print_box)
join_V_boxes =
-
: (int -> nat -> * print_box -> * print_box -> * -> * print_box)
build_H_box =
-
: (int ->
int ->
* ->
(int -> int -> * print_box) ->
(nat # (int -> int -> * print_box)) list ->
* print_box)
build_V_box =
-
: (int ->
int ->
* ->
(int -> int -> * print_box) ->
((print_indent # nat) # (int -> int -> * print_box)) list ->
* print_box)
build_HV_box =
-
: (int ->
int ->
* ->
(int -> int -> * print_box) ->
((nat # print_indent # nat) # (int -> int -> * print_box)) list ->
* print_box)
build_HoV_box =
-
: (int ->
int ->
* ->
(int -> int -> * print_box) ->
((nat # print_indent # nat) # (int -> int -> * print_box)) list ->
* print_box)
build_print_box = - : (int -> int -> * -> * unbuilt_box -> * print_box)
- : (int -> int -> * -> * unbuilt_box -> * print_box)
build_print_box = - : (int -> int -> * -> * unbuilt_box -> * print_box)
Calling Lisp compiler
File PP_printer/boxes compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'loadf `PP_printer/ptree`;;'\
'loadf `PP_printer/treematch`;;'\
'loadf `PP_printer/boxes`;;'\
'compilet `PP_printer/treetobox`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
...() : void
.............................() : void
...................() : void
type print_special defined
type print_int_exp defined
New constructors declared:
H_box : ((nat # print_object) list -> print_box_spec)
V_box : (((print_indent # nat) # print_object) list -> print_box_spec)
HV_box : (((nat # print_indent # nat) # print_object) list ->
print_box_spec)
HoV_box : (((nat # print_indent # nat) # print_object) list ->
print_box_spec)
PF_empty : print_format
PF : (print_box_spec -> print_format)
PF_branch : ((print_test # print_format # print_format) -> print_format)
PO_constant : (string -> print_object)
PO_leaf : ((string # (string -> string)) -> print_object)
PO_subcall : (((string #
((print_tree # address) list ->
(print_tree # address) list)) #
(string # print_int_exp) list) ->
print_object)
PO_context_subcall : ((string #
(string #
((print_tree # address) list ->
(print_tree # address) list)) #
(string # print_int_exp) list) ->
print_object)
PO_format : (print_format -> print_object)
PO_expand : (print_box_spec -> print_object)
PF_H = - : ((nat # print_object) list -> print_format)
PF_V = - : (((print_indent # nat) # print_object) list -> print_format)
PF_HV =
-
: (((nat # print_indent # nat) # print_object) list -> print_format)
PF_HoV =
-
: (((nat # print_indent # nat) # print_object) list -> print_format)
type print_rule defined
type print_rule_function defined
print_special_fun =
-
: (string ->
(string # int) list ->
print_binding ->
print_special list ->
print_binding)
print_rule_fun = - : (print_rule list -> print_rule_function)
() : void
then_try =
-
: (print_rule_function -> print_rule_function -> print_rule_function)
raw_tree_rules =
[((``,
(Var_name(`n`, [Var_children `cl`; Patt_child(Var_child `c`)])),
-),
[],
PF(HV_box[((0, (Abs 0), 0), PO_leaf(`n`, -));
((0, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HoV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`cl`,
-),
[]));
(0,
PO_constant `,`)]));
((0, (Abs 0), 0),
PO_subcall((`c`,
-),
[]))])));
(0, PO_constant `)`)])))]));
((``, (Var_name(`n`, [])), -), [], PF(H_box[(0, PO_leaf(`n`, -))]))]
: print_rule list
raw_tree_rules_fun = - : print_rule_function
expand_binding =
-
: ((* # metavar_binding) list -> (* # metavar_binding) list list)
extract_expanded_from_spec = - : (print_box_spec -> string list)
extract_expanded_from_object = - : (print_object -> string list)
print_tree_to_box =
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
address print_box)
print_box_spec_fun =
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_binding ->
print_binding ->
bool ->
print_box_spec ->
address print_box)
print_format_fun =
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_binding ->
print_format ->
address print_box)
print_object_fun =
-
: (print_rule_function ->
string ->
(string # int) list ->
print_binding ->
print_binding ->
bool ->
print_object ->
(int -> int -> address print_box) list)
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
address print_box)
print_tree_to_box =
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
address print_box)
Calling Lisp compiler
File PP_printer/treetobox compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'loadf `PP_printer/ptree`;;'\
'loadf `PP_printer/treematch`;;'\
'loadf `PP_printer/boxes`;;'\
'loadf `PP_printer/treetobox`;;'\
'compilet `PP_printer/boxtostring`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
...() : void
.............................() : void
...................() : void
.................() : void
join_strings = - : ((string # int) -> (string # int) -> (string # int))
merge_string_lists =
-
: ((string # int # int) list ->
(string # int # int) list ->
(string # int # int) list)
stringify_print_box =
-
: (int -> int -> * print_box -> (string # int # int) list)
fill_in_strings =
-
: (bool -> int -> int -> (string # int # int) list -> string list)
print_box_to_strings = - : (bool -> int -> * print_box -> string list)
- : (bool -> int -> * print_box -> string list)
print_box_to_strings = - : (bool -> int -> * print_box -> string list)
Calling Lisp compiler
File PP_printer/boxtostring compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'loadf `PP_printer/ptree`;;'\
'loadf `PP_printer/treematch`;;'\
'loadf `PP_printer/boxes`;;'\
'loadf `PP_printer/treetobox`;;'\
'loadf `PP_printer/boxtostring`;;'\
'compilet `PP_printer/print`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
...() : void
.............................() : void
...................() : void
.................() : void
.......() : void
display_strings = - : (string list -> void)
output_strings = - : (string -> string list -> void)
insert_strings = - : (string list -> void)
pretty_print =
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void)
pp_write =
-
: (string ->
int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void)
pp =
-
: (print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void)
((-), (-), -)
: ((int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void) #
(string ->
int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void) #
(print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void))
pretty_print =
-
: (int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void)
pp_write =
-
: (string ->
int ->
int ->
print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void)
pp =
-
: (print_rule_function ->
string ->
(string # int) list ->
print_tree ->
void)
Calling Lisp compiler
File PP_printer/print compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/extents`;;'\
'loadf `PP_printer/strings`;;'\
'loadf `PP_printer/ptree`;;'\
'loadf `PP_printer/treematch`;;'\
'loadf `PP_printer/boxes`;;'\
'loadf `PP_printer/treetobox`;;'\
'loadf `PP_printer/boxtostring`;;'\
'loadf `PP_printer/print`;;'\
'compilet `PP_printer/utils`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
......() : void
.........() : void
...() : void
.............................() : void
...................() : void
.................() : void
.......() : void
........() : void
() : void
is_a_member_of = - : (string -> string list -> print_test)
bound_number = - : (string -> print_int_exp)
bound_name =
-
: (string -> (string # int) list -> print_binding -> string)
bound_names =
-
: (string -> (string # int) list -> print_binding -> string list)
bound_child =
-
: (string -> (string # int) list -> print_binding -> print_tree)
bound_children =
-
: (string -> (string # int) list -> print_binding -> print_tree list)
bound_context = - : ((string # int) list -> print_binding -> string)
apply0 = - : (* -> (string # int) list -> print_binding -> *)
apply1 =
-
: ((* -> **) ->
((string # int) list -> print_binding -> *) ->
(string # int) list ->
print_binding ->
**)
apply2 =
-
: ((* -> ** -> ***) ->
((string # int) list -> print_binding -> *) ->
((string # int) list -> print_binding -> **) ->
(string # int) list ->
print_binding ->
***)
new_name =
-
: ((string -> string) ->
string ->
(string # int) list ->
print_binding ->
metavar_binding)
new_names =
-
: (((string # address) list -> (string # address) list) ->
string ->
(string # int) list ->
print_binding ->
metavar_binding)
new_child =
-
: ((print_tree -> print_tree) ->
string ->
(string # int) list ->
print_binding ->
metavar_binding)
new_children =
-
: (((print_tree # address) list -> (print_tree # address) list) ->
string ->
(string # int) list ->
print_binding ->
metavar_binding)
Calling Lisp compiler
File PP_printer/utils compiled
() : void
#(cd PP_parser; cp pp_lang1.build pp_lang1_pp.ml)
(cd PP_parser; cp pp_lang2.build pp_lang2_pp.ml)
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'compilet `PP_parser/pp_lang1_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#
pp_lang1_rules = [] : print_rule list
pp_lang1_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_parser/pp_lang1_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'compilet `PP_parser/pp_lang2_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
pp_lang2_rules = [] : print_rule list
pp_lang2_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_parser/pp_lang2_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'compilet `PP_parser/lex`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
copy_chars =
-
: (int -> (string -> string) -> string -> (string -> void) -> void)
New constructors declared:
Lex_spec : (string -> lex_symb)
Lex_num : (string -> lex_symb)
Lex_id : (string -> lex_symb)
Lex_block : (((string # string) # string list) -> lex_symb)
is_lex_char = - : ((string # string # string) -> bool)
is_lex_ucase = - : (string -> bool)
is_lex_lcase = - : (string -> bool)
is_lex_letter = - : (string -> bool)
is_lex_digit = - : (string -> bool)
is_lex_underscore = - : (string -> bool)
is_lex_eof = - : (string -> bool)
is_lex_eol = - : (string -> bool)
is_lex_space = - : (string -> bool)
lex_error = - : ((string -> string) -> string -> string -> string -> *)
read_char = - : ((* -> string) -> * -> string)
read_number = - : ((* -> string) -> * -> string -> (lex_symb # string))
read_identifier =
-
: ((string -> string) -> string -> string -> (lex_symb # string))
read_block =
-
: ((string -> string) ->
string ->
(string # string) ->
string ->
(lex_symb # string))
read_special =
-
: ((string -> string) ->
string ->
string list ->
string ->
(lex_symb # string))
read_symb =
-
: ((string -> string) ->
string ->
(string # string) list ->
string list ->
string list ->
string ->
(lex_symb # string))
-
: ((string -> string) ->
string ->
(string # string) list ->
string list ->
string list ->
string ->
(lex_symb # string))
read_symb =
-
: ((string -> string) ->
string ->
(string # string) list ->
string list ->
string list ->
string ->
(lex_symb # string))
Calling Lisp compiler
File PP_parser/lex compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'compilet `PP_parser/syntax`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
PP_quotes =
[(`'`, `'`); (`"`, `"`); (`{`, `}`); (`#`, `#`); (`%`, `%`)]
: (string # string) list
PP_keywords =
[`prettyprinter`;
`rules`;
`declarations`;
`abbreviations`;
`with`;
`end`;
`where`;
`if`;
`then`;
`else`;
`h`;
`v`;
`hv`;
`hov`]
: string list
PP_specials =
[`+`;
`-`;
`*`;
`**`;
`***`;
`,`;
`;`;
`:`;
`::`;
`=`;
`:=`;
`->`;
`..`;
`(`;
`)`;
`**[`;
`[`;
`]`;
`<`;
`>`;
`<<`;
`>>`;
`|`]
: string list
syntax_error =
-
: ((string -> string) -> string -> string -> string -> lex_symb -> *)
general_error =
-
: ((string -> string) -> string -> string -> string -> string -> *)
read_PP_symb =
-
: ((string -> string) -> string -> string -> (lex_symb # string))
read_PP_number =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_integer =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_string =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_terminal =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_ML_function =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_identifier =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_name_metavar =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_child_metavar =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_children_metavar =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_metavar_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_min =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_max =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_loop_range =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_loop_link =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_label =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_node_name =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_child =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_child_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_pattern_tree =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_loop =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_test =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_pattern =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_transformation =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_p_special =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_p_special_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_int_expression =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_assignment =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_assignments =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_fun_subcall =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_context_subcall =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_leaf_or_subcall =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_indent =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_box_spec =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_expand =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_format =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_rule =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_rule_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_rules =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_binding =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_binding_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_declarations =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_abbreviations =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_body =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP = - : ((string -> string) -> string -> print_tree)
- : ((string -> string) -> string -> print_tree)
read_PP = - : ((string -> string) -> string -> print_tree)
Calling Lisp compiler
File PP_parser/syntax compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'compilet `PP_parser/convert`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
construction_error = - : (print_tree -> string -> *)
indirect_string = - : (string -> string)
convert_NUM = - : ((print_tree # *) -> (print_tree # ** list))
convert_NEG = - : ((print_tree # *) -> (print_tree # ** list))
convert_ML_FUN = - : ((print_tree # *) -> (print_tree # ** list))
convert_ID_to_VAR = - : ((print_tree # *) -> (print_tree # ** list))
convert_ID_to_TOKCONST =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_METAVAR = - : ((print_tree # *) -> (print_tree # ** list))
convert_METAVAR_to_TOKCONST =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_METAVAR_LIST = - : ((print_tree # *) -> (print_tree # ** list))
convert_MIN = - : ((print_tree # *) -> (print_tree # ** list))
convert_MAX = - : ((print_tree # *) -> (print_tree # ** list))
convert_LOOP_RANGE = - : ((print_tree # *) -> (print_tree # ** list))
convert_LOOP_LINK = - : ((print_tree # *) -> (print_tree # ** list))
convert_LABEL = - : ((print_tree # *) -> (print_tree # ** list))
convert_NODE_NAME =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_CHILD =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_CHILD_LIST =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_PATT_TREE =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_LOOP =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_STRING = - : ((print_tree # *) -> (print_tree # ** list))
convert_TEST =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_PATTERN =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_TRANSFORM =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_P_SPECIAL =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_P_SPECIAL_LIST =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_INT_EXP =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_ASSIGN =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_ASSIGNMENTS =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_F_SUBCALL =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_C_SUBCALL =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_LEAF_OR_SUBCALL =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_TERMINAL = - : ((print_tree # *) -> (print_tree # ** list))
convert_INC = - : ((print_tree # *) -> (print_tree # ** list))
convert_H_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_V_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_HV_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_HOV_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_BOX = - : ((print_tree # *) -> (print_tree # ** list))
convert_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_H_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_V_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HV_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HOV_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_H_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_V_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HV_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HOV_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_BOX_SPEC =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_EXPAND =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_FORMAT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_RULE =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_RULE_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_RULES =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_BINDING = - : ((print_tree # *) -> (print_tree # ** list))
convert_BINDING_LIST_to_LIST =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_BINDING_LIST_to_LETREC =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_DECLARS = - : ((print_tree # *) -> (print_tree # ** list))
convert_ABBREVS =
-
: ((print_tree # *) -> (print_tree # (string # print_tree) list))
convert_BODY =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_PP =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_PP =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
Calling Lisp compiler
File PP_parser/convert compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'loadf `PP_parser/convert`;;'\
'compilet `PP_parser/generate`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
.................................................() : void
PP_to_ML_rules =
[((`name`, (Var_name(`n`, [])), -), [], PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`INTCONST`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`TOKCONST`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_constant ```);
(0, PO_leaf(`n`, -));
(0, PO_constant ```)]));
((``, (Const_name(`VAR`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`CON`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`CON0`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``,
(Const_name(`UNOP`,
[Patt_child(Var_name(`n`, []));
Patt_child(Var_child `c`)])),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0), PO_leaf(`n`, -));
((0, (Abs 0), 0),
PO_subcall((`c`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`APPN`,
[Patt_child(Var_child `c1`); Patt_child(Var_child `c2`)])),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((1, (Abs 1), 0),
PO_subcall((`c1`, -), []));
((1, (Abs 1), 0),
PO_subcall((`c2`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`ABSTR`,
[Patt_child(Var_child `c1`); Patt_child(Var_child `c2`)])),
-),
[],
PF(H_box[(0, PO_constant `(\`);
(0,
PO_format(PF(HV_box[((1, (Abs 1), 0),
PO_format(PF(H_box[(0,
PO_subcall((`c1`,
-),
[]));
(0, PO_constant `.`)])));
((1, (Abs 1), 0),
PO_subcall((`c2`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`LIST`, [Var_children `cl`; Patt_child(Var_child `c`)])),
-),
[],
PF(H_box[(0, PO_constant `[`);
(0,
PO_format(PF(HoV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`cl`, -),
[]));
(0, PO_constant `;`)]));
((0, (Abs 0), 0),
PO_subcall((`c`, -), []))])));
(0, PO_constant `]`)]));
((``, (Const_name(`LIST`, [])), -),
[],
PF(H_box[(0, PO_constant `[]`)]));
((``,
(Print_loop((Const_name(`DUPL`,
[Patt_child(Var_child `cl`);
Patt_child(Link_child(((Val 1), Default),
[]))])),
Var_child `c`)),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`cl`, -),
[]));
(0, PO_constant `,`)]));
((0, (Abs 0), 0),
PO_subcall((`c`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`LETREC`,
[Patt_child(Const_name(`DUPL`,
[Patt_child(Var_child `var1`);
Patt_child(Print_loop((Const_name(`DUPL`,
[Patt_child(Var_child `varl`);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `varl`))]));
Patt_child(Const_name(`DUPL`,
[Patt_child(Var_child `body1`);
Patt_child(Print_loop((Const_name(`DUPL`,
[Patt_child(Var_child `bodyl`);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `bodyl`))]))])),
-),
[],
PF(V_box[(((Abs 0), 0),
PO_format(PF(HV_box[((1, (Inc 1), 0), PO_constant `letrec`);
((1, (Inc 1), 0),
PO_format(PF(H_box[(1,
PO_subcall((`var1`,
-),
[]));
(1, PO_constant `=`)])));
((1, (Inc 1), 0),
PO_subcall((`body1`, -), []))])));
(((Abs 0), 0),
PO_expand(HV_box[((1, (Inc 1), 0), PO_constant `and`);
((1, (Inc 1), 0),
PO_expand(H_box[(1,
PO_subcall((`varl`, -),
[]));
(1, PO_constant `=`)]));
((1, (Inc 1), 0),
PO_subcall((`bodyl`, -), []))]))]));
((``,
(Const_name(`LETREC`,
[Patt_child(Var_child `c1`); Patt_child(Var_child `c2`)])),
-),
[],
PF(HV_box[((1, (Inc 1), 0), PO_constant `letrec`);
((1, (Inc 1), 0),
PO_format(PF(H_box[(1, PO_subcall((`c1`, -), []));
(1, PO_constant `=`)])));
((1, (Inc 1), 0), PO_subcall((`c2`, -), []))]));
((``, (Const_name(`ML_FUN`, [Var_children `cl`])), -),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(V_box[(((Abs 0), 0),
PO_context_subcall(`name`,
(`cl`, -),
[]))])));
(0, PO_constant `)`)]))]
: print_rule list
PP_to_ML_rules_fun = - : print_rule_function
write_strings = - : (((* # string) -> **) -> * -> string list -> void)
generate_rule = - : (print_tree -> string list)
write_rule = - : (((* # string) -> **) -> * -> print_tree -> void)
write_rules = - : (((* # string) -> **) -> * -> print_tree list -> void)
generate_declarations = - : (print_tree -> string list)
write_declarations =
-
: (((* # string) -> **) -> * -> print_tree -> void)
generate_head = - : (string -> string list)
write_head = - : (((* # string) -> **) -> * -> string -> void)
generate_tail = - : (string -> string list)
write_tail = - : (((* # string) -> **) -> * -> string -> void)
generate_ML =
-
: (((string # string) -> void) -> string -> print_tree -> void)
- : (((string # string) -> void) -> string -> print_tree -> void)
generate_ML =
-
: (((string # string) -> void) -> string -> print_tree -> void)
Calling Lisp compiler
File PP_parser/generate compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'loadf `PP_parser/convert`;;'\
'loadf `PP_parser/generate`;;'\
'compilet `PP_parser/PP_to_ML`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
.................................................() : void
...............() : void
PP_to_ML = - : (bool -> string -> string -> void)
Calling Lisp compiler
File PP_parser/PP_to_ML compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'loadf `PP_parser/convert`;;'\
'loadf `PP_parser/generate`;;'\
'loadf `PP_parser/PP_to_ML`;;'\
'PP_to_ML false `PP_parser/pp_lang1` ``;;'\
'PP_to_ML false `PP_parser/pp_lang2` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
.................................................() : void
...............() : void
.() : void
() : void
() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'compilet `PP_parser/pp_lang1_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#
pp_lang1_rules =
[((``, (Const_name(`NUM`, [Patt_child(Var_name(`num`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`num`, -))]));
((``, (Const_name(`NEG`, [Patt_child(Var_child `num`)])), -),
[],
PF(H_box[(0, PO_constant `-`); (0, PO_subcall((`num`, -), []))]));
((``, (Const_name(`STRING`, [Patt_child(Var_name(`string`, []))])), -),
[],
PF(H_box[(0, PO_constant `'`);
(0, PO_leaf(`string`, -));
(0, PO_constant `'`)]));
((``,
(Const_name(`TERMINAL`, [Patt_child(Var_name(`string`, []))])),
-),
[],
PF(H_box[(0, PO_constant `"`);
(0, PO_leaf(`string`, -));
(0, PO_constant `"`)]));
((``, (Const_name(`ML_FUN`, [Var_children `strings`])), -),
[],
PF(H_box[(0, PO_constant `{`);
(0,
PO_format(PF(V_box[(((Abs 0), 0),
PO_subcall((`strings`, -), []))])));
(0, PO_constant `}`)]));
((``, (Const_name(`ID`, [Patt_child(Var_name(`id`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`id`, -))]));
((``, (Const_name(`NAME_META`, [Var_children `id`])), -),
[],
PF(H_box[(0, PO_constant `***`); (0, PO_subcall((`id`, -), []))]));
((``, (Const_name(`CHILD_META`, [Var_children `id`])), -),
[],
PF(H_box[(0, PO_constant `*`); (0, PO_subcall((`id`, -), []))]));
((``, (Const_name(`CHILDREN_META`, [Var_children `id`])), -),
[],
PF(H_box[(0, PO_constant `**`); (0, PO_subcall((`id`, -), []))]));
((``,
(Print_loop((Const_name(`METAVAR_LIST`,
[Patt_child(Var_child `metavars`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`METAVAR_LIST`,
[Patt_child(Var_child `metavar`)]))),
-),
[],
PF(HV_box[((0, (Abs 3), 0),
PO_expand(H_box[(0, PO_subcall((`metavars`, -), []));
(0, PO_constant `;`)]));
((0, (Abs 3), 0), PO_subcall((`metavar`, -), []))]));
((``, (Const_name(`MIN`, [Patt_child(Var_child `num`)])), -),
[],
PF(H_box[(0, PO_subcall((`num`, -), []))]));
((``, (Const_name(`MAX`, [Patt_child(Var_child `num`)])), -),
[],
PF(H_box[(0, PO_subcall((`num`, -), []))]));
((``,
(Const_name(`LOOP_RANGE`,
[Patt_child(Const_name(`MIN`,
[Patt_child(Var_child `num`)]))])),
-),
[],
PF(H_box[(0, PO_subcall((`num`, -), [])); (0, PO_constant `..`)]));
((``,
(Const_name(`LOOP_RANGE`,
[Patt_child(Const_name(`MAX`,
[Patt_child(Var_child `num`)]))])),
-),
[],
PF(H_box[(0, PO_constant `..`); (0, PO_subcall((`num`, -), []))]));
((``,
(Const_name(`LOOP_RANGE`,
[Patt_child(Var_child `min`);
Patt_child(Var_child `max`)])),
-),
[],
PF(H_box[(0, PO_subcall((`min`, -), []));
(0, PO_constant `..`);
(0, PO_subcall((`max`, -), []))]));
((``,
(Const_name(`LOOP_LINK`,
[Patt_child(Var_child `loop_range`);
Patt_child(Var_child `metavar_list`)])),
-),
[],
PF(H_box[(0, PO_constant `<`);
(0, PO_subcall((`loop_range`, -), []));
(0, PO_constant `:`);
(1, PO_subcall((`metavar_list`, -), []));
(0, PO_constant `>`)]));
((``, (Const_name(`LOOP_LINK`, [Var_children `metavar_list`])), -),
[],
PF(H_box[(0, PO_constant `<`);
(0, PO_subcall((`metavar_list`, -), []));
(0, PO_constant `>`)]));
((``, (Const_name(`LABEL`, [Patt_child(Var_child `child_meta`)])), -),
[],
PF(H_box[(0, PO_constant `|`);
(0, PO_subcall((`child_meta`, -), []));
(0, PO_constant `|`)]));
((``,
(Const_name(`NODE_NAME`, [Patt_child(Var_child `node_name`)])),
-),
[],
PF(H_box[(0, PO_subcall((`node_name`, -), []))]));
((``, (Const_name(`CHILD`, [Patt_child(Var_child `child`)])), -),
[],
PF(H_box[(0, PO_subcall((`child`, -), []))]));
((``,
(Print_loop((Const_name(`CHILD_LIST`,
[Patt_child(Var_child `children`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`CHILD_LIST`, [Patt_child(Var_child `child`)]))),
-),
[],
PF(HV_box[((0, (Abs 3), 0),
PO_expand(H_box[(0, PO_subcall((`children`, -), []));
(0, PO_constant `,`)]));
((0, (Abs 3), 0), PO_subcall((`child`, -), []))]));
((``,
(Const_name(`PATT_TREE`,
[Patt_child(Const_name(`NODE_NAME`,
[Patt_child(Var_child `node_name`)]));
Patt_child(Var_child `child_list`)])),
-),
[],
PF(HV_box[((0, (Abs 3), 0), PO_subcall((`node_name`, -), []));
((0, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_constant `(`);
(0, PO_subcall((`child_list`, -), []));
(0, PO_constant `)`)])))]));
((``,
(Const_name(`PATT_TREE`,
[Patt_child(Const_name(`NODE_NAME`,
[Patt_child(Var_child `node_name`)]))])),
-),
[],
PF(H_box[(0, PO_subcall((`node_name`, -), [])); (0, PO_constant `()`)]));
((``, (Const_name(`PATT_TREE`, [Var_children `x`])), -),
[],
PF(HV_box[((0, (Abs 3), 0), PO_subcall((`x`, -), []))]));
((``, (Const_name(`LOOP`, [Patt_child(Var_child `patt_tree`)])), -),
[],
PF(H_box[(0, PO_constant `[`);
(0, PO_subcall((`patt_tree`, -), []));
(0, PO_constant `]`)]));
((``, (Const_name(`TEST`, [Patt_child(Var_child `test`)])), -),
[],
PF(H_box[(0, PO_subcall((`test`, -), []))]));
((``,
(Const_name(`PATTERN`,
[Patt_child(Var_child `string`);
Patt_child(Var_child `patt_tree`);
Var_children `test`])),
-),
[],
PF(H_box[(0, PO_subcall((`string`, -), []));
(0, PO_constant `::`);
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_subcall((`patt_tree`, -), []));
((1, (Abs 3), 0),
PO_expand(HV_box[((1, (Abs 3), 0),
PO_constant `where`);
((1, (Abs 3), 0),
PO_subcall((`test`,
-),
[]))]))])))]));
((``,
(Const_name(`TRANSFORM`, [Patt_child(Var_child `transform`)])),
-),
[],
PF(H_box[(0, PO_subcall((`transform`, -), []))]));
((``,
(Const_name(`P_SPECIAL`,
[Patt_child(Var_child `metavar`);
Patt_child(Var_child `transform`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1, PO_subcall((`metavar`, -), []));
(1, PO_constant `=`)])));
((1, (Abs 3), 0), PO_subcall((`transform`, -), []))]));
((``,
(Print_loop((Const_name(`P_SPECIAL_LIST`,
[Patt_child(Var_child `p_specials`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`P_SPECIAL_LIST`,
[Patt_child(Var_child `p_special`)]))),
-),
[],
PF(HoV_box[((1, (Abs 0), 0),
PO_expand(H_box[(0, PO_subcall((`p_specials`, -), []));
(0, PO_constant `;`)]));
((1, (Abs 0), 0), PO_subcall((`p_special`, -), []))]))]
: print_rule list
pp_lang1_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_parser/pp_lang1_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'compilet `PP_parser/pp_lang2_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
pp_lang2_rules =
[((``, (Const_name(`INT_EXP`, [Patt_child(Var_child `int_exp`)])), -),
[],
PF(H_box[(0, PO_subcall((`int_exp`, -), []))]));
((``,
(Const_name(`ASSIGN`,
[Patt_child(Var_child `id`); Patt_child(Var_child `exp`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1, PO_subcall((`id`, -), []));
(1, PO_constant `:=`)])));
((1, (Abs 3), 0), PO_subcall((`exp`, -), []))]));
((``,
(Print_loop((Const_name(`ASSIGNMENTS`,
[Patt_child(Var_child `assigns`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`ASSIGNMENTS`,
[Patt_child(Var_child `assign`)]))),
-),
[],
PF(HoV_box[((1, (Abs 0), 0),
PO_expand(H_box[(0, PO_subcall((`assigns`, -), []));
(0, PO_constant `;`)]));
((1, (Abs 0), 0), PO_subcall((`assign`, -), []))]));
((``, (Const_name(`F_SUBCALL`, [Patt_child(Var_child `child`)])), -),
[],
PF(H_box[(0, PO_subcall((`child`, -), []))]));
((``,
(Const_name(`F_SUBCALL`,
[Patt_child(Var_child `transform`);
Patt_child(Var_child `metavar`)])),
-),
[],
PF(HV_box[((0, (Abs 3), 0), PO_subcall((`transform`, -), []));
((0, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_constant `(`);
(0, PO_subcall((`metavar`, -), []));
(0, PO_constant `)`)])))]));
((``,
(Const_name(`C_SUBCALL`, [Patt_child(Var_child `f_subcall`)])),
-),
[],
PF(H_box[(0, PO_subcall((`f_subcall`, -), []))]));
((``,
(Const_name(`C_SUBCALL`,
[Patt_child(Var_child `string`);
Patt_child(Var_child `f_subcall`)])),
-),
[],
PF(HV_box[((0, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_subcall((`string`, -), []));
(0, PO_constant `::`)])));
((0, (Abs 3), 0), PO_subcall((`f_subcall`, -), []))]));
((``,
(Const_name(`LEAF_OR_SUBCALL`,
[Patt_child(Var_child `c_subcall`);
Var_children `assigns`])),
-),
[],
PF(HV_box[((1, (Abs 3), 0), PO_subcall((`c_subcall`, -), []));
((1, (Abs 3), 0),
PO_expand(V_box[(((Abs 0), 0), PO_constant `with`);
(((Abs 3), 0),
PO_subcall((`assigns`, -), []));
(((Abs 0), 0), PO_constant `end with`)]))]));
((``, (Const_name(`INC`, [Patt_child(Var_child `num`)])), -),
[],
PF(H_box[(0, PO_constant `+`); (0, PO_subcall((`num`, -), []))]));
((``, (Const_name(`H_PARAMS`, [Patt_child(Var_child `num`)])), -),
[],
PF(H_box[(0, PO_subcall((`num`, -), []))]));
((``,
(Const_name(`V_PARAMS`,
[Patt_child(Var_child `indent`);
Patt_child(Var_child `num`)])),
-),
[],
PF(H_box[(0, PO_subcall((`indent`, -), []));
(0, PO_constant `,`);
(0, PO_subcall((`num`, -), []))]));
((``,
(Const_name(`HV_PARAMS`,
[Patt_child(Var_child `num1`);
Patt_child(Var_child `indent`);
Patt_child(Var_child `num2`)])),
-),
[],
PF(H_box[(0, PO_subcall((`num1`, -), []));
(0, PO_constant `,`);
(0, PO_subcall((`indent`, -), []));
(0, PO_constant `,`);
(0, PO_subcall((`num2`, -), []))]));
((``,
(Const_name(`HOV_PARAMS`,
[Patt_child(Var_child `num1`);
Patt_child(Var_child `indent`);
Patt_child(Var_child `num2`)])),
-),
[],
PF(H_box[(0, PO_subcall((`num1`, -), []));
(0, PO_constant `,`);
(0, PO_subcall((`indent`, -), []));
(0, PO_constant `,`);
(0, PO_subcall((`num2`, -), []))]));
((``, (Const_name(`H_BOX`, [Patt_child(Var_child `h_params`)])), -),
[],
PF(H_box[(1, PO_constant `h`); (1, PO_subcall((`h_params`, -), []))]));
((``, (Const_name(`V_BOX`, [Patt_child(Var_child `v_params`)])), -),
[],
PF(H_box[(1, PO_constant `v`); (1, PO_subcall((`v_params`, -), []))]));
((``, (Const_name(`HV_BOX`, [Patt_child(Var_child `hv_params`)])), -),
[],
PF(H_box[(1, PO_constant `hv`); (1, PO_subcall((`hv_params`, -), []))]));
((``, (Const_name(`HOV_BOX`, [Patt_child(Var_child `hov_params`)])), -),
[],
PF(H_box[(1, PO_constant `hov`);
(1, PO_subcall((`hov_params`, -), []))]));
((``, (Const_name(`OBJECT`, [Patt_child(Var_child `object`)])), -),
[],
PF(H_box[(0, PO_subcall((`object`, -), []))]));
((``,
(Const_name(`H_OBJECT`,
[Var_children `h_params`; Patt_child(Var_child `object`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_expand(H_box[(0, PO_constant `<`);
(0, PO_subcall((`h_params`, -), []));
(0, PO_constant `>`)]));
((1, (Abs 3), 0), PO_subcall((`object`, -), []))]));
((``,
(Const_name(`V_OBJECT`,
[Var_children `v_params`; Patt_child(Var_child `object`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_expand(H_box[(0, PO_constant `<`);
(0, PO_subcall((`v_params`, -), []));
(0, PO_constant `>`)]));
((1, (Abs 3), 0), PO_subcall((`object`, -), []))]));
((``,
(Const_name(`HV_OBJECT`,
[Var_children `hv_params`;
Patt_child(Var_child `object`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_expand(H_box[(0, PO_constant `<`);
(0, PO_subcall((`hv_params`, -), []));
(0, PO_constant `>`)]));
((1, (Abs 3), 0), PO_subcall((`object`, -), []))]));
((``,
(Const_name(`HOV_OBJECT`,
[Var_children `hov_params`;
Patt_child(Var_child `object`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_expand(H_box[(0, PO_constant `<`);
(0, PO_subcall((`hov_params`, -), []));
(0, PO_constant `>`)]));
((1, (Abs 3), 0), PO_subcall((`object`, -), []))]));
((``,
(Print_loop((Const_name(`H_OBJECT_LIST`,
[Patt_child(Var_child `h_objects`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`H_OBJECT_LIST`,
[Patt_child(Var_child `h_object`)]))),
-),
[],
PF(HoV_box[((1, (Abs 0), 0), PO_subcall((`h_objects`, -), []));
((1, (Abs 0), 0), PO_subcall((`h_object`, -), []))]));
((``,
(Print_loop((Const_name(`V_OBJECT_LIST`,
[Patt_child(Var_child `v_objects`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`V_OBJECT_LIST`,
[Patt_child(Var_child `v_object`)]))),
-),
[],
PF(HoV_box[((1, (Abs 0), 0), PO_subcall((`v_objects`, -), []));
((1, (Abs 0), 0), PO_subcall((`v_object`, -), []))]));
((``,
(Print_loop((Const_name(`HV_OBJECT_LIST`,
[Patt_child(Var_child `hv_objects`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`HV_OBJECT_LIST`,
[Patt_child(Var_child `hv_object`)]))),
-),
[],
PF(HoV_box[((1, (Abs 0), 0), PO_subcall((`hv_objects`, -), []));
((1, (Abs 0), 0), PO_subcall((`hv_object`, -), []))]));
((``,
(Print_loop((Const_name(`HOV_OBJECT_LIST`,
[Patt_child(Var_child `hov_objects`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`HOV_OBJECT_LIST`,
[Patt_child(Var_child `hov_object`)]))),
-),
[],
PF(HoV_box[((1, (Abs 0), 0), PO_subcall((`hov_objects`, -), []));
((1, (Abs 0), 0), PO_subcall((`hov_object`, -), []))]));
((``,
(Const_name(`BOX_SPEC`,
[Patt_child(Var_child `box`);
Patt_child(Var_child `object_list`)])),
-),
[],
PF(H_box[(0, PO_constant `<`);
(0, PO_subcall((`box`, -), []));
(0, PO_constant `>`);
(1, PO_subcall((`object_list`, -), []))]));
((``, (Const_name(`EXPAND`, [Patt_child(Var_child `box_spec`)])), -),
[],
PF(H_box[(0, PO_constant `**[`);
(0, PO_subcall((`box_spec`, -), []));
(0, PO_constant `]`)]));
((``, (Const_name(`FORMAT`, [])), -),
[],
PF(H_box[(0, PO_constant `[]`)]));
((``, (Const_name(`FORMAT`, [Patt_child(Var_child `box_spec`)])), -),
[],
PF(H_box[(0, PO_constant `[`);
(0, PO_subcall((`box_spec`, -), []));
(0, PO_constant `]`)]));
((``,
(Const_name(`FORMAT`,
[Patt_child(Var_child `test`);
Patt_child(Var_child `format1`);
Patt_child(Var_child `format2`)])),
-),
[],
PF(HoV_box[((1, (Abs 0), 0),
PO_format(PF(H_box[(1, PO_constant `if`);
(1, PO_subcall((`test`, -), []))])));
((1, (Abs 0), 0),
PO_format(PF(H_box[(1, PO_constant `then`);
(1, PO_subcall((`format1`, -), []))])));
((1, (Abs 0), 0),
PO_format(PF(H_box[(1, PO_constant `else`);
(1, PO_subcall((`format2`, -), []))])))]));
((``,
(Const_name(`RULE`,
[Patt_child(Const_name(`PATTERN`,
[Patt_child(Var_child `string`);
Patt_child(Var_child `patt_tree`);
Var_children `test`]));
Var_children `p_specials`;
Patt_child(Var_child `format`)])),
-),
[],
PF(H_box[(0, PO_subcall((`string`, -), []));
(0, PO_constant `::`);
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_format(PF(H_box[(1,
PO_format(PF(HV_box[((1,
(Abs 3),
0),
PO_subcall((`patt_tree`,
-),
[]));
((1,
(Abs 3),
0),
PO_expand(HV_box[((1,
(Abs 3),
0),
PO_constant `where`);
((1,
(Abs 3),
0),
PO_subcall((`test`,
-),
[]))]))])));
(1,
PO_constant `->`)])));
((1, (Abs 0), 0),
PO_expand(H_box[(1, PO_constant `<<`);
(1,
PO_subcall((`p_specials`,
-),
[]));
(1, PO_constant `>>`)]));
((1, (Abs 0), 0),
PO_subcall((`format`, -), []))])))]));
((``,
(Print_loop((Const_name(`RULE_LIST`,
[Patt_child(Var_child `rules`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`RULE_LIST`, [Patt_child(Var_child `rule`)]))),
-),
[],
PF(V_box[(((Abs 0), 1),
PO_expand(H_box[(0, PO_subcall((`rules`, -), []));
(0, PO_constant `;`)]));
(((Abs 0), 1),
PO_format(PF(H_box[(0, PO_subcall((`rule`, -), []));
(0, PO_constant `;`)])))]));
((``, (Const_name(`RULES`, [Patt_child(Var_child `rule_list`)])), -),
[],
PF(V_box[(((Abs 3), 0), PO_constant `rules`);
(((Abs 3), 0), PO_subcall((`rule_list`, -), []));
(((Abs 0), 1), PO_constant `end rules`)]));
((``,
(Const_name(`BINDING`,
[Patt_child(Var_child `id`);
Patt_child(Var_child `ml_fun`)])),
-),
[],
PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1, PO_subcall((`id`, -), []));
(1, PO_constant `=`)])));
((1, (Abs 3), 0), PO_subcall((`ml_fun`, -), []))]));
((``,
(Print_loop((Const_name(`BINDING_LIST`,
[Patt_child(Var_child `bindings`);
Patt_child(Link_child(((Default), Default),
[]))])),
Const_name(`BINDING_LIST`,
[Patt_child(Var_child `binding`)]))),
-),
[],
PF(V_box[(((Abs 0), 1),
PO_expand(H_box[(0, PO_subcall((`bindings`, -), []));
(0, PO_constant `;`)]));
(((Abs 0), 1),
PO_format(PF(H_box[(0, PO_subcall((`binding`, -), []));
(0, PO_constant `;`)])))]));
((``,
(Const_name(`DECLARS`, [Patt_child(Var_child `binding_list`)])),
-),
[],
PF(V_box[(((Abs 3), 0), PO_constant `declarations`);
(((Abs 3), 0), PO_subcall((`binding_list`, -), []));
(((Abs 0), 1), PO_constant `end declarations`)]));
((``,
(Const_name(`ABBREVS`, [Patt_child(Var_child `binding_list`)])),
-),
[],
PF(V_box[(((Abs 3), 0), PO_constant `abbreviations`);
(((Abs 3), 0), PO_subcall((`binding_list`, -), []));
(((Abs 0), 1), PO_constant `end abbreviations`)]));
((``, (Const_name(`BODY`, [Var_children `x`])), -),
[],
PF(V_box[(((Abs 0), 2), PO_subcall((`x`, -), []))]));
((``,
(Const_name(`PP`,
[Patt_child(Var_child `id`);
Patt_child(Var_child `body`)])),
-),
[],
PF(V_box[(((Abs 0), 1),
PO_format(PF(H_box[(1, PO_constant `prettyprinter`);
(1, PO_subcall((`id`, -), []));
(1, PO_constant `=`)])));
(((Abs 0), 1), PO_subcall((`body`, -), []));
(((Abs 0), 2), PO_constant `end prettyprinter`)]))]
: print_rule list
pp_lang2_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_parser/pp_lang2_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'compilet `PP_parser/lex`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
copy_chars =
-
: (int -> (string -> string) -> string -> (string -> void) -> void)
New constructors declared:
Lex_spec : (string -> lex_symb)
Lex_num : (string -> lex_symb)
Lex_id : (string -> lex_symb)
Lex_block : (((string # string) # string list) -> lex_symb)
is_lex_char = - : ((string # string # string) -> bool)
is_lex_ucase = - : (string -> bool)
is_lex_lcase = - : (string -> bool)
is_lex_letter = - : (string -> bool)
is_lex_digit = - : (string -> bool)
is_lex_underscore = - : (string -> bool)
is_lex_eof = - : (string -> bool)
is_lex_eol = - : (string -> bool)
is_lex_space = - : (string -> bool)
lex_error = - : ((string -> string) -> string -> string -> string -> *)
read_char = - : ((* -> string) -> * -> string)
read_number = - : ((* -> string) -> * -> string -> (lex_symb # string))
read_identifier =
-
: ((string -> string) -> string -> string -> (lex_symb # string))
read_block =
-
: ((string -> string) ->
string ->
(string # string) ->
string ->
(lex_symb # string))
read_special =
-
: ((string -> string) ->
string ->
string list ->
string ->
(lex_symb # string))
read_symb =
-
: ((string -> string) ->
string ->
(string # string) list ->
string list ->
string list ->
string ->
(lex_symb # string))
-
: ((string -> string) ->
string ->
(string # string) list ->
string list ->
string list ->
string ->
(lex_symb # string))
read_symb =
-
: ((string -> string) ->
string ->
(string # string) list ->
string list ->
string list ->
string ->
(lex_symb # string))
Calling Lisp compiler
File PP_parser/lex compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'compilet `PP_parser/syntax`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
PP_quotes =
[(`'`, `'`); (`"`, `"`); (`{`, `}`); (`#`, `#`); (`%`, `%`)]
: (string # string) list
PP_keywords =
[`prettyprinter`;
`rules`;
`declarations`;
`abbreviations`;
`with`;
`end`;
`where`;
`if`;
`then`;
`else`;
`h`;
`v`;
`hv`;
`hov`]
: string list
PP_specials =
[`+`;
`-`;
`*`;
`**`;
`***`;
`,`;
`;`;
`:`;
`::`;
`=`;
`:=`;
`->`;
`..`;
`(`;
`)`;
`**[`;
`[`;
`]`;
`<`;
`>`;
`<<`;
`>>`;
`|`]
: string list
syntax_error =
-
: ((string -> string) -> string -> string -> string -> lex_symb -> *)
general_error =
-
: ((string -> string) -> string -> string -> string -> string -> *)
read_PP_symb =
-
: ((string -> string) -> string -> string -> (lex_symb # string))
read_PP_number =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_integer =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_string =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_terminal =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_ML_function =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_identifier =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_name_metavar =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_child_metavar =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_children_metavar =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_metavar_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_min =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_max =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_loop_range =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_loop_link =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_label =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_node_name =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_child =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_child_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_pattern_tree =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_loop =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_test =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_pattern =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_transformation =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_p_special =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_p_special_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_int_expression =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_assignment =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_assignments =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_fun_subcall =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_context_subcall =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_leaf_or_subcall =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_indent =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_params =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_box =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_object =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_h_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_v_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hv_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_hov_object_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_box_spec =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_expand =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_format =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_rule =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_rule_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_rules =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_binding =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_binding_list =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_declarations =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_abbreviations =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP_body =
-
: ((string -> string) ->
string ->
(lex_symb # string) ->
(print_tree # lex_symb # string))
read_PP = - : ((string -> string) -> string -> print_tree)
- : ((string -> string) -> string -> print_tree)
read_PP = - : ((string -> string) -> string -> print_tree)
Calling Lisp compiler
File PP_parser/syntax compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'compilet `PP_parser/convert`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
construction_error = - : (print_tree -> string -> *)
indirect_string = - : (string -> string)
convert_NUM = - : ((print_tree # *) -> (print_tree # ** list))
convert_NEG = - : ((print_tree # *) -> (print_tree # ** list))
convert_ML_FUN = - : ((print_tree # *) -> (print_tree # ** list))
convert_ID_to_VAR = - : ((print_tree # *) -> (print_tree # ** list))
convert_ID_to_TOKCONST =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_METAVAR = - : ((print_tree # *) -> (print_tree # ** list))
convert_METAVAR_to_TOKCONST =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_METAVAR_LIST = - : ((print_tree # *) -> (print_tree # ** list))
convert_MIN = - : ((print_tree # *) -> (print_tree # ** list))
convert_MAX = - : ((print_tree # *) -> (print_tree # ** list))
convert_LOOP_RANGE = - : ((print_tree # *) -> (print_tree # ** list))
convert_LOOP_LINK = - : ((print_tree # *) -> (print_tree # ** list))
convert_LABEL = - : ((print_tree # *) -> (print_tree # ** list))
convert_NODE_NAME =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_CHILD =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_CHILD_LIST =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_PATT_TREE =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_LOOP =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_STRING = - : ((print_tree # *) -> (print_tree # ** list))
convert_TEST =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_PATTERN =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_TRANSFORM =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_P_SPECIAL =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_P_SPECIAL_LIST =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_INT_EXP =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_ASSIGN =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_ASSIGNMENTS =
-
: ((print_tree # (string # print_tree) list) -> (print_tree # * list))
convert_F_SUBCALL =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_C_SUBCALL =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_LEAF_OR_SUBCALL =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_TERMINAL = - : ((print_tree # *) -> (print_tree # ** list))
convert_INC = - : ((print_tree # *) -> (print_tree # ** list))
convert_H_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_V_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_HV_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_HOV_PARAMS = - : ((print_tree # *) -> (print_tree # ** list))
convert_BOX = - : ((print_tree # *) -> (print_tree # ** list))
convert_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_H_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_V_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HV_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HOV_OBJECT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_H_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_V_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HV_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_HOV_OBJECT_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_BOX_SPEC =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_EXPAND =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_FORMAT =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_RULE =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_RULE_LIST =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_RULES =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_BINDING = - : ((print_tree # *) -> (print_tree # ** list))
convert_BINDING_LIST_to_LIST =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_BINDING_LIST_to_LETREC =
-
: ((print_tree # *) -> (print_tree # ** list))
convert_DECLARS = - : ((print_tree # *) -> (print_tree # ** list))
convert_ABBREVS =
-
: ((print_tree # *) -> (print_tree # (string # print_tree) list))
convert_BODY =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_PP =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
convert_PP =
-
: ((print_tree # (string # print_tree) list) ->
(print_tree # (string # print_tree) list))
Calling Lisp compiler
File PP_parser/convert compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'loadf `PP_parser/convert`;;'\
'compilet `PP_parser/generate`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
.................................................() : void
PP_to_ML_rules =
[((`name`, (Var_name(`n`, [])), -), [], PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`INTCONST`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`TOKCONST`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_constant ```);
(0, PO_leaf(`n`, -));
(0, PO_constant ```)]));
((``, (Const_name(`VAR`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`CON`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``, (Const_name(`CON0`, [Patt_child(Var_name(`n`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`n`, -))]));
((``,
(Const_name(`UNOP`,
[Patt_child(Var_name(`n`, []));
Patt_child(Var_child `c`)])),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0), PO_leaf(`n`, -));
((0, (Abs 0), 0),
PO_subcall((`c`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`APPN`,
[Patt_child(Var_child `c1`); Patt_child(Var_child `c2`)])),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((1, (Abs 1), 0),
PO_subcall((`c1`, -), []));
((1, (Abs 1), 0),
PO_subcall((`c2`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`ABSTR`,
[Patt_child(Var_child `c1`); Patt_child(Var_child `c2`)])),
-),
[],
PF(H_box[(0, PO_constant `(\`);
(0,
PO_format(PF(HV_box[((1, (Abs 1), 0),
PO_format(PF(H_box[(0,
PO_subcall((`c1`,
-),
[]));
(0, PO_constant `.`)])));
((1, (Abs 1), 0),
PO_subcall((`c2`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`LIST`, [Var_children `cl`; Patt_child(Var_child `c`)])),
-),
[],
PF(H_box[(0, PO_constant `[`);
(0,
PO_format(PF(HoV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`cl`, -),
[]));
(0, PO_constant `;`)]));
((0, (Abs 0), 0),
PO_subcall((`c`, -), []))])));
(0, PO_constant `]`)]));
((``, (Const_name(`LIST`, [])), -),
[],
PF(H_box[(0, PO_constant `[]`)]));
((``,
(Print_loop((Const_name(`DUPL`,
[Patt_child(Var_child `cl`);
Patt_child(Link_child(((Val 1), Default),
[]))])),
Var_child `c`)),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`cl`, -),
[]));
(0, PO_constant `,`)]));
((0, (Abs 0), 0),
PO_subcall((`c`, -), []))])));
(0, PO_constant `)`)]));
((``,
(Const_name(`LETREC`,
[Patt_child(Const_name(`DUPL`,
[Patt_child(Var_child `var1`);
Patt_child(Print_loop((Const_name(`DUPL`,
[Patt_child(Var_child `varl`);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `varl`))]));
Patt_child(Const_name(`DUPL`,
[Patt_child(Var_child `body1`);
Patt_child(Print_loop((Const_name(`DUPL`,
[Patt_child(Var_child `bodyl`);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `bodyl`))]))])),
-),
[],
PF(V_box[(((Abs 0), 0),
PO_format(PF(HV_box[((1, (Inc 1), 0), PO_constant `letrec`);
((1, (Inc 1), 0),
PO_format(PF(H_box[(1,
PO_subcall((`var1`,
-),
[]));
(1, PO_constant `=`)])));
((1, (Inc 1), 0),
PO_subcall((`body1`, -), []))])));
(((Abs 0), 0),
PO_expand(HV_box[((1, (Inc 1), 0), PO_constant `and`);
((1, (Inc 1), 0),
PO_expand(H_box[(1,
PO_subcall((`varl`, -),
[]));
(1, PO_constant `=`)]));
((1, (Inc 1), 0),
PO_subcall((`bodyl`, -), []))]))]));
((``,
(Const_name(`LETREC`,
[Patt_child(Var_child `c1`); Patt_child(Var_child `c2`)])),
-),
[],
PF(HV_box[((1, (Inc 1), 0), PO_constant `letrec`);
((1, (Inc 1), 0),
PO_format(PF(H_box[(1, PO_subcall((`c1`, -), []));
(1, PO_constant `=`)])));
((1, (Inc 1), 0), PO_subcall((`c2`, -), []))]));
((``, (Const_name(`ML_FUN`, [Var_children `cl`])), -),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(V_box[(((Abs 0), 0),
PO_context_subcall(`name`,
(`cl`, -),
[]))])));
(0, PO_constant `)`)]))]
: print_rule list
PP_to_ML_rules_fun = - : print_rule_function
write_strings = - : (((* # string) -> **) -> * -> string list -> void)
generate_rule = - : (print_tree -> string list)
write_rule = - : (((* # string) -> **) -> * -> print_tree -> void)
write_rules = - : (((* # string) -> **) -> * -> print_tree list -> void)
generate_declarations = - : (print_tree -> string list)
write_declarations =
-
: (((* # string) -> **) -> * -> print_tree -> void)
generate_head = - : (string -> string list)
write_head = - : (((* # string) -> **) -> * -> string -> void)
generate_tail = - : (string -> string list)
write_tail = - : (((* # string) -> **) -> * -> string -> void)
generate_ML =
-
: (((string # string) -> void) -> string -> print_tree -> void)
- : (((string # string) -> void) -> string -> print_tree -> void)
generate_ML =
-
: (((string # string) -> void) -> string -> print_tree -> void)
Calling Lisp compiler
File PP_parser/generate compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/pp_lang1_pp`;;'\
'loadf `PP_parser/pp_lang2_pp`;;'\
'loadf `PP_parser/lex`;;'\
'loadf `PP_parser/syntax`;;'\
'loadf `PP_parser/convert`;;'\
'loadf `PP_parser/generate`;;'\
'compilet `PP_parser/PP_to_ML`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#..() : void
..() : void
....................() : void
.......................................................() : void
.................................................() : void
...............() : void
PP_to_ML = - : (bool -> string -> string -> void)
Calling Lisp compiler
File PP_parser/PP_to_ML compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'compilet `PP_hol/hol_trees`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#
New constructors declared:
No_types : type_selection
Hidden_types : type_selection
Useful_types : type_selection
All_types : type_selection
type_to_print_tree = - : (type -> print_tree)
term_to_print_tree = - : (bool -> type_selection -> term -> print_tree)
thm_to_print_tree =
-
: (bool -> bool -> type_selection -> thm -> print_tree)
Calling Lisp compiler
File PP_hol/hol_trees compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'loadf `PP_hol/hol_trees`;;'\
'compilet `PP_hol/precedence`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#....() : void
type_prec = - : (string -> int)
min_type_prec = 0 : int
max_type_prec = 400 : int
term_prec = - : (string -> int)
min_term_prec = 0 : int
max_term_prec = 1700 : int
Calling Lisp compiler
File PP_hol/precedence compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'PP_to_ML false `PP_hol/hol_type` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'loadf `PP_hol/hol_trees`;;'\
'loadf `PP_hol/precedence`;;'\
'compilet `PP_hol/hol_type_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#....() : void
......() : void
hol_type_rules =
[((`type`, (Const_name(`VAR`, [Patt_child(Var_name(`op`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`op`, -))]));
((`type`, (Const_name(`OP`, [Patt_child(Var_name(`op`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`op`, -))]));
((`type`,
(Const_name(`OP`,
[Patt_child(Var_name(`op`, []));
Patt_child(Var_child `type1`);
Patt_child(Var_child `type2`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1,
PO_subcall((`type1`,
-),
[(`prec`,
-)]));
(1,
PO_leaf(`op`, -))])));
((1, (Abs 3), 0),
PO_subcall((`type2`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`type`,
(Const_name(`OP`,
[Patt_child(Var_name(`op`, []));
Var_children `types`;
Patt_child(Var_child `type`)])),
-),
[],
PF(HV_box[((0, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((0, (Inc 3), 0),
PO_expand(H_box[(0,
PO_subcall((`types`,
-),
[(`prec`,
-)]));
(0,
PO_constant `,`)]));
((0, (Inc 3), 0),
PO_subcall((`type`,
-),
[(`prec`,
-)]))])));
(0, PO_constant `)`)])));
((0, (Abs 3), 0), PO_leaf(`op`, -))]));
((`type`, (Const_name(`type`, [Patt_child(Var_child `type`)])), -),
[],
PF(H_box[(0, PO_constant `":`);
(0, PO_subcall((`type`, -), [(`prec`, -)]));
(0, PO_constant `"`)]));
((`term`, (Var_child `type`), -),
[],
PF(H_box[(0, PO_context_subcall(`type`, (`type`, -), [(`prec`, -)]))]))]
: print_rule list
hol_type_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_hol/hol_type_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'PP_to_ML false `PP_hol/hol_term` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'loadf `PP_hol/hol_trees`;;'\
'loadf `PP_hol/precedence`;;'\
'loadf `PP_hol/hol_type_pp`;;'\
'compilet `PP_hol/hol_term_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#....() : void
......() : void
..() : void
hol_term_rules =
[((`term`,
(Const_name(`CONST`,
[Patt_child(Const_name(`NIL`, [])); Wild_children])),
-),
[],
PF(H_box[(0, PO_constant `[]`)]));
((`term`, (Const_name(`VAR`, [Patt_child(Var_name(`var`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`var`, -))]));
((`term`,
(Const_name(`VAR`,
[Patt_child(Var_name(`var`, []));
Patt_child(Const_name(`type`,
[Patt_child(Var_child `type`)]))])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0), PO_leaf(`var`, -));
((0, (Abs 0), 0),
PO_format(PF(H_box[(0, PO_constant `:`);
(0,
PO_subcall((`type`,
-),
[]))])))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`CONST`, [Patt_child(Var_name(`const`, []))])),
-),
[],
PF(H_box[(0, PO_leaf(`const`, -))]));
((`term`,
(Const_name(`CONST`,
[Patt_child(Var_name(`const`, []));
Patt_child(Const_name(`type`,
[Patt_child(Var_child `type`)]))])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0), PO_leaf(`const`, -));
((0, (Abs 0), 0),
PO_format(PF(H_box[(0, PO_constant `:`);
(0,
PO_subcall((`type`,
-),
[]))])))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `comps`)]));
Patt_child(Link_child(((Val 1), Default),
[`op`]))])),
Var_child `comp`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`comps`,
-),
[(`prec`,
-)]));
(0, PO_leaf(`op`, -))]));
((0, (Abs 0), 0),
PO_subcall((`comp`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `args`)]));
Patt_child(Link_child(((Val 1), Default),
[`op`]))])),
Var_child `arg`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_expand(HV_box[((1, (Abs 0), 0),
PO_subcall((`args`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_leaf(`op`, -))]));
((1, (Abs 0), 0),
PO_subcall((`arg`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `arg1`)]));
Patt_child(Var_child `arg2`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1,
PO_subcall((`arg1`,
-),
[(`prec`,
-)]));
(1,
PO_leaf(`op`, -))])));
((1, (Abs 3), 0),
PO_subcall((`arg2`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`, []));
Wild_children]));
Patt_child(Var_child `arg`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0, PO_leaf(`op`, -));
(0, PO_subcall((`arg`, -), [(`prec`, -)]));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Const_name(`ABS`,
[Patt_child(Var_child `bvs`);
Patt_child(Link_child(((Val 1),
Default),
[`op`]))]))])),
Var_child `body`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(0,
PO_leaf(`op`, -));
(0,
PO_format(PF(HV_box[((1,
(Abs 0),
0),
PO_subcall((`bvs`,
-),
[(`prec`,
-)]))])));
(0, PO_constant `.`)])));
((1, (Abs 3), 0),
PO_subcall((`body`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`ABS`,
[Patt_child(Var_child `bvs`);
Patt_child(Link_child(((Val 1), Default),
[]))])),
Var_child `body`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_constant `\`);
(0,
PO_format(PF(HV_box[((1,
(Abs 0),
0),
PO_subcall((`bvs`,
-),
[(`prec`,
-)]))])));
(0, PO_constant `.`)])));
((1, (Abs 3), 0),
PO_subcall((`body`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`COND`,
[]));
Wild_children]));
Patt_child(Var_child `cond`)]));
Patt_child(Var_child `x`)]));
Patt_child(Var_child `y`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_format(PF(HV_box[((1, (Abs 0), 0),
PO_subcall((`cond`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_constant `=>`)])));
((1, (Abs 0), 0),
PO_format(PF(HV_box[((1, (Abs 0), 0),
PO_subcall((`x`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_constant `|`)])));
((1, (Abs 0), 0),
PO_subcall((`y`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term_let`,
(Print_loop((Const_name(`ABS`,
[Patt_child(Var_child `args`);
Patt_child(Link_child(((Default), Default),
[]))])),
Wild_child)),
-),
[],
PF(H_box[(1, PO_context_subcall(`term`, (`args`, -), []))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`LET`,
[]));
Wild_children]));
Patt_child(Print_link((((Default),
Default),
[]),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`LET`,
[]));
Wild_children]));
Patt_child (Wild_child)]));
Patt_child (Wild_child)])))]));
Patt_child(Print_label(`argsl`,
Print_loop((Const_name(`ABS`,
[Patt_child (Wild_child);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `letbodyl`)))])),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`LET`,
[]));
Wild_children]));
Patt_child(Const_name(`ABS`,
[Patt_child(Var_child `bv`);
Patt_child(Print_loop((Const_name(`ABS`,
[Patt_child(Var_child `bvl`);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `body`))]))]));
Patt_child(Print_label(`args`,
Print_loop((Const_name(`ABS`,
[Patt_child (Wild_child);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `letbody`)))]))),
-),
[(`argsl`, -); (`letbodyl`, -)],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1,
PO_constant `let`);
(1,
PO_subcall((`bv`,
-),
[(`prec`,
-)]));
(1,
PO_context_subcall(`term_let`,
(`args`,
-),
[(`prec`,
-)]));
(1,
PO_constant `=`)])));
((1, (Abs 3), 0),
PO_subcall((`letbody`,
-),
[(`prec`,
-)]))])));
((1, (Abs 0), 0),
PO_expand(HV_box[((1, (Abs 3), 0),
PO_expand(H_box[(1,
PO_constant `and`);
(1,
PO_subcall((`bvl`,
-),
[(`prec`,
-)]));
(1,
PO_context_subcall(`term_let`,
(`argsl`,
-),
[(`prec`,
-)]));
(1,
PO_constant `=`)]));
((1, (Abs 3), 0),
PO_subcall((`letbodyl`,
-),
[(`prec`,
-)]))]));
((1, (Abs 0), 0),
PO_format(PF(H_box[(1,
PO_constant `in`);
(1,
PO_subcall((`body`,
-),
[(`prec`,
-)]))])))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`CONS`,
[]));
Wild_children]));
Patt_child(Var_child `elems`)]));
Patt_child(Print_link((((Default), Default),
[]),
Const_name(`COMB`,
[Wild_children])))])),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`CONS`,
[]));
Wild_children]));
Patt_child(Var_child `elem`)]));
Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`NIL`,
[]));
Wild_children]))]))),
-),
[],
PF(H_box[(0, PO_constant `[`);
(0,
PO_format(PF(HoV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`elems`,
-),
[(`prec`,
-)]));
(0, PO_constant `;`)]));
((0, (Abs 0), 0),
PO_subcall((`elem`, -), [(`prec`, -)]))])));
(0, PO_constant `]`)]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Link_child(((Val 1), Default),
[]));
Patt_child(Var_child `rands`)])),
Var_child `rator`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_subcall((`rator`, -), [(`prec`, -)]));
((1, (Abs 3), 0),
PO_subcall((`rands`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`, (Const_name(`term`, [Patt_child(Var_child `term`)])), -),
[],
PF(H_box[(0, PO_constant `"`);
(0, PO_subcall((`term`, -), [(`prec`, -)]));
(0, PO_constant `"`)]));
((`thm`, (Var_child `term`), -),
[],
PF(H_box[(0, PO_context_subcall(`term`, (`term`, -), [(`prec`, -)]))]))]
: print_rule list
hol_term_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_hol/hol_term_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'PP_to_ML false `PP_hol/hol_thm` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'loadf `PP_hol/hol_trees`;;'\
'loadf `PP_hol/precedence`;;'\
'loadf `PP_hol/hol_type_pp`;;'\
'loadf `PP_hol/hol_term_pp`;;'\
'compilet `PP_hol/hol_thm_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#....() : void
......() : void
..() : void
..() : void
hol_thm_rules =
[((`thm`, (Const_name(`dot`, [])), -),
[],
PF(H_box[(0, PO_constant `.`)]));
((`thm`, (Const_name(`term`, [Patt_child(Var_child `term`)])), -),
[],
PF(H_box[(0, PO_subcall((`term`, -), []))]));
((`thm`,
(Const_name(`thm`,
[Patt_child(Var_child `concl`);
Patt_child(Const_name(`dots`, [Var_children `dots`]))])),
-),
[],
PF(H_box[(1, PO_format(PF(H_box[(0, PO_subcall((`dots`, -), []))])));
(1, PO_constant `|-`);
(1, PO_subcall((`concl`, -), []))]));
((`thm`,
(Const_name(`thm`,
[Patt_child(Var_child `concl`);
Patt_child(Const_name(`hyp`,
[Var_children `hyps`;
Patt_child(Var_child `hyp`)]))])),
-),
[],
PF(HoV_box[((1, (Abs 0), 0),
PO_expand(H_box[(0, PO_subcall((`hyps`, -), []));
(0, PO_constant `,`)]));
((1, (Abs 0), 0), PO_subcall((`hyp`, -), []));
((1, (Abs 0), 0),
PO_format(PF(H_box[(1, PO_constant `|-`);
(1, PO_subcall((`concl`, -), []))])))]));
((`thm`,
(Const_name(`thm`,
[Patt_child(Var_child `concl`);
Patt_child(Const_name(`hyp`, []))])),
-),
[],
PF(H_box[(1, PO_constant `|-`); (1, PO_subcall((`concl`, -), []))]))]
: print_rule list
hol_thm_rules_fun = - : print_rule_function
Calling Lisp compiler
File PP_hol/hol_thm_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'loadf `PP_hol/hol_trees`;;'\
'loadf `PP_hol/precedence`;;'\
'loadf `PP_hol/hol_type_pp`;;'\
'loadf `PP_hol/hol_term_pp`;;'\
'loadf `PP_hol/hol_thm_pp`;;'\
'compilet `PP_hol/new_printers`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#....() : void
......() : void
..() : void
..() : void
..() : void
hol_rules_fun = - : print_rule_function
pp_convert_type = - : (type -> print_tree)
pp_convert_term = - : (term -> print_tree)
pp_convert_thm = - : (thm -> print_tree)
pp_convert_all_thm = - : (thm -> print_tree)
pp_print_type = - : (type -> void)
pp_print_term = - : (term -> void)
pp_print_thm = - : (thm -> void)
pp_print_all_thm = - : (thm -> void)
pp_print_theory = - : (string -> void)
Calling Lisp compiler
File PP_hol/new_printers compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `PP_printer/PP_printer`;;'\
'loadf `PP_parser/PP_parser`;;'\
'loadf `PP_hol/hol_trees`;;'\
'loadf `PP_hol/precedence`;;'\
'loadf `PP_hol/hol_type_pp`;;'\
'loadf `PP_hol/hol_term_pp`;;'\
'loadf `PP_hol/hol_thm_pp`;;'\
'loadf `PP_hol/new_printers`;;'\
'compilet `PP_hol/link_to_hol`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
..................................................................................................................() : void
#.................................................................................................................................................() : void
#....() : void
......() : void
..() : void
..() : void
..() : void
..........() : void
- : (type -> void)
- : (term -> void)
- : (thm -> void)
- : (term -> void)
Calling Lisp compiler
File PP_hol/link_to_hol compiled
() : void
#===> library prettyp rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/prettyp'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/trs'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `extents`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Calling Lisp compiler
File extents compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'compilet `sets`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
no_rep = - : (* list -> bool)
remove_rep = - : (* list -> * list)
is_subset = - : (* list -> * list -> bool)
Calling Lisp compiler
File sets compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'compilet `extract`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
get_ids = - : (term -> (term list # term list # term list))
get_consts = - : (term -> term list)
get_freevars = - : (term -> term list)
get_boundvars = - : (term -> term list)
get_types = - : (term -> type list)
is_primtype = - : (type -> bool)
subtypes = - : (type -> type list)
prim_subtypes = - : (type -> type list)
get_primtypes = - : (term -> type list)
get_primvartypes = - : (term -> type list)
Calling Lisp compiler
File extract compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'compilet `struct`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
merge = - : ((* # **) list -> (* # **) list -> (* # **) list)
join =
-
: (((term # term) list # (type # type) list) ->
((term # term) list # (type # type) list) ->
((term # term) list # (type # type) list))
remove_bv =
-
: (term ->
((term # term) list # (type # type) list) ->
((term # term) list # (type # type) list))
match_type = - : (type -> type -> (type # type) list)
match_term =
-
: (term -> term -> ((term # term) list # (type # type) list))
match_internal_term =
-
: (term -> term -> ((term # term) list # (type # type) list))
show_wildvar = - : (wildvar -> term)
make_wildvar = - : (term -> wildvar)
wildvarlist = - : (term list -> wildvar list)
show_wildtype = - : (wildtype -> type)
make_wildtype = - : (type -> wildtype)
wildtypelist = - : (type list -> wildtype list)
show_termpattern =
-
: (termpattern -> (term # wildvar list # wildtype list))
make_termpattern =
-
: ((term # wildvar list # wildtype list) -> termpattern)
show_full_termpattern =
-
: (termpattern -> (term # term list # type list))
make_full_termpattern =
-
: ((term # term list # type list) -> termpattern)
autotermpattern = - : (term -> termpattern)
show_matching =
-
: (matching -> ((wildvar # term) list # (wildtype # type) list))
null_matching = - : matching
make_matching = - : (termpattern -> term -> matching)
join_matchings = - : (matching -> matching -> matching)
show_full_matching =
-
: (matching -> ((term # term) list # (type # type) list))
match_of_var = - : (matching -> wildvar -> term)
match_of_type = - : (matching -> wildtype -> type)
New constructors declared:
Nomatch : result_of_match
Match : ((matching # (void -> result_of_match)) -> result_of_match)
Match_null = Match((-), -) : result_of_match
approms =
-
: ((void -> result_of_match) ->
(void -> result_of_match) ->
void ->
result_of_match)
bool_to_rom = - : (bool -> result_of_match)
rom_to_bool = - : (result_of_match -> bool)
type side_condition defined
Calling Lisp compiler
File struct compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'loadf `struct`;;'\
'compilet `name`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
........................() : void
show_wildchar = - : (wildchar -> string)
make_wildchar = - : (string -> wildchar)
show_namepattern = - : (namepattern -> (string # wildchar # wildchar))
make_namepattern = - : ((string # wildchar # wildchar) -> namepattern)
show_full_namepattern = - : (namepattern -> (string # string # string))
make_full_namepattern = - : ((string # string # string) -> namepattern)
wildchar1 = `?` : string
wildcharn = `*` : string
autonamepattern = - : (string -> namepattern)
namematch = - : (namepattern -> string -> bool)
Calling Lisp compiler
File name compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'loadf `struct`;;'\
'loadf `name`;;'\
'compilet `thmkind`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
........................() : void
.......() : void
New constructors declared:
Axiom : thmkind
Definition : thmkind
Theorem : thmkind
Calling Lisp compiler
File thmkind compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'loadf `struct`;;'\
'loadf `name`;;'\
'loadf `thmkind`;;'\
'compilet `matching`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
........................() : void
.......() : void
.() : void
type foundthm defined
New constructors declared:
Kind' : (thmkind -> thmpattern_rep)
Thryname' : (namepattern -> thmpattern_rep)
Thmname' : (namepattern -> thmpattern_rep)
Conc' : (termpattern -> thmpattern_rep)
HypP' : (termpattern list -> thmpattern_rep)
HypF' : (termpattern list -> thmpattern_rep)
Side' : (side_condition -> thmpattern_rep)
Andalso' : ((thmpattern_rep # thmpattern_rep) -> thmpattern_rep)
Orelse' : ((thmpattern_rep # thmpattern_rep) -> thmpattern_rep)
Not' : (thmpattern_rep -> thmpattern_rep)
Where' : ((thmpattern_rep # thmpattern_rep) -> thmpattern_rep)
show_thmpattern = - : (thmpattern -> thmpattern_rep)
Kind = - : (thmkind -> thmpattern)
Thryname = - : (namepattern -> thmpattern)
Thmname = - : (namepattern -> thmpattern)
Conc = - : (termpattern -> thmpattern)
HypP = - : (termpattern list -> thmpattern)
HypF = - : (termpattern list -> thmpattern)
Side = - : (side_condition -> thmpattern)
Andalso = - : ((thmpattern # thmpattern) -> thmpattern)
Orelse = - : ((thmpattern # thmpattern) -> thmpattern)
Not = - : (thmpattern -> thmpattern)
Where = - : ((thmpattern # thmpattern) -> thmpattern)
thmmatch = - : (thmpattern -> foundthm -> bool)
() : void
() : void
() : void
thmfilter = - : (thmpattern -> foundthm list -> foundthm list)
Calling Lisp compiler
File matching compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'loadf `struct`;;'\
'loadf `name`;;'\
'loadf `thmkind`;;'\
'loadf `matching`;;'\
'compilet `sidecond`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
........................() : void
.......() : void
.() : void
.......() : void
containsfn = - : (termpattern -> term -> void -> result_of_match)
() : void
Contains = - : (wildvar -> termpattern -> thmpattern)
() : void
contains = - : (term -> term -> thmpattern)
() : void
Matches = - : (wildvar -> termpattern -> thmpattern)
() : void
matches = - : (term -> term -> thmpattern)
dest_binder = - : (term -> (term # term))
strip_binders = - : (term -> term)
() : void
Has_body = - : (wildvar -> termpattern -> thmpattern)
() : void
has_body = - : (term -> term -> thmpattern)
Test1term = - : ((term -> bool) -> wildvar -> thmpattern)
test1term = - : ((term -> bool) -> term -> thmpattern)
Test1type = - : ((type -> bool) -> wildtype -> thmpattern)
test1type = - : ((type -> bool) -> type -> thmpattern)
Test2terms =
-
: ((term -> term -> bool) -> wildvar -> wildvar -> thmpattern)
test2terms = - : ((term -> term -> bool) -> term -> term -> thmpattern)
Test2types =
-
: ((type -> type -> bool) -> wildtype -> wildtype -> thmpattern)
test2types = - : ((type -> type -> bool) -> type -> type -> thmpattern)
Calling Lisp compiler
File sidecond compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'loadf `struct`;;'\
'loadf `name`;;'\
'loadf `thmkind`;;'\
'loadf `matching`;;'\
'loadf `sidecond`;;'\
'compilet `search`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
........................() : void
.......() : void
.() : void
.......() : void
.......................() : void
get_theorems = - : (string -> foundthm list)
New constructors declared:
Theory : (string -> searchpath)
Ancestors : ((string list # string list) -> searchpath)
New constructors declared:
List : (foundthm list -> source)
Paths : (searchpath list -> source)
do_once_only = - : (* list -> * list)
searchseq = - : (string list -> string list -> string list)
flatten_paths = - : (searchpath list -> string list)
New constructors declared:
Endofsearch : (foundthm list -> searchstep)
Step : ((foundthm list # (void -> searchstep)) -> searchstep)
find_theorems = - : (thmpattern -> source -> searchstep)
show_step = - : (searchstep -> foundthm list)
continue_search = - : (searchstep -> searchstep)
Calling Lisp compiler
File search compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf `extents`;;'\
'loadf `sets`;;'\
'loadf `extract`;;'\
'loadf `struct`;;'\
'loadf `name`;;'\
'loadf `thmkind`;;'\
'loadf `matching`;;'\
'loadf `sidecond`;;'\
'loadf `search`;;'\
'compilet `user`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
...() : void
..........() : void
........................() : void
.......() : void
.() : void
.......() : void
.......................() : void
..........() : void
FT = - : (thmpattern -> source -> searchstep)
CS = - : (searchstep -> searchstep)
run_search = - : (searchstep -> foundthm list)
full_search = - : (thmpattern -> source -> foundthm list)
search_until_find = - : (searchstep -> searchstep)
search_n_theories = - : (int -> searchstep -> searchstep)
search_n_until_find = - : (int -> searchstep -> searchstep)
ancestors_excluding = - : (string list -> string list -> searchpath)
Ancestry = - : (string list -> searchpath)
List_from = - : (searchstep -> source)
kind = - : (thmkind -> thmpattern)
thryname = - : (string -> thmpattern)
thmname = - : (string -> thmpattern)
conc = - : (term -> thmpattern)
hypP = - : (term list -> thmpattern)
hypF = - : (term list -> thmpattern)
side = - : (side_condition -> thmpattern)
BigAnd = - : (thmpattern list -> thmpattern)
BigOr = - : (thmpattern list -> thmpattern)
Calling Lisp compiler
File user compiled
() : void
#===> library trs rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/trs'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/latex-hol'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `filters`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
spec_list =
[(`_`, `\US `);
(`#`, `\SH `);
(`&`, `\AM `);
(`%`, `\PC `);
(`$`, `\DO `);
(`\`, `\BS `);
(`'`, `\PR `);
(`~`, `\TI `);
(`*`, `\AS `);
(`<`, `\LES `);
(`|`, `\BA `);
(`>`, `\GRE `);
(`[`, `\LB `);
(`]`, `\RB `);
(`^`, `\CI `);
(`{`, `\LC `);
(`}`, `\RC `)]
: (string # string) list
do_char = - : (string -> string)
filter_id = - : (string -> string)
dovar = - : (string -> string)
symb_of = - : (string -> string)
doinfix = - : (string -> string)
Calling Lisp compiler
File filters compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'compilet `hol_trees`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#
New constructors declared:
No_types : type_selection
Hidden_types : type_selection
Useful_types : type_selection
All_types : type_selection
type_to_print_tree = - : (type -> print_tree)
term_to_print_tree = - : (bool -> type_selection -> term -> print_tree)
thm_to_print_tree =
-
: (bool -> bool -> type_selection -> thm -> print_tree)
Calling Lisp compiler
File hol_trees compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'loadf `hol_trees`;;'\
'compilet `precedence`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#....() : void
is_res_quan = - : (string -> bool)
type_prec = - : (string -> int)
min_type_prec = 0 : int
max_type_prec = 400 : int
term_prec = - : (string -> int)
min_term_prec = 0 : int
max_term_prec = 1800 : int
Calling Lisp compiler
File precedence compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'PP_to_ML false `latex_type` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'loadf `filters`;;'\
'loadf `hol_trees`;;'\
'loadf `precedence`;;'\
'compilet `latex_type_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#......() : void
....() : void
.......() : void
latex_type_rules =
[((`type`, (Const_name(`VAR`, [Patt_child(Var_name(`op`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`op`, -))]));
((`type`, (Const_name(`OP`, [Patt_child(Var_name(`op`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`op`, -))]));
((`type`,
(Const_name(`OP`,
[Patt_child(Var_name(`op`, []));
Patt_child(Var_child `type1`);
Patt_child(Var_child `type2`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1,
PO_subcall((`type1`,
-),
[(`prec`,
-)]));
(1,
PO_leaf(`op`, -))])));
((1, (Abs 3), 0),
PO_subcall((`type2`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`type`,
(Const_name(`OP`,
[Patt_child(Var_name(`op`, []));
Var_children `types`;
Patt_child(Var_child `type`)])),
-),
[],
PF(HV_box[((0, (Abs 3), 0),
PO_format(PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HV_box[((0, (Inc 3), 0),
PO_expand(H_box[(0,
PO_subcall((`types`,
-),
[(`prec`,
-)]));
(0,
PO_constant `,`)]));
((0, (Inc 3), 0),
PO_subcall((`type`,
-),
[(`prec`,
-)]))])));
(0, PO_constant `)`)])));
((0, (Abs 3), 0), PO_leaf(`op`, -))]));
((`type`, (Const_name(`type`, [Patt_child(Var_child `type`)])), -),
[],
PF(H_box[(0, PO_constant `":`);
(0, PO_subcall((`type`, -), [(`prec`, -)]));
(0, PO_constant `"`)]));
((`term`, (Var_child `type`), -),
[],
PF(H_box[(0, PO_context_subcall(`type`, (`type`, -), [(`prec`, -)]))]))]
: print_rule list
latex_type_rules_fun = - : print_rule_function
Calling Lisp compiler
File latex_type_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'PP_to_ML false `latex_thm` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'PP_to_ML false `latex_term` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'loadf `filters`;;'\
'loadf `hol_trees`;;'\
'loadf `precedence`;;'\
'loadf `latex_type_pp`;;'\
'compilet `latex_term_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#......() : void
....() : void
.......() : void
..() : void
latex_term_rules =
[((`term`,
(Const_name(`CONST`,
[Patt_child(Const_name(`NIL`, [])); Wild_children])),
-),
[],
PF(H_box[(0, PO_constant `\NIL `)]));
((`term`, (Const_name(`VAR`, [Patt_child(Var_name(`var`, []))])), -),
[],
PF(H_box[(0, PO_leaf(`var`, -))]));
((`term`,
(Const_name(`VAR`,
[Patt_child(Var_name(`var`, []));
Patt_child(Const_name(`type`,
[Patt_child(Var_child `type`)]))])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0), PO_leaf(`var`, -));
((0, (Abs 0), 0),
PO_format(PF(H_box[(0, PO_constant `:`);
(0,
PO_subcall((`type`,
-),
[]))])))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`CONST`, [Patt_child(Var_name(`const`, []))])),
-),
[],
PF(H_box[(0, PO_leaf(`const`, -))]));
((`term`,
(Const_name(`CONST`,
[Patt_child(Var_name(`const`, []));
Patt_child(Const_name(`type`,
[Patt_child(Var_child `type`)]))])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0), PO_leaf(`const`, -));
((0, (Abs 0), 0),
PO_format(PF(H_box[(0, PO_constant `:`);
(0,
PO_subcall((`type`,
-),
[]))])))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `comps`)]));
Patt_child(Link_child(((Val 1), Default),
[`op`]))])),
Var_child `comp`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`comps`,
-),
[(`prec`,
-)]));
(0, PO_leaf(`op`, -))]));
((0, (Abs 0), 0),
PO_subcall((`comp`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `args`)]));
Patt_child(Link_child(((Val 1), Default),
[`op`]))])),
Var_child `arg`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0), PO_constant `(`);
((1, (Abs 0), 0),
PO_expand(HV_box[((1, (Abs 0), 0),
PO_subcall((`args`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_constant `)\:\CONST{EXP}\:(`)]));
((1, (Abs 0), 0),
PO_subcall((`arg`, -), [(`prec`, -)]));
((1, (Abs 0), 0), PO_constant `)`)])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `args`)]));
Patt_child(Link_child(((Val 1), Default),
[`op`]))])),
Var_child `arg`)),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_expand(HV_box[((1, (Abs 0), 0),
PO_subcall((`args`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_leaf(`op`, -))]));
((1, (Abs 0), 0),
PO_subcall((`arg`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `arg1`)]));
Patt_child(Var_child `arg2`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1,
PO_subcall((`arg1`,
-),
[(`prec`,
-)]));
(1,
PO_leaf(`op`, -))])));
((1, (Abs 3), 0),
PO_subcall((`arg2`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`, []));
Wild_children]));
Patt_child(Var_child `arg`)])),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0, PO_leaf(`op`, -));
(0, PO_subcall((`arg`, -), [(`prec`, -)]));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Var_child `pred`)]));
Patt_child(Const_name(`ABS`,
[Patt_child(Var_child `bvs`);
Patt_child(Link_child(((Val 1),
Default),
[`op`;
`pred`]))]))])),
Var_child `body`)),
-),
[(`bv`, -); (`bvs`, -)],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF(H_box[(0, PO_constant `(`)])),
PF_empty)));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(0,
PO_leaf(`op`, -));
(0,
PO_format(PF(H_box[(1,
PO_subcall((`bv`,
-),
[]));
(1,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(1,
PO_expand(H_box[(0,
PO_constant `\,`);
(0,
PO_subcall((`bvs`,
-),
[(`prec`,
-)]))]))]))))])));
(0,
PO_constant `\RESDOT `);
(0,
PO_format(PF(H_box[(1,
PO_subcall((`pred`,
-),
[(`prec`,
-)]))])));
(0,
PO_constant `\DOT`)])));
((1, (Abs 3), 0),
PO_subcall((`body`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF(H_box[(0, PO_constant `)`)])),
PF_empty)))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Var_name(`op`,
[]));
Wild_children]));
Patt_child(Const_name(`ABS`,
[Patt_child(Var_child `bvs`);
Patt_child(Link_child(((Val 1),
Default),
[`op`]))]))])),
Var_child `body`)),
-),
[(`bv`, -); (`bvs`, -)],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF(H_box[(0, PO_constant `(`)])),
PF_empty)));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(0,
PO_leaf(`op`, -));
(0,
PO_format(PF(H_box[(1,
PO_subcall((`bv`,
-),
[]));
(1,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(1,
PO_expand(H_box[(0,
PO_constant `\,`);
(0,
PO_subcall((`bvs`,
-),
[(`prec`,
-)]))]))]))))])));
(0,
PO_constant `\DOT`)])));
((1, (Abs 3), 0),
PO_subcall((`body`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF(H_box[(0, PO_constant `)`)])),
PF_empty)))]));
((`term`,
(Print_loop((Const_name(`ABS`,
[Patt_child(Var_child `bvs`);
Patt_child(Print_link((((Default), Default),
[]),
Const_name(`ABS`,
[Wild_children])))])),
Const_name(`ABS`,
[Patt_child(Var_child `bv`);
Patt_child(Var_child `body`)]))),
-),
[],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_format(PF(H_box[(1,
PO_constant `\LAMBDA`);
(1,
PO_format(PF(H_box[(1,
PO_expand(H_box[(1,
PO_subcall((`bvs`,
-),
[(`prec`,
-)]));
(1,
PO_constant `\,`)]))])));
(1,
PO_subcall((`bv`,
-),
[]));
(1,
PO_constant `\DOT`)])));
((1, (Abs 3), 0),
PO_subcall((`body`, -), [(`prec`, -)]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`COND`,
[]));
Wild_children]));
Patt_child(Var_child `cond`)]));
Patt_child(Var_child `x`)]));
Patt_child(Var_child `y`)])),
-),
[],
PF(H_box[(0, PO_constant `(`);
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_format(PF(HV_box[((1, (Abs 0), 0),
PO_subcall((`cond`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_constant `\Rightarrow `)])));
((1, (Abs 0), 0),
PO_format(PF(HV_box[((1, (Abs 0), 0),
PO_subcall((`x`,
-),
[(`prec`,
-)]));
((1, (Abs 0), 0),
PO_constant `\mid `)])));
((1, (Abs 0), 0),
PO_subcall((`y`, -), [(`prec`, -)]))])));
(0, PO_constant `)`)]));
((`term_let`,
(Print_loop((Const_name(`ABS`,
[Patt_child(Var_child `args`);
Patt_child(Link_child(((Default), Default),
[]))])),
Wild_child)),
-),
[],
PF(H_box[(1, PO_context_subcall(`term`, (`args`, -), []))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`LET`,
[]));
Wild_children]));
Patt_child(Print_link((((Default),
Default),
[]),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`LET`,
[]));
Wild_children]));
Patt_child (Wild_child)]));
Patt_child (Wild_child)])))]));
Patt_child(Print_label(`argsl`,
Print_loop((Const_name(`ABS`,
[Patt_child (Wild_child);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `letbodyl`)))])),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`LET`,
[]));
Wild_children]));
Patt_child(Const_name(`ABS`,
[Patt_child(Var_child `bv`);
Patt_child(Print_loop((Const_name(`ABS`,
[Patt_child(Var_child `bvl`);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `body`))]))]));
Patt_child(Print_label(`args`,
Print_loop((Const_name(`ABS`,
[Patt_child (Wild_child);
Patt_child(Link_child(((Default),
Default),
[]))])),
Var_child `letbody`)))]))),
-),
[(`argsl`, -); (`letbodyl`, -)],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HoV_box[((1, (Abs 0), 0),
PO_format(PF(HV_box[((1, (Abs 1), 0),
PO_format(PF(H_box[(1,
PO_constant `\KEYWD{let}\;`);
(1,
PO_subcall((`bv`,
-),
[(`prec`,
-)]));
(1,
PO_context_subcall(`term_let`,
(`args`,
-),
[(`prec`,
-)]));
(1,
PO_constant `=`)])));
((1, (Abs 1), 0),
PO_subcall((`letbody`,
-),
[(`prec`,
-)]))])));
((1, (Abs 0), 0),
PO_expand(HV_box[((1, (Abs 1), 0),
PO_expand(HV_box[((1,
(Abs 0),
0),
PO_constant `\;\KEYWD{and}`);
((1,
(Abs 0),
0),
PO_subcall((`bvl`,
-),
[(`prec`,
-)]));
((1,
(Abs 0),
0),
PO_context_subcall(`term_let`,
(`argsl`,
-),
[(`prec`,
-)]));
((1,
(Abs 0),
0),
PO_constant `=`)]));
((1, (Abs 1), 0),
PO_subcall((`letbodyl`,
-),
[(`prec`,
-)]))]));
((1, (Abs 0), 0),
PO_format(PF(V_box[(((Abs 0), 0),
PO_constant `\;\KEYWD{in}`);
(((Abs 0), 0),
PO_format(PF(HV_box[((1,
(Abs 0),
0),
PO_subcall((`body`,
-),
[(`prec`,
-)]))])))])))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`CONS`,
[]));
Wild_children]));
Patt_child(Var_child `elems`)]));
Patt_child(Print_link((((Default), Default),
[]),
Const_name(`COMB`,
[Wild_children])))])),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`CONS`,
[]));
Wild_children]));
Patt_child(Var_child `elem`)]));
Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`NIL`,
[]));
Wild_children]))]))),
-),
[],
PF(H_box[(0, PO_constant `[`);
(0,
PO_format(PF(HoV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`elems`,
-),
[(`prec`,
-)]));
(0, PO_constant `;`)]));
((0, (Abs 0), 0),
PO_subcall((`elem`, -), [(`prec`, -)]))])));
(0, PO_constant `]`)]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Link_child(((Val 1), Default),
[]));
Patt_child(Var_child `rands`)])),
Var_child `rator`)),
-),
[(`rands`, -)],
PF(H_box[(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `(`)]))));
(0,
PO_format(PF(HV_box[((1, (Abs 3), 0),
PO_subcall((`rator`, -), [(`prec`, -)]));
((1, (Abs 3), 0),
PO_expand(H_box[(0, PO_constant `\,`);
(0,
PO_subcall((`rands`,
-),
[(`prec`,
-)]))]))])));
(0,
PO_format(PF_branch((-),
(PF_empty),
PF(H_box[(0, PO_constant `)`)]))))]));
((`term`, (Const_name(`term`, [Patt_child(Var_child `term`)])), -),
[],
PF(H_box[(0, PO_constant `"`);
(0, PO_subcall((`term`, -), [(`prec`, -)]));
(0, PO_constant `"`)]));
((`thm`, (Var_child `term`), -),
[],
PF(H_box[(0, PO_context_subcall(`term`, (`term`, -), [(`prec`, -)]))]))]
: print_rule list
latex_term_rules_fun = - : print_rule_function
Calling Lisp compiler
File latex_term_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'loadf `filters`;;'\
'loadf `hol_trees`;;'\
'loadf `precedence`;;'\
'loadf `latex_type_pp`;;'\
'loadf `latex_term_pp`;;'\
'compilet `latex_thm_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#......() : void
....() : void
.......() : void
..() : void
..() : void
latex_thm_rules =
[((`thm`, (Const_name(`dot`, [])), -),
[],
PF(H_box[(0, PO_constant `.`)]));
((`thm`, (Const_name(`term`, [Patt_child(Var_child `term`)])), -),
[],
PF(H_box[(0, PO_subcall((`term`, -), []))]));
((`thm`,
(Const_name(`thm`,
[Patt_child(Var_child `concl`);
Patt_child(Const_name(`dots`, [Var_children `dots`]))])),
-),
[],
PF(H_box[(1, PO_format(PF(H_box[(0, PO_subcall((`dots`, -), []))])));
(1, PO_constant `\THM`);
(1, PO_subcall((`concl`, -), []))]));
((`thm`,
(Const_name(`thm`,
[Patt_child(Var_child `concl`);
Patt_child(Const_name(`hyp`,
[Var_children `hyps`;
Patt_child(Var_child `hyp`)]))])),
-),
[],
PF(HoV_box[((1, (Abs 0), 0),
PO_expand(H_box[(0, PO_subcall((`hyps`, -), []));
(0, PO_constant `,`)]));
((1, (Abs 0), 0), PO_subcall((`hyp`, -), []));
((1, (Abs 0), 0),
PO_format(PF(H_box[(1, PO_constant `\THM`);
(1, PO_subcall((`concl`, -), []))])))]));
((`thm`,
(Const_name(`thm`,
[Patt_child(Var_child `concl`);
Patt_child(Const_name(`hyp`, []))])),
-),
[],
PF(H_box[(1, PO_constant `\THM`); (1, PO_subcall((`concl`, -), []))]))]
: print_rule list
latex_thm_rules_fun = - : print_rule_function
Calling Lisp compiler
File latex_thm_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'PP_to_ML false `latex_sets` ``;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#() : void
echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'loadf `filters`;;'\
'loadf `hol_trees`;;'\
'loadf `precedence`;;'\
'loadf `latex_type_pp`;;'\
'loadf `latex_term_pp`;;'\
'loadf `latex_thm_pp`;;'\
'compilet `latex_sets_pp`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#......() : void
....() : void
.......() : void
..() : void
..() : void
..() : void
latex_sets_rules =
[((`term`,
(Const_name(`CONST`,
[Patt_child(Const_name(`EMPTY`, [])); Wild_children])),
-),
[],
PF(H_box[(0, PO_constant `\EMPTYSET `)]));
((`term`,
(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`GSPEC`,
[]));
Wild_children]));
Patt_child(Const_name(`ABS`,
[Patt_child(Var_child `var`);
Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child (Wild_child)]));
Patt_child(Var_child `elem`)]));
Patt_child(Var_child `spec`)]))]))])),
-),
[],
PF(H_box[(0, PO_constant `\BEGINSET `);
(0,
PO_format(PF(HV_box[((1, (Abs 1), 0),
PO_subcall((`elem`, -), [(`prec`, -)]));
((1, (Abs 1), 0),
PO_constant `\SUCHTHAT `);
((1, (Abs 1), 0),
PO_subcall((`spec`, -), [(`prec`, -)]))])));
(0, PO_constant `\ENDSET `)]));
((`term`,
(Print_loop((Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`INSERT`,
[]));
Wild_children]));
Patt_child(Var_child `elems`)]));
Patt_child(Print_link((((Default), Default),
[]),
Const_name(`COMB`,
[Wild_children])))])),
Const_name(`COMB`,
[Patt_child(Const_name(`COMB`,
[Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`INSERT`,
[]));
Wild_children]));
Patt_child(Var_child `elem`)]));
Patt_child(Const_name(`CONST`,
[Patt_child(Const_name(`EMPTY`,
[]));
Wild_children]))]))),
-),
[],
PF(H_box[(0, PO_constant `\BEGINSET `);
(0,
PO_format(PF(HV_box[((0, (Abs 0), 0),
PO_expand(H_box[(0,
PO_subcall((`elems`,
-),
[(`prec`,
-)]));
(0, PO_constant `,`)]));
((0, (Abs 0), 0),
PO_subcall((`elem`, -), [(`prec`, -)]))])));
(0, PO_constant `\ENDSET `)]))]
: print_rule list
latex_sets_rules_fun = - : print_rule_function
Calling Lisp compiler
File latex_sets_pp compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'loadf(library_pathname() ^ `/prettyp/PP_printer`);;'\
'loadf(library_pathname() ^ `/prettyp/PP_parser`);;'\
'loadf `filters`;;'\
'loadf `hol_trees`;;'\
'loadf `precedence`;;'\
'loadf `latex_sets_pp`;;'\
'loadf `latex_thm_pp`;;'\
'loadf `latex_term_pp`;;'\
'loadf `latex_type_pp`;;'\
'compilet `formaters`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Updating help search path
....................................................................................................................() : void
#Updating help search path
...................................................................................................................................................() : void
#......() : void
....() : void
.......() : void
..() : void
..() : void
..() : void
..() : void
output_strings = - : (string -> string list -> void)
latex_hol_rules_fun = - : print_rule_function
pp_convert_type = - : (type -> print_tree)
pp_convert_term = - : (term -> print_tree)
pp_convert_thm = - : (thm -> print_tree)
pp_convert_all_thm = - : (thm -> print_tree)
latex_type = - : (type -> void)
latex_term = - : (term -> void)
latex_thm = - : (thm -> void)
latex_all_thm = - : (thm -> void)
latex_type_to = - : (string -> type -> void)
latex_type_add_to = - : (string -> type -> void)
latex_term_to = - : (string -> term -> void)
latex_term_add_to = - : (string -> term -> void)
latex_thm_to = - : (string -> thm -> void)
latex_thm_add_to = - : (string -> thm -> void)
latex_all_thm_to = - : (string -> thm -> void)
latex_all_thm_add_to = - : (string -> thm -> void)
latex_theory_to = - : (string -> bool -> string -> void)
latex_thm_tag = `@t ` : string
latex_thm_end = `` : string
latex_theorems_to =
-
: (string -> (string -> thm) -> string list -> void)
latex_all_theorems_to =
-
: (string -> (string -> thm) -> string list -> void)
latex_theorems_add_to =
-
: (string -> (string -> thm) -> string list -> void)
Calling Lisp compiler
File formaters compiled
() : void
#===>Library latex-hol rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/latex-hol'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/more_arithmetic'
rm -f ineq.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `ineq`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Loading library taut ...
Updating help search path
........................................
Library taut loaded.
() : void
NOT_EQ = |- !t1 t2. (t1 = t2) = (~t1 = ~t2)
Theorem EQ_LESS_EQ autoloading from theory `arithmetic` ...
EQ_LESS_EQ = |- !m n. (m = n) = m <= n /\ n <= m
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
NOT_EQ_LESS_EQ = |- !a b. ~(a = b) = a < b \/ b < a
Theorem LESS_CASES_IMP autoloading from theory `arithmetic` ...
LESS_CASES_IMP = |- !m n. ~m < n /\ ~(m = n) ==> n < m
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
Theorem LESS_ANTISYM autoloading from theory `arithmetic` ...
LESS_ANTISYM = |- !m n. ~(m < n /\ n < m)
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
LESS_IS_NOT_LESS_OR_EQ = |- !x y. x < y = ~y <= x
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
GEN_INDUCTION =
|- !P. P 0 /\ (!n. (!m. m < n ==> P m) ==> P n) ==> (!n. P n)
Theorem LESS_EQ_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQ_ANTISYM = |- !m n. ~(m < n /\ n <= m)
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
GREATER_EQ_ANTISYM = |- !n m. ~(n >= m /\ n < m)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Theorem LESS_EQUAL_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQUAL_ANTISYM = |- !n m. n <= m /\ m <= n ==> (n = m)
LESS_EQ_LESS_EQ_EQ = |- !m n. m <= n /\ n <= m = (m = n)
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
NOT_LESS_AND_GREATER = |- !n m. n < m ==> ~m < n
() : void
File ineq loaded
() : void
#rm -f pre.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `pre`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Theorem PRE_SUC_EQ autoloading from theory `arithmetic` ...
PRE_SUC_EQ = |- !m n. 0 < n ==> ((m = PRE n) = (SUC m = n))
SUC_PRE = |- !n. 0 < n ==> (SUC(PRE n) = n)
Theorem LESS_MONO autoloading from theory `prim_rec` ...
LESS_MONO = |- !m n. m < n ==> (SUC m) < (SUC n)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
Theorem PRE autoloading from theory `prim_rec` ...
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
PRE_MONO = |- !m n. (PRE m) < (PRE n) ==> m < n
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
PRE_MONO_LESS_EQ = |- !m n. m < n ==> (PRE m) <= (PRE n)
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
PRE_LESS_EQ = |- !n. (PRE n) <= n
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
PRE_ADD = |- !n m. 0 < n ==> (PRE(n + m) = (PRE n) + m)
SUC_LESS_PRE = |- !m n. (SUC m) < n ==> m < (PRE n)
SUC_LESS_EQ_PRE = |- !m n. 0 < n ==> (SUC m) <= n ==> m <= (PRE n)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
Theorem INDUCTION autoloading from theory `num` ...
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
PRE_K_K = |- !k. 0 < k ==> (PRE k) < k
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem LESS_EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem SUB_ADD autoloading from theory `arithmetic` ...
SUB_ADD = |- !m n. n <= m ==> ((m - n) + n = m)
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
Theorem NOT_LESS_EQUAL autoloading from theory `arithmetic` ...
NOT_LESS_EQUAL = |- !m n. ~m <= n = n < m
Theorem SUB_EQ_0 autoloading from theory `arithmetic` ...
SUB_EQ_0 = |- !m n. (m - n = 0) = m <= n
NOT_LESS_SUB = |- !m n. ~m < (m - n)
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
Theorem LESS_EQ_LESS_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_LESS_TRANS = |- !m n p. m <= n /\ n < p ==> m < p
PRE_LESS = |- !b. 0 < b /\ b < a ==> (PRE b) < a
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
LESS_IMP_LESS_EQ_PRE = |- !m n. 0 < n ==> (m < n = m <= (PRE n))
() : void
File pre loaded
() : void
#rm -f suc.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `suc`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Theorem NOT_SUC_LESS_EQ_0 autoloading from theory `arithmetic` ...
NOT_SUC_LESS_EQ_0 = |- !n. ~(SUC n) <= 0
NOT_FORALL_SUC_LESS_EQ = |- ~(!n m. (SUC m) <= n)
Theorem LESS_EQ_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQ_ANTISYM = |- !m n. ~(m < n /\ n <= m)
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
NOT_0_GREATER_EQ_SUC = |- !n. ~0 >= (SUC n)
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
SUC_GREATER_EQ_SUC = |- !n m. (SUC m) >= (SUC n) = m >= n
LESS_EQ_MONO_EQ = |- !n m. (SUC n) <= (SUC m) = n <= m
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
LESS_EQ_LESS_SUC = |- !m n. m <= n = m < (SUC n)
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
SUC_LESS_EQ = |- !m n. m <= n /\ ~(m = n) ==> (SUC m) <= n
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem SUC_ID autoloading from theory `prim_rec` ...
SUC_ID = |- !n. ~(SUC n = n)
NOT_SUC_LESS_EQ_SELF = |- !n. ~(SUC n) <= n
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
SUC_0 = |- 1 = SUC 0
Theorem SUC_NOT autoloading from theory `arithmetic` ...
SUC_NOT = |- !n. ~(0 = SUC n)
SUC_NOT_0 = |- !n. ~(SUC n = 0)
() : void
File suc loaded
() : void
#rm -f add.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `add`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Theory suc loaded
() : void
[(); (); (); (); (); (); (); ()] : void list
....() : void
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
LESS_LESS_EQ = |- !a b. a < b = (a + 1) <= b
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
ADD_SUC_0 = |- !m. SUC m = (SUC 0) + m
LESS_EQ_MONO_ADD_EQ0 = |- !m n p. m <= n = (p + m) <= (p + n)
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
LESS_EQ_MONO_ADD_EQ1 = |- !m p. (m + p) <= p = m <= 0
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
LESS_EQ_ADD1 = |- !p n. p <= (n + p)
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
ADD_SYM_ASSOC = |- !a b c. a + (b + c) = b + (a + c)
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
LESS_EQ_SPLIT = |- !m n p. (m + n) <= p ==> n <= p /\ m <= p
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
ADDL_GREATER = |- !m n p. m < n ==> m < (p + n)
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Theorem LESS_EQ_LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_LESS_EQ_MONO =
|- !m n p q. m <= p /\ n <= q ==> (m + n) <= (p + q)
ADDL_GREATER_EQ = |- !m n p. m <= n ==> m <= (p + n)
ADDR_GREATER = |- !m n p. m < n ==> m < (n + p)
ADDR_GREATER_EQ = |- !m n p. m <= n ==> m <= (n + p)
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
LESS_LESS_MONO = |- !m n p q. m < p /\ n < q ==> (m + n) < (p + q)
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
LESS_LESS_EQ_MONO =
|- (!m n p q. m < p /\ n <= q ==> (m + n) < (p + q)) /\
(!m n p q. m <= p /\ n < q ==> (m + n) < (p + q))
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
ADD_EQ_LESS_IMP_LESS = |- !n m k l. (k + m = l + n) /\ k < l ==> n < m
LESS_ADD_ASSOC = |- !a b c d. a < (b + c) ==> a < (b + (c + d))
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
GREATER_EQ_SPLIT = |- !m n p. p >= (m + n) ==> p >= n /\ p >= m
Theorem LESS_MONO_ADD autoloading from theory `arithmetic` ...
LESS_MONO_ADD = |- !m n p. m < n ==> (m + p) < (n + p)
LESS_TRANS_ADD = |- !m n p q. m < (n + p) /\ p < q ==> m < (n + q)
Definition GREATER autoloading from theory `arithmetic` ...
GREATER = |- !m n. m > n = n < m
Definition GREATER_OR_EQ autoloading from theory `arithmetic` ...
GREATER_OR_EQ = |- !m n. m >= n = m > n \/ (m = n)
ADD_GREATER_EQ = |- !m n. (m + n) >= m
ADD_MONO_LESS = |- !m n p. (m + p) < (m + n) = p < n
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Theorem SUC_ID autoloading from theory `prim_rec` ...
SUC_ID = |- !n. ~(SUC n = n)
Theorem SUC_0 autoloading from theory `suc` ...
SUC_0 = |- 1 = SUC 0
NOT_1_TWICE = |- !n. ~(1 = n + n)
Theorem LESS_EQ_LESS_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_LESS_TRANS = |- !m n p. m <= n /\ n < p ==> m < p
SUM_LESS = |- !m n p. (m + n) < p ==> m < p /\ n < p
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
NOT_LESS_IMP_LESS_EQ_ADD1 = |- !a b. ~a < b ==> b <= (a + 1)
NOT_ADD_LESS = |- !m n. ~(m + n) < n
ADD_EQ_LESS_EQ = |- !m n p. (m + n = p) ==> m <= p
SUC_LESS_N_LESS = |- !m n. (m + 1) < n ==> m < n
Theorem LESS_ADD_SUC autoloading from theory `arithmetic` ...
LESS_ADD_SUC = |- !m n. m < (m + (SUC n))
LESS_ADD1 = |- !a. a < (a + 1)
() : void
File add loaded
() : void
#rm -f zero_ineq.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `zero`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
[();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
();
()]
: void list
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
Theorem LESS_EQ_LESS_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_LESS_TRANS = |- !m n p. m <= n /\ n < p ==> m < p
M_LESS_0_LESS = |- !m n. m < n ==> 0 < n
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Theorem LESS_LEMMA1 autoloading from theory `prim_rec` ...
LESS_LEMMA1 = |- !m n. m < (SUC n) ==> (m = n) \/ m < n
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
LESS1EQ0 = |- !m. m < 1 = (m = 0)
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
NOT_EQ_0 = |- !m. ~(m = 0) ==> m >= 1
Theorem LESS_0_CASES autoloading from theory `arithmetic` ...
LESS_0_CASES = |- !m. (0 = m) \/ 0 < m
Theorem NOT_LESS_EQUAL autoloading from theory `arithmetic` ...
NOT_LESS_EQUAL = |- !m n. ~m <= n = n < m
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
LESS_EQ_0_EQ = |- !m. m <= 0 ==> (m = 0)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
GREATER_NOT_ZERO = |- !x. 0 < x ==> ~(x = 0)
NOT_0_AND_MORE = |- !x. ~((x = 0) /\ 0 < x)
() : void
File zero loaded
() : void
#rm -f sub.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `sub`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Theory add loaded
() : void
Theory zero_ineq loaded
() : void
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
Theorem LESS_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
Theorem LESS_EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
NUM_LESS_EQ_PLUS_CONV = - : (term -> conv)
NUM_EQ_PLUS_CONV = - : (term -> conv)
NUM_LESS_PLUS_CONV = - : (term -> conv)
File num_convs loaded
() : void
[(); (); (); (); (); ()] : void list
Theorem PRE autoloading from theory `prim_rec` ...
PRE = |- (PRE 0 = 0) /\ (!m. PRE(SUC m) = m)
Theorem SUB_MONO_EQ autoloading from theory `arithmetic` ...
SUB_MONO_EQ = |- !n m. (SUC n) - (SUC m) = n - m
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
SUB_SUC_PRE_SUB = |- !n m. 0 < n ==> (n - (SUC m) = (PRE n) - m)
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem ADD_SUC autoloading from theory `arithmetic` ...
ADD_SUC = |- !m n. SUC(m + n) = m + (SUC n)
ADD_SUC = |- SUC(m + n) = m + (SUC n)
Definition SUB autoloading from theory `arithmetic` ...
SUB =
|- (!m. 0 - m = 0) /\ (!m n. (SUC m) - n = (m < n => 0 | SUC(m - n)))
Theorem LESS_SUC_NOT autoloading from theory `arithmetic` ...
LESS_SUC_NOT = |- !m n. m < n ==> ~n < (SUC m)
SUB_SUC = |- !k m. m < k ==> (k - m = SUC(k - (SUC m)))
Theorem SUB_ADD autoloading from theory `arithmetic` ...
SUB_ADD = |- !m n. n <= m ==> ((m - n) + n = m)
SUB_LESS_TO_LESS_ADDR =
|- !m n p. p <= m ==> ((m - p) < n = m < (n + p))
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
SUB_LESS_TO_LESS_ADDL =
|- !m n p. n <= m ==> ((m - n) < p = m < (n + p))
LESS_SUB_TO_ADDR_LESS =
|- !m n p. p <= m ==> (n < (m - p) = (n + p) < m)
LESS_SUB_TO_ADDL_LESS =
|- !m n p. n <= m ==> (p < (m - n) = (n + p) < m)
SUC_SUB =
|- !m n.
(m < n ==> ((SUC m) - n = 0)) /\
(~m < n ==> ((SUC m) - n = SUC(m - n)))
Theorem SUB_LESS_EQ autoloading from theory `arithmetic` ...
SUB_LESS_EQ = |- !n m. (n - m) <= n
LESS_SUB_BOUND = |- !k l. k < l ==> (l - k) <= l
Theorem LESS_IMP_LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_IMP_LESS_OR_EQ = |- !m n. m < n ==> m <= n
SUB_SUB_ID = |- !k l. l < k ==> (k - (k - l) = l)
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
Theorem SUB_EQ_0 autoloading from theory `arithmetic` ...
SUB_EQ_0 = |- !m n. (m - n = 0) = m <= n
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
LESS_SUB_IMP_INV = |- !k l. 0 < (k - l) ==> l < k
Theorem ADDL_GREATER_EQ autoloading from theory `add` ...
ADDL_GREATER_EQ = |- !m n p. m <= n ==> m <= (p + n)
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
LESS_EQ_ADD_SUB1 = |- !m n p. p <= n ==> (m + (n - p) = (m + n) - p)
LESS_EQ_SUB_ADD = |- !m n p. p <= m ==> ((m - p) + n = (m + n) - p)
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
GREATER_EQ_SUB_LESS_TO_ADD =
|- !n m p. p >= n ==> ((p - n) < m = p < (n + m))
SUB_GREATER_EQ_ADD = |- !n m p. p >= n ==> ((p - n) >= m = p >= (n + m))
SUB_LE_ADD = |- !n m p. n <= p ==> (m <= (p - n) = (n + m) <= p)
Theorem LESS_EQ_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQ_ANTISYM = |- !m n. ~(m < n /\ n <= m)
NOT_SUB_0 = |- !m n. m < n ==> ~(n - m = 0)
NOT_0_SUB = |- !m n. ~(m - n = 0) ==> ~(m = 0)
Theorem NOT_EQ_0 autoloading from theory `zero_ineq` ...
NOT_EQ_0 = |- !m. ~(m = 0) ==> m >= 1
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
SUB_1_LESS = |- !m n. ~(m = 0) /\ m < (SUC n) ==> (m - 1) < n
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
SUB_1_LESS_EQ = |- !m n. m < n ==> (n - 1) >= m
ADD_LESS_EQ_SUB = |- !n m p. n <= p ==> ((n + m) <= p = m <= (p - n))
PRE_SUB_SUC = |- !m n. m < n ==> (PRE(n - m) = n - (SUC m))
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
LESS_PRE = |- !i m. i < (m - 1) ==> i < m
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
PRE_LESS_LESS_SUC = |- !i m. i < (m - 1) /\ 0 < m ==> (i + 1) < m
Theorem SUC_0 autoloading from theory `suc` ...
SUC_0 = |- 1 = SUC 0
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Theorem SUB_PLUS autoloading from theory `arithmetic` ...
SUB_PLUS = |- !a b c. a - (b + c) = (a - b) - c
SUB_PRE_SUB_1 = |- !a b. 0 < b ==> ((a - (PRE b)) - 1 = a - b)
LESS_SUB_IMP_SUM_LESS = |- !i m. i < (m - 1) /\ 1 < m ==> (i + 1) < m
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c - c = 0
SUB_SELF = |- !c. c - c = 0
Theorem ADD_SUB autoloading from theory `arithmetic` ...
ADD_SUB = |- !a c. (a + c) - c = a
ADD_SUB_SYM = |- !a c. (c + a) - c = a
SUB_ADD_SELF = |- !m n. ~m < n ==> ((m - n) + n = m)
Theorem LESS_ANTISYM autoloading from theory `arithmetic` ...
LESS_ANTISYM = |- !m n. ~(m < n /\ n < m)
Theorem ADD_MONO_LESS autoloading from theory `add` ...
ADD_MONO_LESS = |- !m n p. (m + p) < (m + n) = p < n
Theorem LESS_MONO_ADD autoloading from theory `arithmetic` ...
LESS_MONO_ADD = |- !m n p. m < n ==> (m + p) < (n + p)
Theorem NOT_LESS_EQUAL autoloading from theory `arithmetic` ...
NOT_LESS_EQUAL = |- !m n. ~m <= n = n < m
Definition GREATER autoloading from theory `arithmetic` ...
GREATER = |- !m n. m > n = n < m
SMALLER_SUM = |- !m n p. m < p /\ n < p ==> ~((m + n) - p) > m
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
NOT_LESS_SUB = |- !m n. ~m < (m - n)
SUB_BOTH_SIDES = |- !m n p. (m = n) ==> (m - p = n - p)
Theorem LESS_EQ_LESS_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_LESS_TRANS = |- !m n p. m <= n /\ n < p ==> m < p
SUB_LESS_BOTH_SIDES = |- !m n p. p <= m /\ m < n ==> (m - p) < (n - p)
Theorem LESS_LESS_MONO autoloading from theory `add` ...
LESS_LESS_MONO = |- !m n p q. m < p /\ n < q ==> (m + n) < (p + q)
LESS_TWICE_IMP_LESS_SUB =
|- !a b m. a < m /\ b < m /\ m <= (a + b) ==> ((a + b) - m) < m
Theorem SUB_LESS_OR autoloading from theory `arithmetic` ...
SUB_LESS_OR = |- !m n. n < m ==> n <= (m - 1)
Theorem OR_LESS autoloading from theory `arithmetic` ...
OR_LESS = |- !m n. (SUC m) <= n ==> m < n
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
SUB_LESS_EQ_SUB_SUC =
|- !a b c n. 0 < c /\ a <= (b - n) ==> (a - c) <= (b - (SUC n))
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
SUB_EQ_SUB_ADD_SUB =
|- !a b c. a <= b /\ b <= c ==> (c - a = (c - b) + (b - a))
Theorem ADD_EQ_SUB autoloading from theory `arithmetic` ...
ADD_EQ_SUB = |- !m n p. n <= p ==> ((m + n = p) = (m = p - n))
ADD_EQ_IMP_SUB_EQ = |- !a b c. (a = b + c) ==> (a - b = c)
Theorem LESS_0_CASES autoloading from theory `arithmetic` ...
LESS_0_CASES = |- !m. (0 = m) \/ 0 < m
SUB_GREATER_0 = |- !a b. a < b ==> (b - a) > 0
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
LESS_EQ_SUB_1 = |- !a b. a <= b ==> (a - 1) <= (b - 1)
SUB_LESS_EQ_SUB1 = |- !x. x > 0 ==> (!a. (a - x) <= (a - 1))
() : void
File sub loaded
() : void
#rm -f mult.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mult`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Theorem LESS_MONO_MULT autoloading from theory `arithmetic` ...
LESS_MONO_MULT = |- !m n p. m <= n ==> (m * p) <= (n * p)
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
LESS_MONO_MULT1 = |- !m n p. m <= n ==> (p * m) <= (p * n)
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Theorem LESS_EQ_LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_LESS_EQ_MONO =
|- !m n p q. m <= p /\ n <= q ==> (m + n) <= (p + q)
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
Theorem INDUCTION autoloading from theory `num` ...
INDUCTION = |- !P. P 0 /\ (!n. P n ==> P(SUC n)) ==> (!n. P n)
LESS_MULT_PLUS_DIFF = |- !n k l. k < l ==> ((k * n) + n) <= (l * n)
Theorem LESS_LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem TIMES2 autoloading from theory `arithmetic` ...
TIMES2 = |- !n. 2 * n = n + n
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Definition EXP autoloading from theory `arithmetic` ...
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
ONE_LESS_TWO_EXP_SUC = |- !n. 1 < (2 EXP (SUC n))
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
NOT_MULT_LESS_0 = |- !m n. 0 < m /\ 0 < n ==> 0 < (m * n)
EXP1 = |- !n. n EXP 1 = n
Theorem ZERO_LESS_EXP autoloading from theory `arithmetic` ...
ZERO_LESS_EXP = |- !m n. 0 < ((SUC n) EXP m)
ZERO_LESS_TWO_EXP = |- !n. 0 < (2 EXP n)
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
ONE_LESS_EQ_TWO_EXP = |- !n. 1 <= (2 EXP n)
() : void
File mult loaded
() : void
#rm -f odd_even.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `odd_even`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Definition EVEN autoloading from theory `arithmetic` ...
EVEN = |- (EVEN 0 = T) /\ (!n. EVEN(SUC n) = ~EVEN n)
Definition ODD autoloading from theory `arithmetic` ...
ODD = |- (ODD 0 = F) /\ (!n. ODD(SUC n) = ~ODD n)
EVEN_ODD_0 = |- EVEN 0 /\ ~ODD 0
NOT_EVEN_ODD_SUC_EVEN_ODD =
|- !n. (~EVEN(SUC n) = EVEN n) /\ (~ODD(SUC n) = ODD n)
Theorem EVEN_ODD autoloading from theory `arithmetic` ...
EVEN_ODD = |- !n. EVEN n = ~ODD n
Theorem ODD_EVEN autoloading from theory `arithmetic` ...
ODD_EVEN = |- !n. ODD n = ~EVEN n
EVEN_ODD_SUC = |- !n. (EVEN(SUC n) = ODD n) /\ (ODD(SUC n) = EVEN n)
Theorem ODD_ADD autoloading from theory `arithmetic` ...
ODD_ADD = |- !m n. ODD(m + n) = ~(ODD m = ODD n)
Theorem EVEN_ADD autoloading from theory `arithmetic` ...
EVEN_ADD = |- !m n. EVEN(m + n) = (EVEN m = EVEN n)
EVEN_ODD_PLUS_CASES =
|- !n m.
(ODD n /\ ODD m ==> EVEN(n + m)) /\
(ODD n /\ EVEN m ==> ODD(n + m)) /\
(EVEN n /\ EVEN m ==> EVEN(n + m))
Theorem EVEN_MULT autoloading from theory `arithmetic` ...
EVEN_MULT = |- !m n. EVEN(m * n) = EVEN m \/ EVEN n
EVEN_IMPL_MULT = |- !n m. EVEN n \/ EVEN m ==> EVEN(n * m)
Theorem ODD_MULT autoloading from theory `arithmetic` ...
ODD_MULT = |- !m n. ODD(m * n) = ODD m /\ ODD n
ODD_IMPL_MULT = |- !n m. ODD n /\ ODD m ==> ODD(n * m)
MULT_ODD = |- !n m. ODD(n * m) ==> ODD n /\ ODD m
MULT_EVEN = |- !n m. EVEN(n * m) ==> EVEN n \/ EVEN m
() : void
File odd_even loaded
() : void
#rm -f min_max.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `minmax`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
MAX_DEF = |- !n p. MAX n p = (n <= p => p | n)
Theorem ZERO_LESS_EQ autoloading from theory `arithmetic` ...
ZERO_LESS_EQ = |- !n. 0 <= n
MAX_0 = |- !n. MAX 0 n = n
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
MAX_SYM = |- !n p. MAX n p = MAX p n
MAX_REFL = |- !n. MAX n n = n
Theorem LESS_EQ_SUC_REFL autoloading from theory `arithmetic` ...
LESS_EQ_SUC_REFL = |- !m. m <= (SUC m)
MAX_SUC = |- !n. MAX n(SUC n) = SUC n
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
SUC_MAX = |- !n p. MAX(SUC n)(SUC p) = SUC(MAX n p)
MIN_DEF = |- !n p. MIN n p = (n <= p => n | p)
MIN_0 = |- !n. MIN 0 n = 0
MIN_SYM = |- !n p. MIN n p = MIN p n
MIN_REFL = |- !n. MIN n n = n
MIN_SUC = |- !n. MIN n(SUC n) = n
SUC_MIN = |- !n p. MIN(SUC n)(SUC p) = SUC(MIN n p)
() : void
File minmax loaded
() : void
#rm -f div_mod.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `div_mod`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
0 : int
() : void
Theorem LESS_MOD autoloading from theory `arithmetic` ...
LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
Theorem SUC_LESS autoloading from theory `prim_rec` ...
SUC_LESS = |- !m n. (SUC m) < n ==> m < n
SUC_MOD = |- !n m. (SUC n) < m ==> ((SUC n) MOD m = SUC(n MOD m))
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
NOT_MULT_LESS_0 = |- !m n. 0 < m /\ 0 < n ==> 0 < (m * n)
Theorem MOD_TIMES autoloading from theory `arithmetic` ...
MOD_TIMES = |- !n. 0 < n ==> (!q r. ((q * n) + r) MOD n = r MOD n)
Theorem MULT_ASSOC autoloading from theory `arithmetic` ...
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
Theorem MOD_MULT autoloading from theory `arithmetic` ...
MOD_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) MOD n = r)
Theorem DA autoloading from theory `arithmetic` ...
DA = |- !k n. 0 < n ==> (?r q. (k = (q * n) + r) /\ r < n)
MOD_MULT_MOD =
|- !m n. 0 < n /\ 0 < m ==> (!x. (x MOD (n * m)) MOD n = x MOD n)
MULT_LEFT_1 = |- !m. 1 * m = m
MULT_RIGHT_1 = |- !m. m * 1 = m
Theorem DIV_MULT autoloading from theory `arithmetic` ...
DIV_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) DIV n = q)
Theorem ADD_0 autoloading from theory `arithmetic` ...
ADD_0 = |- !m. m + 0 = m
MULT_DIV = |- !n q. 0 < n ==> ((q * n) DIV n = q)
DIV_ONE = |- !q. q DIV (SUC 0) = q
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
Definition MULT autoloading from theory `arithmetic` ...
MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
LESS_DIV_EQ_ZERO = |- !r n. r < n ==> (r DIV n = 0)
Theorem MOD_EQ_0 autoloading from theory `arithmetic` ...
MOD_EQ_0 = |- !n. 0 < n ==> (!k. (k * n) MOD n = 0)
SUC_MOD_SELF = |- !n. (SUC n) MOD (SUC n) = 0
Definition DIVISION autoloading from theory `arithmetic` ...
DIVISION =
|- !n.
0 < n ==> (!k. (k = ((k DIV n) * n) + (k MOD n)) /\ (k MOD n) < n)
Theorem MULT_SUC_EQ autoloading from theory `arithmetic` ...
MULT_SUC_EQ = |- !p m n. (n * (SUC p) = m * (SUC p)) = (n = m)
SUC_DIV_SELF = |- !n. (SUC n) DIV (SUC n) = 1
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
ADD_DIV_SUC_DIV = |- !n. 0 < n ==> (!r. (n + r) DIV n = SUC(r DIV n))
Theorem RIGHT_ADD_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
ADD_DIV_ADD_DIV =
|- !n. 0 < n ==> (!x r. ((x * n) + r) DIV n = x + (r DIV n))
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
SUC_DIV_CASES =
|- !n.
0 < n ==>
(!x. ((SUC x) DIV n = x DIV n) \/ ((SUC x) DIV n = SUC(x DIV n)))
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
Less_lemma = |- !m n. m < n ==> (?p. (n = m + p) /\ 0 < p)
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
LESS_MONO_DIV =
|- !n. 0 < n ==> (!p q. p < q ==> (p DIV n) <= (q DIV n))
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
LESS_EQ_MONO_DIV =
|- !n. 0 < n ==> (!p q. p <= q ==> (p DIV n) <= (q DIV n))
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Theorem LESS_LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
Less_MULT_lemma = |- !r m p. 0 < p ==> r < m ==> r < (p * m)
Theorem LESS_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
Less_MULT_ADD_lemma =
|- !m n r r'.
0 < m /\ 0 < n /\ r < m /\ r' < n ==> ((r' * m) + r) < (n * m)
Theorem ADD_INV_0_EQ autoloading from theory `arithmetic` ...
ADD_INV_0_EQ = |- !m n. (m + n = m) = (n = 0)
DIV_DIV_DIV_MULT =
|- !m n. 0 < m /\ 0 < n ==> (!x. (x DIV m) DIV n = x DIV (m * n))
() : void
File div_mod loaded
() : void
#rm -f more_arithmetic.th
echo 'set_flag(`abort_when_fail`,true);;'\
'loadt `mk_more_arithmetic`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
Theory ineq loaded
() : void
Theory pre loaded
() : void
Theory sub loaded
() : void
Theory mult loaded
() : void
Theory min_max loaded
() : void
Theory odd_even loaded
() : void
Theory div_mod loaded
() : void
() : void
File mk_more_arithmetic loaded
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `num_convs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
Theorem LESS_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
Theorem LESS_EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
NUM_LESS_EQ_PLUS_CONV = - : (term -> conv)
NUM_EQ_PLUS_CONV = - : (term -> conv)
NUM_LESS_PLUS_CONV = - : (term -> conv)
Calling Lisp compiler
File num_convs compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `num_tac`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
GEN_INDUCT_RULE = - : (thm -> thm -> thm)
GEN_INDUCT_TAC = - : tactic
Calling Lisp compiler
File num_tac compiled
() : void
#===> library more_arithmetic rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/more_arithmetic'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/numeral'
echo 'set_flag(`abort_when_fail`,true);;' \
'loadt `numeral_theory`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
false : bool
() : void
def_buffer = "T" : term
new_defn = - : (string list -> thm)
define = - : (term -> void)
File define loaded
() : void
Theorem LESS_0 autoloading from theory `prim_rec` ...
LESS_0 = |- !n. 0 < (SUC n)
Theorem NOT_SUC autoloading from theory `num` ...
NOT_SUC = |- !n. ~(SUC n = 0)
Theorem NOT_LESS_0 autoloading from theory `prim_rec` ...
NOT_LESS_0 = |- !n. ~n < 0
NOT_0_IMP_0_LESS = |- !n. ~(n = 0) = 0 < n
Theorem LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_EQ_TRANS = |- !m n p. m <= n /\ n <= p ==> m <= p
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
LESS_OR_EQ_IMP_LESS_OR_EQ_ADD = |- !m n p. m <= n ==> m <= (n + p)
Theorem LESS_EQ_MONO autoloading from theory `arithmetic` ...
LESS_EQ_MONO = |- !n m. (SUC n) <= (SUC m) = n <= m
Definition ADD autoloading from theory `arithmetic` ...
ADD = |- (!n. 0 + n = n) /\ (!m n. (SUC m) + n = SUC(m + n))
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
Definition MULT autoloading from theory `arithmetic` ...
MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
MULT_NONNEG_MONO_LESS_OR_EQ = |- !m n. 0 < m ==> n <= (m * n)
Theorem LESS_LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
ADDR_GREATER = |- !m n p. m < n ==> m < (n + p)
ADDL_GREATER = |- !m n p. m < n ==> m < (p + n)
Theorem LENGTH_APPEND autoloading from theory `list` ...
LENGTH_APPEND =
|- !l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)
Theorem LENGTH_SNOC autoloading from theory `list` ...
LENGTH_SNOC = |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
Theorem LENGTH_REVERSE autoloading from theory `list` ...
LENGTH_REVERSE = |- !l. LENGTH(REVERSE l) = LENGTH l
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
LENGTH_CLAUSES =
|- (LENGTH[] = 0) /\
(!h t. LENGTH(CONS h t) = SUC(LENGTH t)) /\
(!x l. LENGTH(SNOC x l) = SUC(LENGTH l)) /\
(!l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)) /\
(!l. LENGTH(REVERSE l) = LENGTH l)
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
Theorem LESS_EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_EQ_MONO_ADD_EQ = |- !m n p. (m + p) <= (n + p) = m <= n
Theorem RIGHT_ADD_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
Theorem LESS_ADD_1 autoloading from theory `arithmetic` ...
LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))
LESS_MULT_PLUS_DIFF = |- !n k l. k < l ==> ((k * n) + n) <= (l * n)
Theorem LAST autoloading from theory `list` ...
LAST = |- !x l. LAST(SNOC x l) = x
Theorem BUTLAST autoloading from theory `list` ...
BUTLAST = |- !x l. BUTLAST(SNOC x l) = l
Theorem NULL autoloading from theory `list` ...
NULL = |- NULL[] /\ (!h t. ~NULL(CONS h t))
Theorem SNOC_INDUCT autoloading from theory `list` ...
SNOC_INDUCT =
|- !P. P[] /\ (!l. P l ==> (!x. P(SNOC x l))) ==> (!l. P l)
SNOC_BUTLAST = |- !l. ~NULL l ==> (SNOC(LAST l)(BUTLAST l) = l)
Theorem LESS_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
LESS_LESS_MONO = |- !m n p q. m < p /\ n < q ==> (m + n) < (p + q)
Theorem LESS_EQ_REFL autoloading from theory `arithmetic` ...
LESS_EQ_REFL = |- !m. m <= m
Theorem LESS_EQUAL_ANTISYM autoloading from theory `arithmetic` ...
LESS_EQUAL_ANTISYM = |- !n m. n <= m /\ m <= n ==> (n = m)
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
NOT_EQ_LESS_EQ = |- !a b. ~(a = b) = a < b \/ b < a
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
GREATER_NOT_ZERO = |- !x. 0 < x ==> ~(x = 0)
Theorem NOT_LESS_EQUAL autoloading from theory `arithmetic` ...
NOT_LESS_EQUAL = |- !m n. ~m <= n = n < m
LESS_IS_NOT_LESS_OR_EQ = |- !x y. x < y = ~y <= x
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Definition REPLICATE autoloading from theory `list` ...
REPLICATE =
|- (!x. REPLICATE 0 x = []) /\
(!n x. REPLICATE(SUC n)x = CONS x(REPLICATE n x))
Theorem LENGTH_REPLICATE autoloading from theory `list` ...
LENGTH_REPLICATE = |- !n x. LENGTH(REPLICATE n x) = n
LENGTH_REPLICATE = |- !n e. LENGTH(REPLICATE n e) = n
Definition ALL_EL autoloading from theory `list` ...
ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
EVERY_REPLICATE = |- !n e. ALL_EL($= e)(REPLICATE n e)
() : void
IS_NORMALIZED =
|- !digits. IS_NORMALIZED digits = (digits = []) \/ 0 < (HD digits)
IS_NORMALIZED_NIL = |- IS_NORMALIZED[]
Theorem NOT_CONS_NIL autoloading from theory `list` ...
NOT_CONS_NIL = |- !h t. ~(CONS h t = [])
Definition HD autoloading from theory `list` ...
HD = |- !h t. HD(CONS h t) = h
IS_NORMALIZED_CONS = |- !e l. IS_NORMALIZED(CONS e l) = 0 < e
() : void
IS_BASEN =
|- !radix digits. IS_BASEN radix digits = ALL_EL($> radix)digits
IS_BASEN_NIL = |- !r. IS_BASEN r[]
Definition GREATER autoloading from theory `arithmetic` ...
GREATER = |- !m n. m > n = n < m
IS_BASEN_CONS = |- !r l e. IS_BASEN r(CONS e l) = e < r /\ IS_BASEN r l
IS_BASEN_CONS_IMP_LESS =
|- !r l e. 1 < r ==> IS_BASEN r(CONS e l) ==> e < r
IS_BASEN_CONS_IMP_IS_BASEN =
|- !r l e. 1 < r ==> IS_BASEN r(CONS e l) ==> IS_BASEN r l
Theorem list_Axiom autoloading from theory `list` ...
list_Axiom =
|- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
BASEN =
|- (!radix. BASEN radix[] = 0) /\
(!radix digit digits.
BASEN radix(CONS digit digits) =
(digit * (radix EXP (LENGTH digits))) + (BASEN radix digits))
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
BASEN_ZEROS = |- !r n. BASEN r(REPLICATE n 0) = 0
Theorem SUC_LESS autoloading from theory `prim_rec` ...
SUC_LESS = |- !m n. (SUC m) < n ==> m < n
Theorem ZERO_LESS_EXP autoloading from theory `arithmetic` ...
ZERO_LESS_EXP = |- !m n. 0 < ((SUC n) EXP m)
one_less_exp_lemma = . |- !m. 0 < (r EXP m)
BASEN_EMPTY_EQ_0 =
|- !r l. 1 < r ==> IS_NORMALIZED l ==> ((BASEN r l = 0) = (l = []))
BASEN_CONS_0 = |- !r l. BASEN r(CONS 0 l) = BASEN r l
Theorem MULT_ASSOC autoloading from theory `arithmetic` ...
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Definition EXP autoloading from theory `arithmetic` ...
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
Definition SNOC autoloading from theory `list` ...
SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
BASEN_SNOC = |- !r e l. BASEN r(SNOC e l) = ((BASEN r l) * r) + e
BASEN_DIGIT_EQ_DIGIT = |- !r e. BASEN r[e] = e
BASEN_EXP_N = |- !r n. BASEN r(CONS 1(REPLICATE n 0)) = r EXP n
BASEN_LESS_EXP_LENGTH =
|- !r l. 1 < r ==> IS_BASEN r l ==> (BASEN r l) < (r EXP (LENGTH l))
Theorem SUB_LESS_OR autoloading from theory `arithmetic` ...
SUB_LESS_OR = |- !m n. n < m ==> n <= (m - 1)
BASEN_LESS_OR_EQ_EXP_LENGTH =
|- !r l.
1 < r ==> IS_BASEN r l ==> (BASEN r l) <= ((r EXP (LENGTH l)) - 1)
Theorem DIV_MULT autoloading from theory `arithmetic` ...
DIV_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) DIV n = q)
Theorem MOD_MULT autoloading from theory `arithmetic` ...
MOD_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) MOD n = r)
numeral_lemma =
|- !r' n r q q'.
r' < n ==>
r < n ==>
((q * n) + r = (q' * n) + r') ==>
(r = r') /\ (q = q')
basen_and_eq_lemma = ..... |- (BASEN r l1 = BASEN r l2) /\ (h = h')
Theorem CONS_11 autoloading from theory `list` ...
CONS_11 = |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
Theorem SUC_NOT autoloading from theory `arithmetic` ...
SUC_NOT = |- !n. ~(0 = SUC n)
Theorem list_INDUCT autoloading from theory `list` ...
list_INDUCT =
|- !P. P[] /\ (!t. P t ==> (!h. P(CONS h t))) ==> (!l. P l)
BASEN_11 =
|- !r l1 l2.
1 < r ==>
IS_BASEN r l1 ==>
IS_BASEN r l2 ==>
(LENGTH l1 = LENGTH l2) ==>
(BASEN r l1 = BASEN r l2) ==>
(l1 = l2)
Theorem SUB_0 autoloading from theory `arithmetic` ...
SUB_0 = |- !m. (0 - m = 0) /\ (m - 0 = m)
Theorem SUB_MONO_EQ autoloading from theory `arithmetic` ...
SUB_MONO_EQ = |- !n m. (SUC n) - (SUC m) = n - m
BASEN_EXP_LESS_OR_EQ =
|- !r l.
1 < r ==>
~NULL l ==>
IS_NORMALIZED l ==>
IS_BASEN r l ==>
(r EXP ((LENGTH l) - 1)) <= (BASEN r l)
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
BASEN_EXP_LESS =
|- !r l.
IS_BASEN r l ==>
IS_NORMALIZED l ==>
~NULL l ==>
1 < r ==>
((r EXP ((LENGTH l) - 1)) - 1) < (BASEN r l)
BASEN_ONTO = |- !r l. ?n. BASEN r l = n
Theorem LEFT_ADD_DISTRIB autoloading from theory `arithmetic` ...
LEFT_ADD_DISTRIB = |- !m n p. p * (m + n) = (p * m) + (p * n)
Theorem EXP_ADD autoloading from theory `arithmetic` ...
EXP_ADD = |- !p q n. n EXP (p + q) = (n EXP p) * (n EXP q)
Definition APPEND autoloading from theory `list` ...
APPEND =
|- (!l. APPEND[]l = l) /\
(!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
BASEN_APPEND =
|- !r l m.
BASEN r(APPEND l m) =
((r EXP (LENGTH m)) * (BASEN r l)) + (BASEN r m)
IS_BASEN_APPEND =
|- !r l m. IS_BASEN r(APPEND l m) = IS_BASEN r l /\ IS_BASEN r m
Theorem LESS_MOD autoloading from theory `arithmetic` ...
LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
Theorem MOD_TIMES autoloading from theory `arithmetic` ...
MOD_TIMES = |- !n. 0 < n ==> (!q r. ((q * n) + r) MOD n = r MOD n)
Theorem LESS_MONO_EQ autoloading from theory `arithmetic` ...
LESS_MONO_EQ = |- !m n. (SUC m) < (SUC n) = m < n
Theorem num_CASES autoloading from theory `arithmetic` ...
num_CASES = |- !m. (m = 0) \/ (?n. m = SUC n)
Theorem SUC_SUB1 autoloading from theory `arithmetic` ...
SUC_SUB1 = |- !m. (SUC m) - 1 = m
Definition TL autoloading from theory `list` ...
TL = |- !h t. TL(CONS h t) = t
Theorem list_CASES autoloading from theory `list` ...
list_CASES = |- !l. (l = []) \/ (?t h. l = CONS h t)
BASEN_TRAILING =
|- !r l.
1 < r ==>
IS_BASEN r l ==>
~NULL l ==>
(BASEN r(TL l) = (BASEN r l) MOD (r EXP ((LENGTH l) - 1)))
Theorem SNOC_APPEND autoloading from theory `list` ...
SNOC_APPEND = |- !x l. SNOC x l = APPEND l[x]
BASEN_LEADING =
|- !r l.
1 < r ==>
IS_BASEN r l ==>
~NULL l ==>
(BASEN r(BUTLAST l) = (BASEN r l) DIV r)
Theorem LESS_EQ_EXISTS autoloading from theory `arithmetic` ...
LESS_EQ_EXISTS = |- !m n. m <= n = (?p. n = m + p)
Theorem LESS_THM autoloading from theory `prim_rec` ...
LESS_THM = |- !m n. m < (SUC n) = (m = n) \/ m < n
NORMALIZED_LENGTHS_LEMMA =
|- !l1 l2 r.
~(1 < r /\
IS_BASEN r l1 /\
IS_BASEN r l2 /\
IS_NORMALIZED l1 /\
IS_NORMALIZED l2 /\
(BASEN r l1 = BASEN r l2) /\
(LENGTH l1) < (LENGTH l2))
NORMALIZED_LENGTHS =
|- !l1 l2 r.
1 < r ==>
IS_BASEN r l1 ==>
IS_BASEN r l2 ==>
IS_NORMALIZED l1 ==>
IS_NORMALIZED l2 ==>
(BASEN r l1 = BASEN r l2) ==>
(LENGTH l1 = LENGTH l2)
NORMALIZED_BASEN_11 =
|- !l1 l2 r.
1 < r ==>
IS_BASEN r l1 ==>
IS_BASEN r l2 ==>
IS_NORMALIZED l1 ==>
IS_NORMALIZED l2 ==>
(BASEN r l1 = BASEN r l2) ==>
(l1 = l2)
Definition DIVISION autoloading from theory `arithmetic` ...
DIVISION =
|- !n.
0 < n ==> (!k. (k = ((k DIV n) * n) + (k MOD n)) /\ (k MOD n) < n)
div_mod_lemma =
. |- (n = ((n DIV (r EXP m)) * (r EXP m)) + (n MOD (r EXP m))) /\
(n MOD (r EXP m)) < (r EXP m)
BASEN_ONTO_MOD_LEMMA =
|- !m n r.
?l. 1 < r ==> n < (r EXP m) ==> (LENGTH l = m) /\ (n = BASEN r l)
BASEN_MOD_ONTO_LEMMA =
|- !n m r. ?l. 1 < r ==> (LENGTH l = n) /\ (BASEN r l = m MOD (r EXP n))
BASEN_DIGITS_EXISTS =
|- ?f.
!n m r.
1 < r ==>
(LENGTH(f r n m) = n) /\ (BASEN r(f r n m) = m MOD (r EXP n))
BASEN_DIGITS =
|- !n m r.
1 < r ==>
(LENGTH(BASEN_DIGITS r n m) = n) /\
(BASEN r(BASEN_DIGITS r n m) = m MOD (r EXP n))
SELECT_TAC = - : tactic
EXP_1 = |- !r. r EXP 1 = r
MULT_POS_MONO = |- !m n. 0 < n ==> m <= (m * n)
POS_EXP_POS = |- !r x. 0 < r ==> 0 < x ==> r <= (r EXP x)
LESS_LEMMA1 = |- !m n. m < (SUC n) ==> (m = n) \/ m < n
LESS_MONO_REV = |- !m n. (SUC m) < (SUC n) ==> m < n
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
MULT_LESS_MULT = |- !m n p q. m < n ==> p < q ==> (m * p) < (n * q)
MULT_POS_STRICT_MONO = |- !m n p. n < p ==> n < ((SUC m) * p)
Theorem LESS_EXP_SUC_MONO autoloading from theory `arithmetic` ...
LESS_EXP_SUC_MONO =
|- !n m. ((SUC(SUC m)) EXP n) < ((SUC(SUC m)) EXP (SUC n))
EXP_LESS_EXP = |- !m n n'. 1 < m ==> n < n' ==> (m EXP n) < (m EXP n')
EXP_2_STRICT_MONO = |- !m n. 1 < m ==> 1 < n ==> m < (m EXP n)
NUM_CASES_DISJ = |- !n m. m < n \/ (m = n) \/ n < m
Theorem LESS_MULT_MONO autoloading from theory `arithmetic` ...
LESS_MULT_MONO = |- !m i n. ((SUC n) * m) < ((SUC n) * i) = m < i
MULT_POS_STRICT_MONO2 =
|- !m n1 n2. 0 < m ==> ((m * n1) < (m * n2) = n1 < n2)
() : void
LOG = |- !r n. LOG r n = (@x. (r EXP x) <= n /\ n < (r EXP (x + 1)))
Theorem LESS_OR autoloading from theory `arithmetic` ...
LESS_OR = |- !m n. m < n ==> (SUC m) <= n
Theorem LESS_0_CASES autoloading from theory `arithmetic` ...
LESS_0_CASES = |- !m. (0 = m) \/ 0 < m
LOG_1 = |- !r. 1 < r ==> (LOG r 1 = 0)
() : void
File numeral_theory loaded
() : void
#rm -f dummy.th
echo 'set_flag(`abort_when_fail`,true);;' \
'new_theory `dummy`;;' \
'load_library `reduce`;;' \
'new_parent `numeral`;;' \
'let t = `numeral` in do' \
'map (\s. autoload_theory(`definition`,t,fst s)) (definitions t);' \
'map (\s. autoload_theory(`theorem`,t,fst s)) (theorems t);;' \
'compilet `numeral_rules`;;' \
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
Loading library reduce ...
Extending help search path.
Loading boolean conversions........
Loading arithmetic conversions..................
Loading general conversions, rule and tactic.....
Library reduce loaded.
() : void
Theory numeral loaded
() : void
[();
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: void list
Theorem LESS_EQ_ADD autoloading from theory `arithmetic` ...
LESS_EQ_ADD = |- !m n. m <= (m + n)
Theorem ADD_ASSOC autoloading from theory `arithmetic` ...
ADD_ASSOC = |- !m n p. m + (n + p) = (m + n) + p
Theorem LESS_EQ_EXISTS autoloading from theory `arithmetic` ...
LESS_EQ_EXISTS = |- !m n. m <= n = (?p. n = m + p)
ADDR_GREATER_EQ = |- !m n p. m <= n ==> m <= (n + p)
Theorem LESS_ANTISYM autoloading from theory `arithmetic` ...
LESS_ANTISYM = |- !m n. ~(m < n /\ n < m)
NOT_LESS_AND_GREATER = |- !n m. n < m ==> ~m < n
Theorem LESS_MONO_ADD_EQ autoloading from theory `arithmetic` ...
LESS_MONO_ADD_EQ = |- !m n p. (m + p) < (n + p) = m < n
Theorem ADD_SYM autoloading from theory `arithmetic` ...
ADD_SYM = |- !m n. m + n = n + m
ADD_MONO_LESS = |- !m n p. (m + p) < (m + n) = p < n
Theorem ADD_SUB autoloading from theory `arithmetic` ...
ADD_SUB = |- !a c. (a + c) - c = a
ADD_EQ_IMP_SUB_EQ = |- !a b c. (a = b + c) ==> (a - b = c)
radices = [10; 16] : int list
max = - : (int -> int -> int)
max_radix = 16 : int
() : void
upto = - : (int -> int list)
zero_upto = - : (int -> int list)
lengthen = - : (* -> int -> * list -> * list)
listify = - : (* -> * list)
firstn = - : (int -> * list -> * list)
butfirstn = - : (int -> * list -> * list)
absolute_value = - : (int -> int)
mk_binary_comb = - : (term -> term -> term -> term)
dest_unary_comb = - : (term -> term -> term)
dest_binary_comb = - : (term -> term -> (term # term))
mk_term_list = - : ((string # type) -> int -> term list)
Definition SNOC autoloading from theory `list` ...
SNOC =
|- (!x. SNOC x[] = [x]) /\
(!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
CONS_OF_SNOC_CONV = - : conv
SNOC_OF_CONS_CONV = - : conv
Definition GREATER autoloading from theory `arithmetic` ...
GREATER = |- !m n. m > n = n < m
Theorem LESS_SUC autoloading from theory `prim_rec` ...
LESS_SUC = |- !m n. m < n ==> m < (SUC n)
Theorem LESS_SUC_REFL autoloading from theory `prim_rec` ...
LESS_SUC_REFL = |- !n. n < (SUC n)
Definition LENGTH autoloading from theory `list` ...
LENGTH = |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
LENGTH_COMPARE_CONV = - : conv
Theorem LESS_NOT_EQ autoloading from theory `prim_rec` ...
LESS_NOT_EQ = |- !m n. m < n ==> ~(m = n)
COMPARE_EQ_RULE = - : (thm -> thm)
COMPARE_LT_RULE = - : (thm -> thm)
Theorem NOT_LESS autoloading from theory `arithmetic` ...
NOT_LESS = |- !m n. ~m < n = n <= m
Definition LESS_OR_EQ autoloading from theory `arithmetic` ...
LESS_OR_EQ = |- !m n. m <= n = m < n \/ (m = n)
COMPARE_LE_RULE = - : (thm -> thm)
Theorem LESS_REFL autoloading from theory `prim_rec` ...
LESS_REFL = |- !n. ~n < n
COMPARE_GT_RULE = - : (thm -> thm)
Theorem GREATER_EQ autoloading from theory `arithmetic` ...
GREATER_EQ = |- !n m. n >= m = m <= n
Definition GREATER_OR_EQ autoloading from theory `arithmetic` ...
GREATER_OR_EQ = |- !m n. m >= n = m > n \/ (m = n)
COMPARE_GE_RULE = - : (thm -> thm)
LENGTH_EQ_CONV = - : conv
is_lt = - : (term -> bool)
LENGTH_LT_CONV = - : conv
is_le = - : (term -> bool)
LENGTH_LE_CONV = - : conv
is_gt = - : (term -> bool)
LENGTH_GT_CONV = - : conv
is_ge = - : (term -> bool)
LENGTH_GE_CONV = - : conv
fast_num_CONV = - : conv
Theorem LESS_TRANS autoloading from theory `arithmetic` ...
LESS_TRANS = |- !m n p. m < n /\ n < p ==> m < p
Theorem EQ_LESS autoloading from theory `prim_rec` ...
EQ_LESS = |- !n. (SUC m = n) ==> m < n
fast_GT_CONV = - : conv
fast_LT_CONV = - : conv
mk_basen = - : (term -> term list -> term)
dest_basen = - : (term -> (term # term))
is_basen = - : (term -> bool)
dest_unary_basen_comb =
-
: (term -> (term # term # term # term # term list))
dest_binary_basen_comb =
-
: (term ->
(term # term # term # term # term list # term # term # term list))
numeral_of_int = - : ((int # int) -> int list)
basen_of_numeral = - : ((int # int list) -> term)
basen_of_int = - : ((int # int) -> term)
numeral_of_basen = - : (term -> (int # int list))
int_of_numeral = - : ((int # int list) -> int)
int_of_basen = - : (term -> int)
Definition ALL_EL autoloading from theory `list` ...
ALL_EL =
|- (!P. ALL_EL P[] = T) /\
(!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
Definition IS_BASEN autoloading from theory `numeral` ...
IS_BASEN =
|- !radix digits. IS_BASEN radix digits = ALL_EL($> radix)digits
Theorem IS_BASEN_NIL autoloading from theory `numeral` ...
IS_BASEN_NIL = |- !r. IS_BASEN r[]
IS_BASEN_CONV = - : conv
Theorem IS_NORMALIZED_CONS autoloading from theory `numeral` ...
IS_NORMALIZED_CONS = |- !e l. IS_NORMALIZED(CONS e l) = 0 < e
Theorem IS_NORMALIZED_NIL autoloading from theory `numeral` ...
IS_NORMALIZED_NIL = |- IS_NORMALIZED[]
IS_NORMALIZED_CONV = - : conv
Theorem BASEN_CONS_0 autoloading from theory `numeral` ...
BASEN_CONS_0 = |- !r l. BASEN r(CONS 0 l) = BASEN r l
ONCE_BASEN_NORMALIZE_CONV = - : conv
BASEN_NORMALIZE_CONV = - : conv
ONCE_BASEN_DENORMALIZE_CONV = - : conv
BASEN_DENORMALIZE_CONV = - : (int -> conv)
Theorem ADD_CLAUSES autoloading from theory `arithmetic` ...
ADD_CLAUSES =
|- (0 + m = m) /\
(m + 0 = m) /\
((SUC m) + n = SUC(m + n)) /\
(m + (SUC n) = SUC(m + n))
Theorem MULT_CLAUSES autoloading from theory `arithmetic` ...
MULT_CLAUSES =
|- !m n.
(0 * m = 0) /\
(m * 0 = 0) /\
(1 * m = m) /\
(m * 1 = m) /\
((SUC m) * n = (m * n) + n) /\
(m * (SUC n) = m + (m * n))
Theorem LESS_MONO_MULT autoloading from theory `arithmetic` ...
LESS_MONO_MULT = |- !m n p. m <= n ==> (m * p) <= (n * p)
Theorem LESS_EQ autoloading from theory `arithmetic` ...
LESS_EQ = |- !m n. m < n = (SUC m) <= n
Definition MULT autoloading from theory `arithmetic` ...
MULT = |- (!n. 0 * n = 0) /\ (!m n. (SUC m) * n = (m * n) + n)
Theorem BASEN_LESS_EXP_LENGTH autoloading from theory `numeral` ...
BASEN_LESS_EXP_LENGTH =
|- !r l. 1 < r ==> IS_BASEN r l ==> (BASEN r l) < (r EXP (LENGTH l))
Theorem LESS_LESS_EQ_TRANS autoloading from theory `arithmetic` ...
LESS_LESS_EQ_TRANS = |- !m n p. m < n /\ n <= p ==> m < p
Definition BASEN autoloading from theory `numeral` ...
BASEN =
|- (!radix. BASEN radix[] = 0) /\
(!radix digit digits.
BASEN radix(CONS digit digits) =
(digit * (radix EXP (LENGTH digits))) + (BASEN radix digits))
BASEN_COMPARE_CONV = - : conv
BASEN_EQ_CONV = - : conv
BASEN_LT_CONV = - : conv
BASEN_LE_CONV = - : conv
BASEN_GT_CONV = - : conv
BASEN_GE_CONV = - : conv
Theorem ADD_SUC autoloading from theory `arithmetic` ...
ADD_SUC = |- !m n. SUC(m + n) = m + (SUC n)
fast_add = - : (int -> int -> thm)
fast_add_with_carry = - : (int -> int -> int -> thm)
fast_mul_with_carry = - : (int -> int -> int -> thm)
Theorem MOD_TIMES autoloading from theory `arithmetic` ...
MOD_TIMES = |- !n. 0 < n ==> (!q r. ((q * n) + r) MOD n = r MOD n)
Definition DIVISION autoloading from theory `arithmetic` ...
DIVISION =
|- !n.
0 < n ==> (!k. (k = ((k DIV n) * n) + (k MOD n)) /\ (k MOD n) < n)
Theorem EQ_MONO_ADD_EQ autoloading from theory `arithmetic` ...
EQ_MONO_ADD_EQ = |- !m n p. (m + p = n + p) = (m = n)
Theorem RIGHT_ADD_DISTRIB autoloading from theory `arithmetic` ...
RIGHT_ADD_DISTRIB = |- !m n p. (m + n) * p = (m * p) + (n * p)
Theorem DIV_UNIQUE autoloading from theory `arithmetic` ...
DIV_UNIQUE =
|- !n k q. (?r. (k = (q * n) + r) /\ r < n) ==> (k DIV n = q)
Theorem MOD_MULT autoloading from theory `arithmetic` ...
MOD_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) MOD n = r)
Theorem DIV_MULT autoloading from theory `arithmetic` ...
DIV_MULT = |- !n r. r < n ==> (!q. ((q * n) + r) DIV n = q)
fast_div_mod = - : (int -> int -> (thm # thm))
basen_add_basecase =
|- !r.
((BASEN r[]) + (BASEN r[]) = BASEN r[0]) /\
(LENGTH[] = LENGTH[]) /\
(LENGTH[] = LENGTH[])
Theorem MULT_ASSOC autoloading from theory `arithmetic` ...
MULT_ASSOC = |- !m n p. m * (n * p) = (m * n) * p
Definition EXP autoloading from theory `arithmetic` ...
EXP = |- (!m. m EXP 0 = 1) /\ (!m n. m EXP (SUC n) = m * (m EXP n))
basen_add_step_lemma =
|- !r.
0 < r ==>
(!x y xs ys z zs.
((BASEN r xs) + (BASEN r ys) = BASEN r(CONS z zs)) /\
(LENGTH xs = LENGTH ys) /\
(LENGTH xs = LENGTH zs) ==>
((BASEN r(CONS x xs)) + (BASEN r(CONS y ys)) =
BASEN r(CONS(((x + y) + z) DIV r)(CONS(((x + y) + z) MOD r)zs))) /\
(LENGTH(CONS x xs) = LENGTH(CONS y ys)) /\
(LENGTH(CONS x xs) = LENGTH(CONS(((x + y) + z) MOD r)zs)))
PURE_BASEN_ADD_CONV = - : conv
BASEN_ADD_CONV = - : conv
Theorem ADD_0 autoloading from theory `arithmetic` ...
ADD_0 = |- !m. m + 0 = m
Theorem ADD1 autoloading from theory `arithmetic` ...
ADD1 = |- !m. SUC m = m + 1
PURE_BASEN_SUC_CONV = - : conv
BASEN_SUC_CONV = - : conv
Theorem SUB_EQ_0 autoloading from theory `arithmetic` ...
SUB_EQ_0 = |- !m n. (m - n = 0) = m <= n
Theorem SUB_EQUAL_0 autoloading from theory `arithmetic` ...
SUB_EQUAL_0 = |- !c. c - c = 0
BASEN_SUB_CONV = - : conv
Theorem PRE_SUB1 autoloading from theory `arithmetic` ...
PRE_SUB1 = |- !m. PRE m = m - 1
PURE_BASEN_PRE_CONV = - : conv
BASEN_PRE_CONV = - : conv
basen_mul_basecase =
|- !r n.
((BASEN r[]) * (BASEN r[n]) = BASEN r[0]) /\ (LENGTH[] = LENGTH[])
Theorem MULT_SYM autoloading from theory `arithmetic` ...
MULT_SYM = |- !m n. m * n = n * m
Theorem BASEN_DIGIT_EQ_DIGIT autoloading from theory `numeral` ...
BASEN_DIGIT_EQ_DIGIT = |- !r e. BASEN r[e] = e
basen_mul_step_lemma =
|- !r.
(0 < r = T) ==>
(!n x xs y ys.
((BASEN r xs) * (BASEN r[n]) = BASEN r(CONS y ys)) /\
(LENGTH xs = LENGTH ys) ==>
((BASEN r(CONS x xs)) * (BASEN r[n]) =
BASEN r(CONS(((n * x) + y) DIV r)(CONS(((n * x) + y) MOD r)ys))) /\
(LENGTH(CONS x xs) = LENGTH(CONS(((n * x) + y) MOD r)ys)))
PURE_BASEN_MUL_BY_DIGIT_CONV = - : conv
basen_mul_sum_basecase = |- !r x. BASEN r[BASEN r x] = BASEN r x
basen_mul_sum_step_lemma =
|- !r x1 x2 xs.
BASEN r(CONS(BASEN r x1)(CONS(BASEN r x2)xs)) =
BASEN r(CONS(((BASEN r x1) * r) + (BASEN r x2))xs)
Theorem LEFT_ADD_DISTRIB autoloading from theory `arithmetic` ...
LEFT_ADD_DISTRIB = |- !m n p. p * (m + n) = (p * m) + (p * n)
Theorem BASEN_SNOC autoloading from theory `numeral` ...
BASEN_SNOC = |- !r e l. BASEN r(SNOC e l) = ((BASEN r l) * r) + e
basen_extend_mul_lemma =
|- !x r y more_zs.
(x * (BASEN r[y]) = BASEN r more_zs) ==>
(!ys zs.
(x * (BASEN r ys) = BASEN r zs) ==>
(x * (BASEN r(SNOC y ys)) = BASEN r[BASEN r zs;BASEN r more_zs]))
PURE_BASEN_MUL_EXTEND_RULE = - : (term -> thm -> thm)
basen_mul_combine_pps_basecase =
|- !r y.
(BASEN r[BASEN r[];BASEN r[y]] = BASEN r[0;y]) /\
(LENGTH[y] = SUC(LENGTH[])) /\
(LENGTH[y] = SUC(LENGTH[]))
basen_mul_combine_pps_step_lemma =
|- !r.
0 < r ==>
(!x y xs ys z zs.
(BASEN r[BASEN r xs;BASEN r ys] = BASEN r(CONS z zs)) /\
(LENGTH ys = SUC(LENGTH xs)) /\
(LENGTH zs = SUC(LENGTH xs)) ==>
(BASEN r[BASEN r(CONS x xs);BASEN r(CONS y ys)] =
BASEN r(CONS(((x + y) + z) DIV r)(CONS(((x + y) + z) MOD r)zs))) /\
(LENGTH(CONS y ys) = SUC(LENGTH(CONS x xs))) /\
(LENGTH(CONS(((x + y) + z) MOD r)zs) = SUC(LENGTH(CONS x xs))))
PURE_BASEN_MUL_COMBINE_PPS_CONV = - : conv
BASEN_MUL_COMBINE_PPS_CONV = - : conv
BASEN_MUL_EXTEND_RULE = - : (term -> thm -> thm)
basen_mul_basecase = |- !r x. x * (BASEN r[]) = BASEN r[]
BASEN_MUL_SNOC_CONV = - : conv
STEP_BASEN_MUL_CONV = - : conv
Theorem INV_SUC_EQ autoloading from theory `prim_rec` ...
INV_SUC_EQ = |- !m n. (SUC m = SUC n) = (m = n)
Theorem LENGTH_MAP autoloading from theory `list` ...
LENGTH_MAP = |- !l f. LENGTH(MAP f l) = LENGTH l
Theorem BASEN_APPEND autoloading from theory `numeral` ...
BASEN_APPEND =
|- !r l m.
BASEN r(APPEND l m) =
((r EXP (LENGTH m)) * (BASEN r l)) + (BASEN r m)
Definition MAP autoloading from theory `list` ...
MAP =
|- (!f. MAP f[] = []) /\ (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
BASEN_MUL_CONV = - : conv
LESS_DIV = |- !n k. k < n ==> (k DIV n = 0)
Theorem LESS_MOD autoloading from theory `arithmetic` ...
LESS_MOD = |- !n k. k < n ==> (k MOD n = k)
LESS_DIV_MOD = |- !n k. k < n ==> (k DIV n = 0) /\ (k MOD n = k)
less_divmod_thm =
|- !dividend divisor r. ((BASEN r[]) * divisor) + dividend = dividend
basen_divmod_conv = - : (term -> conv)
BASEN_DIV_CONV = - : conv
Theorem MOD_UNIQUE autoloading from theory `arithmetic` ...
MOD_UNIQUE =
|- !n k r. (?q. (k = (q * n) + r) /\ r < n) ==> (k MOD n = r)
BASEN_MOD_CONV = - : conv
Theorem EXP_ADD autoloading from theory `arithmetic` ...
EXP_ADD = |- !p q n. n EXP (p + q) = (n EXP p) * (n EXP q)
BASEN_EXP_CONV = - : conv
BASEN_CONV = - : conv
BASEN_OF_NUM_CONV = - : (term -> conv)
NUM_ARITH_CONV = - : conv
NUM_ARITH_RULE = - : (thm -> thm)
NUM_ARITH_TAC = - : tactic
Calling Lisp compiler
File numeral_rules compiled
() : void
#rm -f dummy.th
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/numeral'
make[4]: Entering directory '/<<PKGBUILDDIR>>/Library/ind_defs'
echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `ind-defs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
mk_predv = - : (term list -> term)
checkfilter = - : (* list -> * list -> * list -> * list)
checkside = - : (term -> term -> term)
mk_mk_pred =
-
: ((term # term list # term list) -> (term # term # (term -> term)))
make_rule =
-
: ((term # term # term list # (term -> term)) -> goal -> term)
make_definition = - : ((term # term list) -> goal list -> term)
derive_induction = - : conv
usedef = - : ((term list # thm) -> ((thm -> thm) # conv))
eximp = - : (term list -> thm -> (term # thm))
derive_rule = - : (term -> ((thm -> thm) # conv) -> thm -> thm)
derive_rules = - : conv
prove_inductive_relation_exists =
-
: ((term # term list) -> goal list -> thm)
- : ((term # term list) -> goal list -> thm)
prove_inductive_relation_exists =
-
: ((term # term list) -> goal list -> thm)
new_inductive_definition =
-
: (bool ->
string ->
(term # term list) ->
goal list ->
(thm list # thm))
simp_axiom = - : ((thm # term) -> thm)
reduce_asm = - : (term -> conv)
prove_asm = - : (term -> conv)
simp_concl = - : (thm -> conv)
simp_rule = - : ((thm # term) -> thm)
simp = - : ((thm # term) -> thm)
derive_strong_induction = - : ((thm list # thm) -> thm)
- : ((thm list # thm) -> thm)
derive_strong_induction = - : ((thm list # thm) -> thm)
MK_CONJ_THEN = - : (term -> term -> thm_tactic -> thm_tactical)
MK_CHOOSE_THEN =
-
: (term -> * list -> term -> thm_tactic -> thm_tactical)
MK_THEN = - : (term -> term -> thm_tactic -> thm_tactical)
TACF = - : (term -> term -> thm_tactic -> thm_tactic -> tactic)
TACS = - : (term -> term -> thm_tactic -> thm_tactic -> tactic list)
mkred = - : (term -> term list -> conv)
RED_CASE = - : (term -> term -> conv)
APPLY_CASE = - : (conv list -> conv)
RED_WHERE = - : (term -> term -> conv)
is_param = - : (* list -> (* # *) list -> * -> bool)
RULE_INDUCT_THEN = - : (thm -> thm_tactic -> thm_tactic -> tactic)
- : (thm -> thm_tactic -> thm_tactic -> tactic)
RULE_INDUCT_THEN = - : (thm -> thm_tactic -> thm_tactic -> tactic)
axiom_tac = - : thm_tactic
prove_conj = - : (thm list -> conv)
RULE_TAC = - : thm_tactic
- : thm_tactic
RULE_TAC = - : thm_tactic
reduce =
-
: (term list ->
thm list ->
thm list ->
(term # term) list ->
(thm list # (term # term) list))
REDUCE = - : conv
- : conv
REDUCE = - : conv
MATCH_MP = - : (thm -> thm -> thm)
LIST_NOT_FORALL = - : ((thm -> (thm # *)) -> thm -> (thm # *))
simp_axiom =
-
: ((thm -> thm -> thm) -> term list -> thm -> thm -> (thm # thm))
crul = - : (term -> thm -> thm)
CONJ_RUL = - : (term -> thm -> thm)
LIST_EXISTS_THEN = - : ((thm -> thm) -> thm -> thm)
RULE = - : (thm -> thm -> thm)
EXISTS_IMP2 = - : (term -> thm -> thm)
efn = - : (term -> thm -> thm)
RULE2 = - : (* -> thm -> thm -> thm)
NOT_NOT = - : (thm -> thm)
simp_rule =
-
: ((thm -> thm -> thm) ->
term ->
term list ->
thm ->
thm ->
(thm # thm))
simp = - : (term -> (thm -> thm -> thm) -> thm -> thm -> (thm # thm))
LIST_DE_MORGAN =
-
: ((* -> thm -> (thm # thm)) -> * list -> thm -> (thm # thm))
derive_cases_thm = - : ((thm list # thm) -> thm)
- : ((thm list # thm) -> thm)
derive_cases_thm = - : ((thm list # thm) -> thm)
Calling Lisp compiler
File ind-defs compiled
() : void
#echo 'set_flag(`abort_when_fail`,true);;'\
'compilet `ind_defs`;;'\
'quit();;' | /<<PKGBUILDDIR>>/hol
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#false : bool
() : void
Calling Lisp compiler
File ind_defs compiled
() : void
#===> library ind_defs rebuilt
make[4]: Leaving directory '/<<PKGBUILDDIR>>/Library/ind_defs'
=======> library rebuilt
make[3]: Leaving directory '/<<PKGBUILDDIR>>/Library'
date
Thu Jan 19 18:31:35 UTC 2023
make[2]: Leaving directory '/<<PKGBUILDDIR>>'
date
Thu Jan 19 18:31:35 UTC 2023
make permissions
make[2]: Entering directory '/<<PKGBUILDDIR>>'
find $(ls -1 | grep -v debian) \
\( -type d -exec chmod 775 {} \; \) -o\
\( -type f -exec chmod 664 {} \; \)
for f in hol hol-lcf basic-hol Manual/LaTeX/makeindex Manual/LaTeX/makeindex.bin/*/makeindex Manual/Reference/bin/mktex Manual/Reference/bin/typecheck ; do\
( if [ -f $f ] ; then\
find $f -exec chmod 775 {} \; ;fi) ; \
done
make[2]: Leaving directory '/<<PKGBUILDDIR>>'
=======> hol Version 2.02 (GCL) and libraries made
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
find -name "raw_*_map" -exec rm {} \;
for i in $(find -maxdepth 1 -name "*hol*"); do \
printf 'install `'/usr/share/hol88-2.02.19940316dfsg'`;;\nlisp `(ml-save "foo")`;;\n' | ./$i &&\
mv foo $i; done
HOL-LCF version 2.02 (GCL) created 19/1/23
#HOL installed (`/usr/share/hol88-2.02.19940316dfsg`)
() : void
#
BASIC-HOL version 2.02 (GCL) created 19/1/23
#HOL installed (`/usr/share/hol88-2.02.19940316dfsg`)
() : void
#
===============================================================================
HOL88 Version 2.02 (GCL), built on 19/1/23
===============================================================================
#HOL installed (`/usr/share/hol88-2.02.19940316dfsg`)
() : void
#touch build-arch-stamp
fakeroot debian/rules binary-arch
find -maxdepth 1 -name "*hol*" | awk '{a=$1;sub("/[^/]*$","",a);printf("%s usr/lib/hol88-2.02.19940316dfsg/%s\n",$1,a);}' >>debian/hol88.install
echo debian/hol88.sh usr/bin >>debian/hol88.install
find Library -name "*.o" | awk '{a=$1;sub("/[^/]*$","",a);printf("%s usr/lib/hol88-2.02.19940316dfsg/%s\n",$1,a);}' >>debian/hol88-library.install
find * -maxdepth 0 -name "*hol*" | awk '{printf("/usr/lib/hol88-2.02.19940316dfsg/%s usr/share/hol88-2.02.19940316dfsg/%s\n",$1,$1);}' >>debian/hol88.links
find Library -name "*.o" | awk '{printf("/usr/lib/hol88-2.02.19940316dfsg/%s usr/share/hol88-2.02.19940316dfsg/%s\n",$1,$1);}' >>debian/hol88-library.links
echo "#!/bin/bash" >debian/hol88.sh
echo >>debian/hol88.sh
echo "exec /usr/lib/hol88-2.02.19940316dfsg/hol" >>debian/hol88.sh
chmod 755 debian/hol88.sh
dh_testdir
dh_testroot
dh_prep -a -X./ml/site.ml.orig -X./contrib/tooltool/Makefile.orig \
-X./contrib/tooltool/events.c.orig -X./contrib/tooltool/func_fix.c.orig \
-X./contrib/tooltool/lex.c.orig -X./contrib/tooltool/parse.y.orig \
-X./contrib/tooltool/patchlevel.h.orig -X./contrib/tooltool/windows.c.orig \
-X./contrib/Xhelp/hol_apro.orig -X./contrib/Xhelp/hol_ref.orig \
-X./contrib/Xhelp/xholhelp.h.orig -X./contrib/Xhelp/hol_thm.orig
dh_installdirs -a
dh_installdirs: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_install -a
dh_install: warning: Compatibility levels before 10 are deprecated (level 9 in use)
mv debian/hol88/usr/bin/hol88.sh debian/hol88/usr/bin/hol88
/usr/bin/make -f debian/rules DH_OPTIONS=-a binary-common
make[1]: Entering directory '/<<PKGBUILDDIR>>'
dh_testdir
dh_testroot
dh_installchangelogs
dh_installchangelogs: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_installdocs
dh_installdocs: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_installexamples
dh_installexamples: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_installman
dh_installman: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_lintian
dh_link
dh_link: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_strip
dh_strip: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_strip: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_compress
dh_compress: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_compress: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_fixperms
dh_makeshlibs
dh_makeshlibs: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_installdeb
dh_installdeb: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_shlibdeps
dh_shlibdeps: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_shlibdeps: warning: Compatibility levels before 10 are deprecated (level 9 in use)
dh_gencontrol
dh_md5sums
dh_builddeb
dpkg-deb: building package 'hol88' in '../hol88_2.02.19940316dfsg-5_armhf.deb'.
dpkg-deb: building package 'hol88-library' in '../hol88-library_2.02.19940316dfsg-5_armhf.deb'.
make[1]: Leaving directory '/<<PKGBUILDDIR>>'
dpkg-genbuildinfo --build=any -O../hol88_2.02.19940316dfsg-5_armhf.buildinfo
dpkg-genchanges --build=any -mRaspbian wandboard test autobuilder <root@raspbian.org> -O../hol88_2.02.19940316dfsg-5_armhf.changes
dpkg-genchanges: info: binary-only arch-specific upload (source code and arch-indep packages not included)
dpkg-source --after-build .
dpkg-buildpackage: info: binary-only upload (no source included)
--------------------------------------------------------------------------------
Build finished at 2023-01-19T18:34:12Z
Finished
--------
I: Built successfully
+------------------------------------------------------------------------------+
| Post Build Chroot |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Changes |
+------------------------------------------------------------------------------+
hol88_2.02.19940316dfsg-5_armhf.changes:
----------------------------------------
Format: 1.8
Date: Sun, 08 Jan 2023 17:11:46 -0500
Source: hol88
Binary: hol88 hol88-library
Architecture: armhf
Version: 2.02.19940316dfsg-5
Distribution: bookworm-staging
Urgency: medium
Maintainer: Raspbian wandboard test autobuilder <root@raspbian.org>
Changed-By: Camm Maguire <camm@debian.org>
Description:
hol88 - Higher Order Logic, system image
hol88-library - Higher Order Logic, binary library modules
Changes:
hol88 (2.02.19940316dfsg-5) unstable; urgency=medium
.
* build-dep latest gcl
Checksums-Sha1:
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a13cad005b40c8b7fbf0f578fc8f2bd8c577a262 9864 hol88_2.02.19940316dfsg-5_armhf.buildinfo
28531b809a2464439a8d57a0c91f657290b3c120 5376676 hol88_2.02.19940316dfsg-5_armhf.deb
Checksums-Sha256:
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c130e672d412e2909c2cfd8bc53e6df9fb005ab11887f31b655d4ef486f0f3a3 9864 hol88_2.02.19940316dfsg-5_armhf.buildinfo
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Files:
ce32b6cf2586275fc550c5563e44c327 3546264 math optional hol88-library_2.02.19940316dfsg-5_armhf.deb
eb085e8bca98f713228e555d64df94a4 9864 math optional hol88_2.02.19940316dfsg-5_armhf.buildinfo
9f9ab747885f25e84db02082ad9412b9 5376676 math optional hol88_2.02.19940316dfsg-5_armhf.deb
+------------------------------------------------------------------------------+
| Package contents |
+------------------------------------------------------------------------------+
hol88-library_2.02.19940316dfsg-5_armhf.deb
-------------------------------------------
new Debian package, version 2.0.
size 3546264 bytes: control archive=3736 bytes.
601 bytes, 15 lines control
11128 bytes, 115 lines md5sums
Package: hol88-library
Source: hol88
Version: 2.02.19940316dfsg-5
Architecture: armhf
Maintainer: Camm Maguire <camm@debian.org>
Installed-Size: 19710
Section: math
Priority: optional
Description: Higher Order Logic, binary library modules
The HOL System is an environment for interactive theorem proving in a
higher-order logic. Its most outstanding feature is its high degree
of programmability through the meta-language ML. The system has a
wide variety of uses from formalizing pure mathematics to
verification of industrial hardware. Academic and industrial sites
world-wide are using HOL.
drwxr-xr-x root/root 0 2023-01-08 22:11 ./
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/abs_theory/
-rw-r--r-- root/root 297976 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/abs_theory/abs_theory_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/
-rw-r--r-- root/root 123514 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/arith_cons_ml.o
-rw-r--r-- root/root 124103 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/decls_ml.o
-rw-r--r-- root/root 66142 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/exists_arith_ml.o
-rw-r--r-- root/root 80077 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/gen_arith_ml.o
-rw-r--r-- root/root 29074 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/instance_ml.o
-rw-r--r-- root/root 46884 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/int_extra_ml.o
-rw-r--r-- root/root 195084 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/norm_arith_ml.o
-rw-r--r-- root/root 62230 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/norm_bool_ml.o
-rw-r--r-- root/root 67105 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/norm_ineqs_ml.o
-rw-r--r-- root/root 48861 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/prenex_ml.o
-rw-r--r-- root/root 106333 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/qconv_ml.o
-rw-r--r-- root/root 106835 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/rationals_ml.o
-rw-r--r-- root/root 124436 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/sol_ranges_ml.o
-rw-r--r-- root/root 197241 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/solve_ineqs_ml.o
-rw-r--r-- root/root 92824 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/solve_ml.o
-rw-r--r-- root/root 65918 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/streams_ml.o
-rw-r--r-- root/root 24946 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/string_extra_ml.o
-rw-r--r-- root/root 59088 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/sub_and_cond_ml.o
-rw-r--r-- root/root 246319 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/sup-inf_ml.o
-rw-r--r-- root/root 116382 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/arith/term_coeffs_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/finite_sets/
-rw-r--r-- root/root 209067 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/finite_sets/fset_conv_ml.o
-rw-r--r-- root/root 59504 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/finite_sets/set_ind_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/ind_defs/
-rw-r--r-- root/root 699283 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/ind_defs/ind-defs_ml.o
-rw-r--r-- root/root 18821 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/ind_defs/ind_defs_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/
-rw-r--r-- root/root 62718 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/filters_ml.o
-rw-r--r-- root/root 157935 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/formaters_ml.o
-rw-r--r-- root/root 76838 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/hol_trees_ml.o
-rw-r--r-- root/root 37621 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_sets_pp_ml.o
-rw-r--r-- root/root 226636 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_term_pp_ml.o
-rw-r--r-- root/root 38255 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_thm_pp_ml.o
-rw-r--r-- root/root 64041 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_type_pp_ml.o
-rw-r--r-- root/root 46267 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/latex-hol/precedence_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/more_arithmetic/
-rw-r--r-- root/root 61923 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/more_arithmetic/num_convs_ml.o
-rw-r--r-- root/root 73389 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/more_arithmetic/num_tac_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/numeral/
-rw-r--r-- root/root 2100033 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/numeral/numeral_rules_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/
-rw-r--r-- root/root 149972 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/all_ml.o
-rw-r--r-- root/root 310844 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/basic_ml.o
-rw-r--r-- root/root 141534 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/both1_ml.o
-rw-r--r-- root/root 241777 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/both2_ml.o
-rw-r--r-- root/root 697391 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/conv_ml.o
-rw-r--r-- root/root 224912 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/exi_ml.o
-rw-r--r-- root/root 33919 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/pair_ml.o
-rw-r--r-- root/root 184045 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pair/syn_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/parser/
-rw-r--r-- root/root 196846 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/parser/general_ml.o
-rw-r--r-- root/root 665120 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/parser/parser_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pred_sets/
-rw-r--r-- root/root 242032 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pred_sets/fset_conv_ml.o
-rw-r--r-- root/root 150524 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pred_sets/gspec_ml.o
-rw-r--r-- root/root 62751 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/pred_sets/set_ind_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/
-rw-r--r-- root/root 179197 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_term_pp_ml.o
-rw-r--r-- root/root 38201 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_thm_pp_ml.o
-rw-r--r-- root/root 76846 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_trees_ml.o
-rw-r--r-- root/root 64028 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_type_pp_ml.o
-rw-r--r-- root/root 26619 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/link_to_hol_ml.o
-rw-r--r-- root/root 74714 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/new_printers_ml.o
-rw-r--r-- root/root 42149 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/precedence_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/
-rw-r--r-- root/root 37857 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/PP_to_ML_ml.o
-rw-r--r-- root/root 605641 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/convert_ml.o
-rw-r--r-- root/root 178280 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/generate_ml.o
-rw-r--r-- root/root 147478 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/lex_ml.o
-rw-r--r-- root/root 184222 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/pp_lang1_pp_ml.o
-rw-r--r-- root/root 244979 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/pp_lang2_pp_ml.o
-rw-r--r-- root/root 633743 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/syntax_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/
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drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/window/
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drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/Library/word/
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drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/doc/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/doc/hol88-library/
-rw-r--r-- root/root 509 2023-01-08 22:11 ./usr/share/doc/hol88-library/changelog.Debian.gz
-rw-r--r-- root/root 1124 2010-11-05 16:09 ./usr/share/doc/hol88-library/copyright
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/abs_theory/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/abs_theory/abs_theory_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/abs_theory/abs_theory_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/arith_cons_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/arith_cons_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/decls_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/decls_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/exists_arith_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/exists_arith_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/gen_arith_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/gen_arith_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/instance_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/instance_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/int_extra_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/int_extra_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/norm_arith_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/norm_arith_ml.o
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lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/prenex_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/prenex_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/qconv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/qconv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/rationals_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/rationals_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/sol_ranges_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/sol_ranges_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/solve_ineqs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/solve_ineqs_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/solve_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/solve_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/streams_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/streams_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/string_extra_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/string_extra_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/sub_and_cond_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/sub_and_cond_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/sup-inf_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/sup-inf_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/arith/term_coeffs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/arith/term_coeffs_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/finite_sets/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/finite_sets/fset_conv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/finite_sets/fset_conv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/finite_sets/set_ind_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/finite_sets/set_ind_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/ind_defs/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/ind_defs/ind-defs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/ind_defs/ind-defs_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/ind_defs/ind_defs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/ind_defs/ind_defs_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/filters_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/filters_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/formaters_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/formaters_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/hol_trees_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/hol_trees_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/latex_sets_pp_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_sets_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/latex_term_pp_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_term_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/latex_thm_pp_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_thm_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/latex_type_pp_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/latex_type_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/latex-hol/precedence_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/latex-hol/precedence_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/more_arithmetic/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/more_arithmetic/num_convs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/more_arithmetic/num_convs_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/more_arithmetic/num_tac_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/more_arithmetic/num_tac_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/numeral/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/numeral/numeral_rules_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/numeral/numeral_rules_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/all_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/all_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/basic_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/basic_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/both1_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/both1_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/both2_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/both2_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/conv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/conv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/exi_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/exi_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/pair_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/pair_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pair/syn_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pair/syn_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/parser/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/parser/general_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/parser/general_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/parser/parser_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/parser/parser_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pred_sets/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pred_sets/fset_conv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pred_sets/fset_conv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pred_sets/gspec_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pred_sets/gspec_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/pred_sets/set_ind_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/pred_sets/set_ind_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_term_pp_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_term_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_thm_pp_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_thm_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_trees_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_trees_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_type_pp_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/hol_type_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/link_to_hol_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/link_to_hol_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/new_printers_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/new_printers_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/precedence_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_hol/precedence_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/PP_to_ML_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/PP_to_ML_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/convert_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/convert_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/generate_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/generate_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/lex_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/lex_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/pp_lang1_pp_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/pp_lang1_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/pp_lang2_pp_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/pp_lang2_pp_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/syntax_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_parser/syntax_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/boxes_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/boxes_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/boxtostring_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/boxtostring_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/extents_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/extents_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/print_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/print_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/ptree_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/ptree_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/strings_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/strings_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/treematch_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/treematch_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/treetobox_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/treetobox_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/utils_ml.o -> ../../../../../lib/hol88-2.02.19940316dfsg/Library/prettyp/PP_printer/utils_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/record_proof/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/record_proof/dummy_funs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/record_proof/dummy_funs_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/record_proof/proof_rec_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/record_proof/proof_rec_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/reduce/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/reduce/arithconv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/reduce/arithconv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/reduce/boolconv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/reduce/boolconv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/reduce/reduce_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/reduce/reduce_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/res_quan/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/res_quan/cond_rewr_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/res_quan/cond_rewr_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/res_quan/res_rules_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/res_quan/res_rules_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/sets/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/sets/fset_conv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/sets/fset_conv_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/sets/gspec_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/sets/gspec_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/sets/set_ind_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/sets/set_ind_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/string/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/string/ascii_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/string/ascii_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/string/string_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/string/string_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/string/string_rules_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/string/string_rules_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/string/stringconv_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/string/stringconv_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/taut/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/taut/taut_check_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/taut/taut_check_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/extents_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/extents_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/extract_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/extract_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/matching_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/matching_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/name_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/name_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/search_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/search_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/sets_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/sets_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/sidecond_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/sidecond_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/struct_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/struct_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/thmkind_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/thmkind_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/trs/user_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/trs/user_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/unwind/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/unwind/unwinding_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/unwind/unwinding_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/basic_close_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/basic_close_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/eq_close_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/eq_close_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/hol_ext_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/hol_ext_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/imp_close_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/imp_close_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/inter_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/inter_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/load_code_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/load_code_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/load_window_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/load_window_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/ml_ext_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/ml_ext_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/tables_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/tables_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/tactic_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/tactic_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/thms_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/thms_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/win_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/win_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/window_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/window_ml.o
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/window/xlabel_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/window/xlabel_ml.o
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/word/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/Library/word/word_convs_ml.o -> ../../../../lib/hol88-2.02.19940316dfsg/Library/word/word_convs_ml.o
hol88_2.02.19940316dfsg-5_armhf.deb
-----------------------------------
new Debian package, version 2.0.
size 5376676 bytes: control archive=972 bytes.
686 bytes, 15 lines control
538 bytes, 8 lines md5sums
Package: hol88
Version: 2.02.19940316dfsg-5
Architecture: armhf
Maintainer: Camm Maguire <camm@debian.org>
Installed-Size: 43303
Depends: libc6 (>= 2.34), libedit2 (>= 2.11-20080614-0), libgmp10 (>= 2:6.2.1+dfsg1), libtirpc3 (>= 1.0.2), libx11-6
Section: math
Priority: optional
Description: Higher Order Logic, system image
The HOL System is an environment for interactive theorem proving in a
higher-order logic. Its most outstanding feature is its high degree
of programmability through the meta-language ML. The system has a
wide variety of uses from formalizing pure mathematics to
verification of industrial hardware. Academic and industrial sites
world-wide are using HOL.
drwxr-xr-x root/root 0 2023-01-08 22:11 ./
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/bin/
-rwxr-xr-x root/root 55 2023-01-08 22:11 ./usr/bin/hol88
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/
-rwxr-xr-x root/root 15410784 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/basic-hol
-rwxr-xr-x root/root 18237064 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/hol
-rwxr-xr-x root/root 10671672 2023-01-08 22:11 ./usr/lib/hol88-2.02.19940316dfsg/hol-lcf
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/doc/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/doc/hol88/
-rw-r--r-- root/root 449 2010-11-05 16:09 ./usr/share/doc/hol88/README.Debian
-rw-r--r-- root/root 503 2023-01-08 22:11 ./usr/share/doc/hol88/changelog.Debian.gz
-rw-r--r-- root/root 1124 2010-11-05 16:09 ./usr/share/doc/hol88/copyright
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/basic-hol -> ../../lib/hol88-2.02.19940316dfsg/basic-hol
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/hol -> ../../lib/hol88-2.02.19940316dfsg/hol
lrwxrwxrwx root/root 0 2023-01-08 22:11 ./usr/share/hol88-2.02.19940316dfsg/hol-lcf -> ../../lib/hol88-2.02.19940316dfsg/hol-lcf
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/man/
drwxr-xr-x root/root 0 2023-01-08 22:11 ./usr/share/man/man1/
-rw-r--r-- root/root 734 2023-01-08 22:11 ./usr/share/man/man1/hol88.1.gz
+------------------------------------------------------------------------------+
| Post Build |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Cleanup |
+------------------------------------------------------------------------------+
Purging /<<BUILDDIR>>
Not cleaning session: cloned chroot in use
+------------------------------------------------------------------------------+
| Summary |
+------------------------------------------------------------------------------+
Build Architecture: armhf
Build-Space: 202340
Build-Time: 3234
Distribution: bookworm-staging
Host Architecture: armhf
Install-Time: 1808
Job: hol88_2.02.19940316dfsg-5
Machine Architecture: armhf
Package: hol88
Package-Time: 5122
Source-Version: 2.02.19940316dfsg-5
Space: 202340
Status: successful
Version: 2.02.19940316dfsg-5
--------------------------------------------------------------------------------
Finished at 2023-01-19T18:34:12Z
Build needed 01:25:22, 202340k disc space