"_build/install/default/share/matita/myshare/AUTHORS" {"matita/myshare/AUTHORS"}
"_build/install/default/share/matita/myshare/LICENSE" {"matita/myshare/LICENSE"}
"_build/install/default/share/matita/myshare/closed.xml" {"matita/myshare/closed.xml"}
- "_build/install/default/share/matita/myshare/help/C/Makefile" {"matita/myshare/help/C/Makefile"}
- "_build/install/default/share/matita/myshare/help/C/TODO" {"matita/myshare/help/C/TODO"}
"_build/install/default/share/matita/myshare/help/C/declarative_tactics_quickref.xml" {"matita/myshare/help/C/declarative_tactics_quickref.xml"}
- "_build/install/default/share/matita/myshare/help/C/docbook.css" {"matita/myshare/help/C/docbook.css"}
- "_build/install/default/share/matita/myshare/help/C/figures/database.dia" {"matita/myshare/help/C/figures/database.dia"}
- "_build/install/default/share/matita/myshare/help/C/figures/database.png" {"matita/myshare/help/C/figures/database.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/matita.png" {"matita/myshare/help/C/figures/matita.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox1.png" {"matita/myshare/help/C/figures/vbox1.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox2.png" {"matita/myshare/help/C/figures/vbox2.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox3.png" {"matita/myshare/help/C/figures/vbox3.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox35.png" {"matita/myshare/help/C/figures/vbox35.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox4.png" {"matita/myshare/help/C/figures/vbox4.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox5.png" {"matita/myshare/help/C/figures/vbox5.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox6.png" {"matita/myshare/help/C/figures/vbox6.png"}
- "_build/install/default/share/matita/myshare/help/C/figures/vbox7.png" {"matita/myshare/help/C/figures/vbox7.png"}
"_build/install/default/share/matita/myshare/help/C/legal.xml" {"matita/myshare/help/C/legal.xml"}
"_build/install/default/share/matita/myshare/help/C/matita.xml" {"matita/myshare/help/C/matita.xml"}
- "_build/install/default/share/matita/myshare/help/C/scripts/fix-symbols.sh" {"matita/myshare/help/C/scripts/fix-symbols.sh"}
"_build/install/default/share/matita/myshare/help/C/sec_commands.xml" {"matita/myshare/help/C/sec_commands.xml"}
"_build/install/default/share/matita/myshare/help/C/sec_declarative_tactics.xml" {"matita/myshare/help/C/sec_declarative_tactics.xml"}
"_build/install/default/share/matita/myshare/help/C/sec_gettingstarted.xml" {"matita/myshare/help/C/sec_gettingstarted.xml"}
"_build/install/default/share/matita/myshare/help/C/sec_usernotation.xml" {"matita/myshare/help/C/sec_usernotation.xml"}
"_build/install/default/share/matita/myshare/help/C/tactic_quickref.xml" {"matita/myshare/help/C/tactic_quickref.xml"}
"_build/install/default/share/matita/myshare/help/C/tactics_quickref.xml" {"matita/myshare/help/C/tactics_quickref.xml"}
- "_build/install/default/share/matita/myshare/help/C/version.txt" {"matita/myshare/help/C/version.txt"}
- "_build/install/default/share/matita/myshare/help/C/version.txt.in" {"matita/myshare/help/C/version.txt.in"}
- "_build/install/default/share/matita/myshare/help/C/xhtml1-transitional.dtd" {"matita/myshare/help/C/xhtml1-transitional.dtd"}
- "_build/install/default/share/matita/myshare/help/C/xsl/matita-fo.xsl" {"matita/myshare/help/C/xsl/matita-fo.xsl"}
- "_build/install/default/share/matita/myshare/help/C/xsl/matita-xhtml.xsl" {"matita/myshare/help/C/xsl/matita-xhtml.xsl"}
- "_build/install/default/share/matita/myshare/help/C/xsl/tactic_quickref.xsl" {"matita/myshare/help/C/xsl/tactic_quickref.xsl"}
"_build/install/default/share/matita/myshare/icons/matita-32.xpm" {"matita/myshare/icons/matita-32.xpm"}
"_build/install/default/share/matita/myshare/icons/matita-bulb-high.png" {"matita/myshare/icons/matita-bulb-high.png"}
"_build/install/default/share/matita/myshare/icons/matita-bulb-low.png" {"matita/myshare/icons/matita-bulb-low.png"}
"_build/install/default/share/matita/myshare/matita.lang" {"matita/myshare/matita.lang"}
"_build/install/default/share/matita/myshare/matita.ma.templ" {"matita/myshare/matita.ma.templ"}
]
+doc: [
+ "_build/install/default/doc/matita/html/WrtCoq.html" {"html/WrtCoq.html"}
+ "_build/install/default/doc/matita/html/authoring.html" {"html/authoring.html"}
+ "_build/install/default/doc/matita/html/axiom_definition_declaration.html" {"html/axiom_definition_declaration.html"}
+ "_build/install/default/doc/matita/html/ch05s02.html" {"html/ch05s02.html"}
+ "_build/install/default/doc/matita/html/cicbrowser.html" {"html/cicbrowser.html"}
+ "_build/install/default/doc/matita/html/command_check.html" {"html/command_check.html"}
+ "_build/install/default/doc/matita/html/command_coercion.html" {"html/command_coercion.html"}
+ "_build/install/default/doc/matita/html/command_include.html" {"html/command_include.html"}
+ "_build/install/default/doc/matita/html/command_include_alias.html" {"html/command_include_alias.html"}
+ "_build/install/default/doc/matita/html/command_qed.html" {"html/command_qed.html"}
+ "_build/install/default/doc/matita/html/command_qed_minus.html" {"html/command_qed_minus.html"}
+ "_build/install/default/doc/matita/html/command_unification_hint.html" {"html/command_unification_hint.html"}
+ "_build/install/default/doc/matita/html/command_universe_constraints.html" {"html/command_universe_constraints.html"}
+ "_build/install/default/doc/matita/html/docbook.css" {"html/docbook.css"}
+ "_build/install/default/doc/matita/html/index.html" {"html/index.html"}
+ "_build/install/default/doc/matita/html/inst_from_src.html" {"html/inst_from_src.html"}
+ "_build/install/default/doc/matita/html/macro_intro.html" {"html/macro_intro.html"}
+ "_build/install/default/doc/matita/html/proofs.html" {"html/proofs.html"}
+ "_build/install/default/doc/matita/html/proofstatus.html" {"html/proofstatus.html"}
+ "_build/install/default/doc/matita/html/sec_commands.html" {"html/sec_commands.html"}
+ "_build/install/default/doc/matita/html/sec_declarative_tactics.html" {"html/sec_declarative_tactics.html"}
+ "_build/install/default/doc/matita/html/sec_gettingstarted.html" {"html/sec_gettingstarted.html"}
+ "_build/install/default/doc/matita/html/sec_install.html" {"html/sec_install.html"}
+ "_build/install/default/doc/matita/html/sec_intro.html" {"html/sec_intro.html"}
+ "_build/install/default/doc/matita/html/sec_license.html" {"html/sec_license.html"}
+ "_build/install/default/doc/matita/html/sec_tacticals.html" {"html/sec_tacticals.html"}
+ "_build/install/default/doc/matita/html/sec_tactics.html" {"html/sec_tactics.html"}
+ "_build/install/default/doc/matita/html/sec_terms.html" {"html/sec_terms.html"}
+ "_build/install/default/doc/matita/html/sec_usernotation.html" {"html/sec_usernotation.html"}
+ "_build/install/default/doc/matita/html/tac_andelim.html" {"html/tac_andelim.html"}
+ "_build/install/default/doc/matita/html/tac_apply.html" {"html/tac_apply.html"}
+ "_build/install/default/doc/matita/html/tac_applyS.html" {"html/tac_applyS.html"}
+ "_build/install/default/doc/matita/html/tac_assume.html" {"html/tac_assume.html"}
+ "_build/install/default/doc/matita/html/tac_assumption.html" {"html/tac_assumption.html"}
+ "_build/install/default/doc/matita/html/tac_auto.html" {"html/tac_auto.html"}
+ "_build/install/default/doc/matita/html/tac_bydone.html" {"html/tac_bydone.html"}
+ "_build/install/default/doc/matita/html/tac_byinduction.html" {"html/tac_byinduction.html"}
+ "_build/install/default/doc/matita/html/tac_bytermweproved.html" {"html/tac_bytermweproved.html"}
+ "_build/install/default/doc/matita/html/tac_case.html" {"html/tac_case.html"}
+ "_build/install/default/doc/matita/html/tac_cases.html" {"html/tac_cases.html"}
+ "_build/install/default/doc/matita/html/tac_change.html" {"html/tac_change.html"}
+ "_build/install/default/doc/matita/html/tac_clear.html" {"html/tac_clear.html"}
+ "_build/install/default/doc/matita/html/tac_conclude.html" {"html/tac_conclude.html"}
+ "_build/install/default/doc/matita/html/tac_constructor.html" {"html/tac_constructor.html"}
+ "_build/install/default/doc/matita/html/tac_cut.html" {"html/tac_cut.html"}
+ "_build/install/default/doc/matita/html/tac_decompose.html" {"html/tac_decompose.html"}
+ "_build/install/default/doc/matita/html/tac_destruct.html" {"html/tac_destruct.html"}
+ "_build/install/default/doc/matita/html/tac_elim.html" {"html/tac_elim.html"}
+ "_build/install/default/doc/matita/html/tac_existselim.html" {"html/tac_existselim.html"}
+ "_build/install/default/doc/matita/html/tac_generalize.html" {"html/tac_generalize.html"}
+ "_build/install/default/doc/matita/html/tac_intro.html" {"html/tac_intro.html"}
+ "_build/install/default/doc/matita/html/tac_intro_clear.html" {"html/tac_intro_clear.html"}
+ "_build/install/default/doc/matita/html/tac_inversion.html" {"html/tac_inversion.html"}
+ "_build/install/default/doc/matita/html/tac_lapply.html" {"html/tac_lapply.html"}
+ "_build/install/default/doc/matita/html/tac_let.html" {"html/tac_let.html"}
+ "_build/install/default/doc/matita/html/tac_letin.html" {"html/tac_letin.html"}
+ "_build/install/default/doc/matita/html/tac_normalize.html" {"html/tac_normalize.html"}
+ "_build/install/default/doc/matita/html/tac_obtain.html" {"html/tac_obtain.html"}
+ "_build/install/default/doc/matita/html/tac_rewrite.html" {"html/tac_rewrite.html"}
+ "_build/install/default/doc/matita/html/tac_rewrite_step.html" {"html/tac_rewrite_step.html"}
+ "_build/install/default/doc/matita/html/tac_suppose.html" {"html/tac_suppose.html"}
+ "_build/install/default/doc/matita/html/tac_thatisequivalentto.html" {"html/tac_thatisequivalentto.html"}
+ "_build/install/default/doc/matita/html/tac_thesisbecomes.html" {"html/tac_thesisbecomes.html"}
+ "_build/install/default/doc/matita/html/tac_weneedtoprove.html" {"html/tac_weneedtoprove.html"}
+ "_build/install/default/doc/matita/html/tac_weproceedbycases.html" {"html/tac_weproceedbycases.html"}
+ "_build/install/default/doc/matita/html/tac_weproceedbyinduction.html" {"html/tac_weproceedbyinduction.html"}
+ "_build/install/default/doc/matita/html/tac_whd.html" {"html/tac_whd.html"}
+ "_build/install/default/doc/matita/html/tacticals.html" {"html/tacticals.html"}
+ "_build/install/default/doc/matita/html/tacticargs.html" {"html/tacticargs.html"}
+ "_build/install/default/doc/matita/matita.pdf"
+]
-
-#include ../../../Makefile.defs
-
XSLTPROC=xsltproc
XHTML_XSL=xsl/matita-xhtml.xsl
MAIN=matita.xml
DEPS := $(wildcard *.xml)
-DESTDIR = /usr/local/share/doc/matita/
-
all: quickref-stamp html-stamp pdf-stamp
quickref-stamp: tactics_quickref.xml declarative_tactics_quickref.xml
html: quickref-stamp html-stamp
html-stamp: $(MAIN) $(DEPS) $(XHTML_XSL)
$(XSLTPROC) $(XHTML_XSL) $<
+ cp *.css html
+ mv *.html html
+ cp -R figures/* html/figures/
touch $@
pdf: quickref-stamp pdf-stamp
%.ps: %.xml
dblatex -r scripts/fix-symbols.sh -t ps $<
-install: install-html install-pdf
-install-pdf: pdf-stamp
- mkdir -p $(DESTDIR)/pdf
- cp matita.pdf $(DESTDIR)/pdf
-
-install-html: html-stamp
- mkdir -p $(DESTDIR)/html
- cp *.html *.css $(DESTDIR)/html
- test -d $(DESTDIR)/html/figures || mkdir $(DESTDIR)/html/figures
- cp figures/* $(DESTDIR)/html/figures/
-
clean:
- rm -f *.html *.pdf *.ps *.dvi *.tex
+ rm -f html/*.html html/*.css html/figures/* *.pdf *.ps *.dvi *.tex
rm -f *-stamp
-
+++ /dev/null
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Matita vs Coq</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_intro.html" title="Chapter 1. Introduction" /><link rel="prev" href="sec_intro.html" title="Chapter 1. Introduction" /><link rel="next" href="sec_install.html" title="Chapter 2. Installation" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Matita vs Coq</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_intro.html">Prev</a> </td><th width="60%" align="center">Chapter 1. Introduction</th><td width="20%" align="right"> <a accesskey="n" href="sec_install.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="WrtCoq"></a>Matita vs Coq</h2></div></div></div><p>
- The system shares a common look&feel with the Coq proof assistant
- and its graphical user interface. The two systems have variants
- of the same logic,
- close proof languages and similar sets of tactics.
- From the user point of view the main lacking features
- with respect to Coq are:
- </p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>proof extraction;</p></li><li class="listitem"><p>an extensible language of tactics;</p></li><li class="listitem"><p>automatic implicit arguments;</p></li><li class="listitem"><p>several ad-hoc decision procedures;</p></li><li class="listitem"><p>several rarely used variants for most of the tactics;</p></li><li class="listitem"><p>sections and local variables. </p></li></ul></div><p>
- Still from the user point of view, the main differences with respect
- to Coq are:
- </p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>the language of tacticals that allows execution of partial tactical application;</p></li><li class="listitem"><p>the unification of the concept of metavariable and existential variable;</p></li><li class="listitem"><p>terms with subterms that cannot be inferred are always allowed as arguments of tactics or other commands;</p></li><li class="listitem"><p>ambiguous terms are disambiguated by direct interaction with the user;</p></li><li class="listitem"><p>theorems and definitions in the library are always accessible without needing to require/include them; right now, only notation needs to be included to become active, but we plan to remove this limitation.</p></li></ul></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_intro.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_intro.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_install.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 1. Introduction </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 2. Installation</td></tr></table></div></body></html>
\ No newline at end of file
+++ /dev/null
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Authoring</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /><link rel="prev" href="cicbrowser.html" title="Browsing and searching" /><link rel="next" href="sec_terms.html" title="Chapter 4. Syntax" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Authoring</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="cicbrowser.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Getting started</th><td width="20%" align="right"> <a accesskey="n" href="sec_terms.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="authoring"></a>Authoring</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="compilation"></a>How to compile a script</h3></div></div></div><p>
- Scripts are compiled to base URIs. Base URIs are of the form
- "cic:/matita/path" and are given once for all for a set
- of scripts using the "root" file.
- </p><p>
- A "root" file has to be placed in the root of a script set,
- for example, consider the following files and directories, and
- assume you keep files in "list" separated from files
- in "sort" (for example the former directory may contain
- functions and proofs about lists, while latter sorting algorithms
- for lists):
-</p><pre class="programlisting">
- list/
- list.ma (* depending just on the standard library *)
- utils/
- swap.ma (* including list.ma *)
- sort/
- qsort.ma (* including utils/swap.ma *)
-</pre><p>
- To be able to compile properly the contents of "list"
- a file called root has to be placed in it. The file should be like
- the following snippet.
-</p><pre class="programlisting">
- baseuri=cic:/matita/mydatastructures
-</pre><p>
- This file tells Matita that objects generated by
- "list.ma" have to be placed in
- "cic:/matita/mydatastructures/list" while
- objects generated by
- "swap.ma" have to be placed in
- "cic:/matita/mydatastructures/utils/swap".
- </p><p>
- Once you created the root file, you must generate a depend file.
- Enter the "list" directory (the root of yuor file set)
- and type "matitadep". Remember to regenerate the depend file
- every time you alter the dependencies of your files (for example
- including other scripts).
- You can now compile you files typing "matitac".
- </p><p>
- To compile the "sort" directory, create a root file
- in "sort/" like the following one and then run
- "matitadep".
-</p><pre class="programlisting">
- baseuri=cic:/matita/myalgorithms
- include_paths=../list
-</pre><p>
- The include_paths field can declare a list of paths separated by space.
- Please omit any "/" from the end of base URIs or paths.
- </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="authoringinterface"></a>The authoring interface</h3></div></div></div><p><span class="emphasis"><em>TODO</em></span></p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="cicbrowser.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_gettingstarted.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_terms.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Browsing and searching </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 4. Syntax</td></tr></table></div></body></html>
\ No newline at end of file
+++ /dev/null
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Definitions and declarations</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="next" href="proofs.html" title="Proofs" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Definitions and declarations</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_terms.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="proofs.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="axiom_definition_declaration"></a>Definitions and declarations</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="axiom"></a><span class="bold"><strong>axiom</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></h3></div></div></div><p><strong class="userinput"><code>axiom H: P</code></strong></p><p><span class="command"><strong>H</strong></span> is declared as an axiom that states <span class="command"><strong>P</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="definition"></a><span class="bold"><strong>definition</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>definition f: T ≝ t</code></strong></p><p><span class="command"><strong>f</strong></span> is defined as <span class="command"><strong>t</strong></span>;
- <span class="command"><strong>T</strong></span> is its type. An error is raised if the type of
- <span class="command"><strong>t</strong></span> is not convertible to <span class="command"><strong>T</strong></span>.</p><p><span class="command"><strong>T</strong></span> is inferred from <span class="command"><strong>t</strong></span> if
- omitted.</p><p><span class="command"><strong>t</strong></span> can be omitted only if <span class="command"><strong>T</strong></span> is
- given. In this case Matita enters in interactive mode and
- <span class="command"><strong>f</strong></span> must be defined by means of tactics.</p><p>Notice that the command is equivalent to <span class="command"><strong>theorem f: T ≝ t</strong></span>.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="discriminator"></a><span class="bold"><strong>discriminator</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></h3></div></div></div><p><strong class="userinput"><code>discriminator i</code></strong></p><p>Defines a new discrimination (injectivity+conflict) principle à la
- McBride for the inductive type <span class="command"><strong>i</strong></span>.</p><p>The principle will use John
- Major's equality if such equality is defined, otherwise it will use
- Leibniz equality; in the former case, it will be called
- <span class="command"><strong>i_jmdiscr</strong></span>, in the latter, <span class="command"><strong>i_discr</strong></span>.
- The command will fail if neither equality is available.</p><p>Discrimination principles are used by the destruct tactic and are
- usually automatically generated by Matita during the definition of the
- corresponding inductive type. This command is thus especially useful
- when the correct equality was not loaded at the time of that
- definition.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="inverter"></a><span class="bold"><strong>inverter</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>for</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> (<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>) [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>inverter n for i (path) : s</code></strong></p><p>Defines a new induction/inversion principle for the inductive type
- <span class="command"><strong>i</strong></span>, called <span class="command"><strong>n</strong></span>.</p><p><span class="command"><strong>(path)</strong></span> must be in the form <span class="command"><strong>(# # # ... #)</strong></span>,
- where each <span class="command"><strong>#</strong></span> can be either <span class="command"><strong>?</strong></span> or
- <span class="command"><strong>%</strong></span>, and the number of symbols is equal to the number of
- right parameters (indices) of <span class="command"><strong>i</strong></span>. Parentheses are
- mandatory. If the j-th symbol is
- <span class="command"><strong>%</strong></span>, Matita will generate a principle providing
- equations for reasoning on the j-th index of <span class="command"><strong>i</strong></span>. If the
- symbol is a <span class="command"><strong>?</strong></span>, no corresponding equation will be
- provided.</p><p><span class="command"><strong>s</strong></span>, which must be a sort, is the target sort of the
- induction/inversion principle and defaults to <span class="command"><strong>Prop</strong></span>.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="letrec"></a><span class="bold"><strong>letrec</strong></span> <span class="emphasis"><em>TODO</em></span></h3></div></div></div><p><span class="emphasis"><em>TODO</em></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="inductive"></a>[<span class="bold"><strong>inductive</strong></span>|<span class="bold"><strong>coinductive</strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args2">args2</a></em></span>]… <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span> [<span class="bold"><strong>|</strong></span>] [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…
-[<span class="bold"><strong>with</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span> [<span class="bold"><strong>|</strong></span>] [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…]…
-</h3></div></div></div><p><strong class="userinput"><code>inductive i x y z: S ≝ k1:T1 | … | kn:Tn with i' : S' ≝ k1':T1' | … | km':Tm'</code></strong></p><p>Declares a family of two mutually inductive types
- <span class="command"><strong>i</strong></span> and <span class="command"><strong>i'</strong></span> whose types are
- <span class="command"><strong>S</strong></span> and <span class="command"><strong>S'</strong></span>, which must be convertible
- to sorts.</p><p>The constructors <span class="command"><strong>ki</strong></span> of type <span class="command"><strong>Ti</strong></span>
- and <span class="command"><strong>ki'</strong></span> of type <span class="command"><strong>Ti'</strong></span> are also
- simultaneously declared. The declared types <span class="command"><strong>i</strong></span> and
- <span class="command"><strong>i'</strong></span> may occur in the types of the constructors, but
- only in strongly positive positions according to the rules of the
- calculus.</p><p>The whole family is parameterized over the arguments <span class="command"><strong>x,y,z</strong></span>.</p><p>If the keyword <span class="command"><strong>coinductive</strong></span> is used, the declared
- types are considered mutually coinductive.</p><p>Elimination principles for the record are automatically generated
- by Matita, if allowed by the typing rules of the calculus according to
- the sort <span class="command"><strong>S</strong></span>. If generated,
- they are named <span class="command"><strong>i_ind</strong></span>, <span class="command"><strong>i_rec</strong></span> and
- <span class="command"><strong>i_rect</strong></span> according to the sort of their induction
- predicate.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="record"></a><span class="bold"><strong>record</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args2">args2</a></em></span>]… <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span><span class="bold"><strong>{</strong></span>[<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>:</strong></span>|<span class="bold"><strong>:></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>;</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>:</strong></span>|<span class="bold"><strong>:></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…<span class="bold"><strong>}</strong></span></h3></div></div></div><p><strong class="userinput"><code>record id x y z: S ≝ { f1: T1; …; fn:Tn }</code></strong></p><p>Declares a new record family <span class="command"><strong>id</strong></span> parameterized over
- <span class="command"><strong>x,y,z</strong></span>.</p><p><span class="command"><strong>S</strong></span> is the type of the record
- and it must be convertible to a sort.</p><p>Each field <span class="command"><strong>fi</strong></span> is declared by giving its type
- <span class="command"><strong>Ti</strong></span>. A record without any field is admitted.</p><p>Elimination principles for the record are automatically generated
- by Matita, if allowed by the typing rules of the calculus according to
- the sort <span class="command"><strong>S</strong></span>. If generated,
- they are named <span class="command"><strong>i_ind</strong></span>, <span class="command"><strong>i_rec</strong></span> and
- <span class="command"><strong>i_rect</strong></span> according to the sort of their induction
- predicate.</p><p>For each field <span class="command"><strong>fi</strong></span> a record projection
- <span class="command"><strong>fi</strong></span> is also automatically generated if projection
- is allowed by the typing rules of the calculus according to the
- sort <span class="command"><strong>S</strong></span>, the type <span class="command"><strong>T1</strong></span> and
- the definability of depending record projections.</p><p>If the type of a field is declared with <span class="command"><strong>:></strong></span>,
- the corresponding record projection becomes an implicit coercion.
- This is just syntactic sugar and it has the same effect of declaring the
- record projection as a coercion later on.</p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_terms.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="proofs.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 4. Syntax </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Proofs</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>interpretation</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /><link rel="prev" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /><link rel="next" href="sec_tacticals.html" title="Chapter 6. Tacticals" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">interpretation</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_usernotation.html">Prev</a> </td><th width="60%" align="center">Chapter 5. Extending the syntax</th><td width="20%" align="right"> <a accesskey="n" href="sec_tacticals.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="idm2123"></a>interpretation</h2></div></div></div><p><strong class="userinput"><code>interpretation "description" 'symbol p<sub>1</sub> … p<sub>n</sub> =
- rhs</code></strong></p><p><a id="interpretation"></a>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>interpretation</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span> [<span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_argument">interpretation_argument</a></em></span>]…
- <span class="bold"><strong>=</strong></span>
- <span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span>
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It declares a bi-directional mapping <span class="command"><strong>{…}</strong></span> between the content-level AST <span class="command"><strong>'symbol t<sub>1</sub> … t<sub>n</sub></strong></span> and the semantic term <span class="command"><strong>rhs[{t<sub>1</sub>}/p<sub>1</sub>;…;{t<sub>n</sub>}/p<sub>n</sub>]</strong></span>
- (the simultaneous substitution in <span class="command"><strong>rhs</strong></span> of the
- interpretation <span class="command"><strong>{…}</strong></span> of every content-level
- actual argument <span class="command"><strong>t<sub>i</sub></strong></span> for its
- corresponding formal parameter
- <span class="command"><strong>p<sub>i</sub></strong></span>). The
- <span class="command"><strong>description</strong></span> must be a textual description of the
- meaning associated to <span class="command"><strong>'symbol</strong></span> by this
- interpretation, and is used by the user interface of Matita to
- provide feedback on the interpretation of ambiguous terms.
- </p></dd><dt><span class="term">Interpretation arguments:</span></dt><dd><div class="table"><a id="idm2170"></a><p class="title"><strong>Table 5.11. interpretation_argument</strong></p><div class="table-contents"><table class="table" summary="interpretation_argument" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.interpretation_argument"></a><span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_argument">interpretation_argument</a></em></span></td><td style="">::=</td><td style="">[<span class="bold"><strong>η</strong></span><span class="bold"><strong>.</strong></span>]… <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">A formal parameter. If the name of the formal parameter is
- prefixed by n symbols "η", then the mapping performs
- (multiple) η-expansions to grant that the semantic actual
- parameter begins with at least n λ-abstractions.</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm2185"></a><p class="title"><strong>Table 5.12. interpretation_rhs</strong></p><div class="table-contents"><table class="table" summary="interpretation_rhs" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.interpretation_rhs"></a><span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span></td><td style="">A constant, specified by its URI</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">A constant, specified by its name, or a bound variable. If
- the constant name is ambiguous, the one corresponding to the
- last implicitly or explicitly specified alias is used.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>?</strong></span></td><td style="">An implicit parameter</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span>
- <span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span>
- [<span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span>]…
- <span class="bold"><strong>)</strong></span></td><td style="">An application</td></tr></tbody></table></div></div><br class="table-break" /></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_usernotation.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_usernotation.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_tacticals.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 5. Extending the syntax </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 6. Tacticals</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Browsing and searching</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /><link rel="prev" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /><link rel="next" href="authoring.html" title="Authoring" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Browsing and searching</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_gettingstarted.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Getting started</th><td width="20%" align="right"> <a accesskey="n" href="authoring.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="cicbrowser"></a>Browsing and searching</h2></div></div></div><p>The CIC browser is used to browse and search the library.
- You can open a new CIC browser selecting "New Cic Browser"
- from the "View" menu of Matita, or by pressing "F3".
- The CIC browser is similar to a traditional Web browser.</p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="browsinglib"></a>Browsing the library</h3></div></div></div><p>To browse the library, type in the location bar the absolute URI of
- the theorem, definition or library fragment you are interested in.
- "cic:/" is the root of the library. Contributions developed
- in Matita are under "cic:/matita"; all the others are
- part of the library of Coq.</p><p>Following the hyperlinks it is possible to navigate in the Web
- of mathematical notions. Proof are rendered in pseudo-natural language
- and mathematical notation is used for formulae. For now, mathematical
- notation must be included in the current script to be activated, but we
- plan to remove this limitation.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="aboutproof"></a>Looking at a proof under development</h3></div></div></div><p>A proof under development is not yet part of the library.
- The special URI "about:proof" can be used to browse the
- proof currently under development, if there is one.
- The "home" button of the CIC browser sets the location bar to
- "about:proof".
- </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_gettingstarted.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_gettingstarted.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="authoring.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 3. Getting started </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Authoring</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>check</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="next" href="command_coercion.html" title="coercion" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">check</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_commands.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_coercion.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_check"></a>check</h2></div></div></div><p><strong class="userinput"><code>check t</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>check</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Action:</span></dt><dd><p>Opens a CIC browser window that shows <span class="command"><strong>t</strong></span>
- together with its type. The command is immediately removed from
- the script.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_commands.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_coercion.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 9. Other commands </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> coercion</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>coercion</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_check.html" title="check" /><link rel="next" href="command_include.html" title="include" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">coercion</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_check.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_include.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_coercion"></a>coercion</h2></div></div></div><p><strong class="userinput"><code>coercion nocomposites c : ty ≝ u on s : S to T</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>coercion</strong></span>
- [ <span class="bold"><strong>nocomposites</strong></span> ] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- [ : <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- <span class="bold"><strong>on</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> : <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- <span class="bold"><strong>to</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ]
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>Declares <span class="command"><strong>c</strong></span> as an implicit coercion.
- If only <span class="command"><strong>c</strong></span> is given, <span class="command"><strong>u</strong></span>
- is the constant named by <span class="command"><strong>c</strong></span>,
- <span class="command"><strong>ty</strong></span> its declared type,
- <span class="command"><strong>s</strong></span> the name of the last variable abstracted in
- in <span class="command"><strong>ty</strong></span>, <span class="command"><strong>S</strong></span> the type of
- this last variable and <span class="command"><strong>T</strong></span> the target of
- <span class="command"><strong>ty</strong></span>. The user can specify all these component to
- have full control on how the coercion is indexed.
- The type of the body of the coercion <span class="command"><strong>u</strong></span> must be
- convertible to the declared one <span class="command"><strong>ty</strong></span>. Let it be
- <span class="command"><strong>∀x1:T1. … ∀x(n-1):T(n-1).Tn</strong></span>.
- Then <span class="command"><strong>s</strong></span> must be one of <span class="command"><strong>x1</strong></span> …
- <span class="command"><strong>xn</strong></span> (possibly prefixed by <span class="command"><strong>_</strong></span>
- if the product is non dependent). Let <span class="command"><strong>s</strong></span>
- be <span class="command"><strong>xi</strong></span> in the following.
- Then <span class="command"><strong>S</strong></span> must be <span class="command"><strong>Ti</strong></span>
- where all bound variables are replaced by <span class="command"><strong>?</strong></span>,
- and <span class="command"><strong>T</strong></span> must be <span class="command"><strong>Tn</strong></span>
- where all bound variable are replaced by <span class="command"><strong>?</strong></span>.
- For example the following command
- declares a coercions from vectors of any length to lists of
- natural numbers.</p><p><strong class="userinput"><code>coercion nocomposites v2l : ∀n:nat.∀v:Vect nat n.
- List nat ≝ l_of_v on _v : Vect nat ? to List nat</code></strong></p><p>Every time a term <span class="command"><strong>x</strong></span>
- of a type that matches <span class="command"><strong>S</strong></span>
- (<span class="command"><strong>Vect nat ?</strong></span> here)
- is used with an expected
- type that matches <span class="command"><strong>T</strong></span>
- (<span class="command"><strong>List nat</strong></span> here), Matita
- automatically replaces <span class="command"><strong>x</strong></span> with
- <span class="command"><strong>(u ? … ? x ? … ?)</strong></span> to avoid a typing error.
- Note that the position of <span class="command"><strong>x</strong></span> is determined by
- <span class="command"><strong>s</strong></span>.</p><p>Implicit coercions are not displayed to the user:
- <span class="command"><strong>(u ? … ? x)</strong></span> is rendered simply
- as <span class="command"><strong>x</strong></span>.</p><p>When a coercion <span class="command"><strong>u</strong></span> is declared
- from source <span class="command"><strong>s</strong></span> to target <span class="command"><strong>t</strong></span>
- and there is already a coercion <span class="command"><strong>u'</strong></span> of
- target <span class="command"><strong>s</strong></span> or source <span class="command"><strong>t</strong></span>,
- a composite implicit coercion is automatically computed
- by Matita unless <span class="bold"><strong>nocomposites</strong></span>
- is specified.</p><p>Note that <span class="command"><strong>Vect nat ?</strong></span> can be replaced with
- <span class="command"><strong>Vect ? ?</strong></span> to index the coercion is a loose way.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_check.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_include.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">check </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> include</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>include</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_coercion.html" title="coercion" /><link rel="next" href="command_include_alias.html" title="include alias" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">include</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_coercion.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_include_alias.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_include"></a>include</h2></div></div></div><p><strong class="userinput"><code>include "s"</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>include</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span></p></dd><dt><span class="term">Action:</span></dt><dd><p>Every <a class="link" href="command_coercion.html" title="coercion">coercion</a>,
- <a class="link" href="sec_usernotation.html#notation">notation</a> and
- <a class="link" href="ch05s02.html#interpretation">interpretation</a> that was active
- when the file <span class="command"><strong>s</strong></span> was compiled last time
- is made active. The same happens for declarations of
- disambiguation
- hints (<a class="link" href="sec_commands.html#command_alias" title="alias">aliases</a>).
- On the contrary, theorem and definitions declared in a file can be
- immediately used without including it.</p><p>The file <span class="command"><strong>s</strong></span> is automatically compiled
- if it is not compiled yet.
- </p><p>
- If the file <span class="command"><strong>s</strong></span> was already included, either
- directly or recursively, the commands does nothing.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_coercion.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_include_alias.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">coercion </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> include alias</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>include alias</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_include.html" title="include" /><link rel="next" href="command_qed.html" title="qed" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">include alias</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_include.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_qed.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_include_alias"></a>include alias</h2></div></div></div><p><strong class="userinput"><code>include alias "s"</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>include</strong></span> <span class="bold"><strong>alias</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span></p></dd><dt><span class="term">Action:</span></dt><dd><p>Every
- <a class="link" href="ch05s02.html#interpretation">interpretation</a>
- declared in the file <span class="command"><strong>s</strong></span> is re-declared
- so to make it the preferred choice for disambiguation.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_include.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_qed.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">include </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> qed</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>qed</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_include_alias.html" title="include alias" /><link rel="next" href="command_qed_minus.html" title="qed-" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">qed</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_include_alias.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_qed_minus.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_qed"></a>qed</h2></div></div></div><p><strong class="userinput"><code>qed</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>qed</strong></span>
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>Saves and indexes the current interactive theorem or
- definition.
- In order to do this, the set of sequents still to be proved
- must be empty.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_include_alias.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_qed_minus.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">include alias </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> qed-</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>qed-</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_qed.html" title="qed" /><link rel="next" href="command_unification_hint.html" title="unification hint" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">qed-</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_qed.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_unification_hint.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_qed_minus"></a>qed-</h2></div></div></div><p><strong class="userinput"><code>qed-</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>qed-</strong></span>
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>Saves the current interactive theorem or
- definition without indexing. Therefore automation will ignore
- it.
- In order to do this, the set of sequents still to be proved
- must be empty.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_qed.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_unification_hint.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">qed </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> unification hint</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>unification hint</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_qed_minus.html" title="qed-" /><link rel="next" href="command_universe_constraints.html" title="universe constraint" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">unification hint</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_qed_minus.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_universe_constraints.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_unification_hint"></a>unification hint</h2></div></div></div><p><strong class="userinput"><code>unification hint n ≔ v1 : T1,… vi : Ti; h1 ≟ t1, … hn ≟ tn ⊢ tl ≡ tr.</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>unification hint</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>
- <span class="bold"><strong>≔</strong></span>
- [ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [ <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ] ,.. ]
- <span class="bold"><strong>;</strong></span>
- [ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>≟</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ,.. ]
- <span class="bold"><strong>⊢</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≡</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>Declares the hint at precedence <span class="command"><strong>n</strong></span></p><p>The file <span class="command"><strong>hints_declaration.ma</strong></span> must be
- included to declare hints with that syntax.</p><p>Unification hints are described in the paper
- "Hints in unification" by
- Asperti, Ricciotti, Sacerdoti and Tassi.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_qed_minus.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_universe_constraints.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">qed- </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> universe constraint</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>universe constraint</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_unification_hint.html" title="unification hint" /><link rel="next" href="sec_license.html" title="Chapter 10. License" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">universe constraint</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_unification_hint.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="sec_license.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_universe_constraints"></a>universe constraint</h2></div></div></div><p>TODO</p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_unification_hint.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_license.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">unification hint </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 10. License</td></tr></table></div></body></html>
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+(install
+ (section doc)
+ (files
+ matita.pdf
+ (glob_files_rec html/*)))
--- /dev/null
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Matita vs Coq</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_intro.html" title="Chapter 1. Introduction" /><link rel="prev" href="sec_intro.html" title="Chapter 1. Introduction" /><link rel="next" href="sec_install.html" title="Chapter 2. Installation" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Matita vs Coq</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_intro.html">Prev</a> </td><th width="60%" align="center">Chapter 1. Introduction</th><td width="20%" align="right"> <a accesskey="n" href="sec_install.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="WrtCoq"></a>Matita vs Coq</h2></div></div></div><p>
+ The system shares a common look&feel with the Coq proof assistant
+ and its graphical user interface. The two systems have variants
+ of the same logic,
+ close proof languages and similar sets of tactics.
+ From the user point of view the main lacking features
+ with respect to Coq are:
+ </p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>proof extraction;</p></li><li class="listitem"><p>an extensible language of tactics;</p></li><li class="listitem"><p>automatic implicit arguments;</p></li><li class="listitem"><p>several ad-hoc decision procedures;</p></li><li class="listitem"><p>several rarely used variants for most of the tactics;</p></li><li class="listitem"><p>sections and local variables. </p></li></ul></div><p>
+ Still from the user point of view, the main differences with respect
+ to Coq are:
+ </p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>the language of tacticals that allows execution of partial tactical application;</p></li><li class="listitem"><p>the unification of the concept of metavariable and existential variable;</p></li><li class="listitem"><p>terms with subterms that cannot be inferred are always allowed as arguments of tactics or other commands;</p></li><li class="listitem"><p>ambiguous terms are disambiguated by direct interaction with the user;</p></li><li class="listitem"><p>theorems and definitions in the library are always accessible without needing to require/include them; right now, only notation needs to be included to become active, but we plan to remove this limitation.</p></li></ul></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_intro.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_intro.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_install.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 1. Introduction </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 2. Installation</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Authoring</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /><link rel="prev" href="cicbrowser.html" title="Browsing and searching" /><link rel="next" href="sec_terms.html" title="Chapter 4. Syntax" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Authoring</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="cicbrowser.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Getting started</th><td width="20%" align="right"> <a accesskey="n" href="sec_terms.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="authoring"></a>Authoring</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="compilation"></a>How to compile a script</h3></div></div></div><p>
+ Scripts are compiled to base URIs. Base URIs are of the form
+ "cic:/matita/path" and are given once for all for a set
+ of scripts using the "root" file.
+ </p><p>
+ A "root" file has to be placed in the root of a script set,
+ for example, consider the following files and directories, and
+ assume you keep files in "list" separated from files
+ in "sort" (for example the former directory may contain
+ functions and proofs about lists, while latter sorting algorithms
+ for lists):
+</p><pre class="programlisting">
+ list/
+ list.ma (* depending just on the standard library *)
+ utils/
+ swap.ma (* including list.ma *)
+ sort/
+ qsort.ma (* including utils/swap.ma *)
+</pre><p>
+ To be able to compile properly the contents of "list"
+ a file called root has to be placed in it. The file should be like
+ the following snippet.
+</p><pre class="programlisting">
+ baseuri=cic:/matita/mydatastructures
+</pre><p>
+ This file tells Matita that objects generated by
+ "list.ma" have to be placed in
+ "cic:/matita/mydatastructures/list" while
+ objects generated by
+ "swap.ma" have to be placed in
+ "cic:/matita/mydatastructures/utils/swap".
+ </p><p>
+ Once you created the root file, you must generate a depend file.
+ Enter the "list" directory (the root of yuor file set)
+ and type "matitadep". Remember to regenerate the depend file
+ every time you alter the dependencies of your files (for example
+ including other scripts).
+ You can now compile you files typing "matitac".
+ </p><p>
+ To compile the "sort" directory, create a root file
+ in "sort/" like the following one and then run
+ "matitadep".
+</p><pre class="programlisting">
+ baseuri=cic:/matita/myalgorithms
+ include_paths=../list
+</pre><p>
+ The include_paths field can declare a list of paths separated by space.
+ Please omit any "/" from the end of base URIs or paths.
+ </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="authoringinterface"></a>The authoring interface</h3></div></div></div><p><span class="emphasis"><em>TODO</em></span></p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="cicbrowser.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_gettingstarted.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_terms.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Browsing and searching </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 4. Syntax</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Definitions and declarations</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="next" href="proofs.html" title="Proofs" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Definitions and declarations</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_terms.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="proofs.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="axiom_definition_declaration"></a>Definitions and declarations</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="axiom"></a><span class="bold"><strong>axiom</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></h3></div></div></div><p><strong class="userinput"><code>axiom H: P</code></strong></p><p><span class="command"><strong>H</strong></span> is declared as an axiom that states <span class="command"><strong>P</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="definition"></a><span class="bold"><strong>definition</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>definition f: T ≝ t</code></strong></p><p><span class="command"><strong>f</strong></span> is defined as <span class="command"><strong>t</strong></span>;
+ <span class="command"><strong>T</strong></span> is its type. An error is raised if the type of
+ <span class="command"><strong>t</strong></span> is not convertible to <span class="command"><strong>T</strong></span>.</p><p><span class="command"><strong>T</strong></span> is inferred from <span class="command"><strong>t</strong></span> if
+ omitted.</p><p><span class="command"><strong>t</strong></span> can be omitted only if <span class="command"><strong>T</strong></span> is
+ given. In this case Matita enters in interactive mode and
+ <span class="command"><strong>f</strong></span> must be defined by means of tactics.</p><p>Notice that the command is equivalent to <span class="command"><strong>theorem f: T ≝ t</strong></span>.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="discriminator"></a><span class="bold"><strong>discriminator</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></h3></div></div></div><p><strong class="userinput"><code>discriminator i</code></strong></p><p>Defines a new discrimination (injectivity+conflict) principle à la
+ McBride for the inductive type <span class="command"><strong>i</strong></span>.</p><p>The principle will use John
+ Major's equality if such equality is defined, otherwise it will use
+ Leibniz equality; in the former case, it will be called
+ <span class="command"><strong>i_jmdiscr</strong></span>, in the latter, <span class="command"><strong>i_discr</strong></span>.
+ The command will fail if neither equality is available.</p><p>Discrimination principles are used by the destruct tactic and are
+ usually automatically generated by Matita during the definition of the
+ corresponding inductive type. This command is thus especially useful
+ when the correct equality was not loaded at the time of that
+ definition.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="inverter"></a><span class="bold"><strong>inverter</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>for</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> (<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>) [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>inverter n for i (path) : s</code></strong></p><p>Defines a new induction/inversion principle for the inductive type
+ <span class="command"><strong>i</strong></span>, called <span class="command"><strong>n</strong></span>.</p><p><span class="command"><strong>(path)</strong></span> must be in the form <span class="command"><strong>(# # # ... #)</strong></span>,
+ where each <span class="command"><strong>#</strong></span> can be either <span class="command"><strong>?</strong></span> or
+ <span class="command"><strong>%</strong></span>, and the number of symbols is equal to the number of
+ right parameters (indices) of <span class="command"><strong>i</strong></span>. Parentheses are
+ mandatory. If the j-th symbol is
+ <span class="command"><strong>%</strong></span>, Matita will generate a principle providing
+ equations for reasoning on the j-th index of <span class="command"><strong>i</strong></span>. If the
+ symbol is a <span class="command"><strong>?</strong></span>, no corresponding equation will be
+ provided.</p><p><span class="command"><strong>s</strong></span>, which must be a sort, is the target sort of the
+ induction/inversion principle and defaults to <span class="command"><strong>Prop</strong></span>.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="letrec"></a><span class="bold"><strong>letrec</strong></span> <span class="emphasis"><em>TODO</em></span></h3></div></div></div><p><span class="emphasis"><em>TODO</em></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="inductive"></a>[<span class="bold"><strong>inductive</strong></span>|<span class="bold"><strong>coinductive</strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args2">args2</a></em></span>]… <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span> [<span class="bold"><strong>|</strong></span>] [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…
+[<span class="bold"><strong>with</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span> [<span class="bold"><strong>|</strong></span>] [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…]…
+</h3></div></div></div><p><strong class="userinput"><code>inductive i x y z: S ≝ k1:T1 | … | kn:Tn with i' : S' ≝ k1':T1' | … | km':Tm'</code></strong></p><p>Declares a family of two mutually inductive types
+ <span class="command"><strong>i</strong></span> and <span class="command"><strong>i'</strong></span> whose types are
+ <span class="command"><strong>S</strong></span> and <span class="command"><strong>S'</strong></span>, which must be convertible
+ to sorts.</p><p>The constructors <span class="command"><strong>ki</strong></span> of type <span class="command"><strong>Ti</strong></span>
+ and <span class="command"><strong>ki'</strong></span> of type <span class="command"><strong>Ti'</strong></span> are also
+ simultaneously declared. The declared types <span class="command"><strong>i</strong></span> and
+ <span class="command"><strong>i'</strong></span> may occur in the types of the constructors, but
+ only in strongly positive positions according to the rules of the
+ calculus.</p><p>The whole family is parameterized over the arguments <span class="command"><strong>x,y,z</strong></span>.</p><p>If the keyword <span class="command"><strong>coinductive</strong></span> is used, the declared
+ types are considered mutually coinductive.</p><p>Elimination principles for the record are automatically generated
+ by Matita, if allowed by the typing rules of the calculus according to
+ the sort <span class="command"><strong>S</strong></span>. If generated,
+ they are named <span class="command"><strong>i_ind</strong></span>, <span class="command"><strong>i_rec</strong></span> and
+ <span class="command"><strong>i_rect</strong></span> according to the sort of their induction
+ predicate.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="record"></a><span class="bold"><strong>record</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args2">args2</a></em></span>]… <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span><span class="bold"><strong>{</strong></span>[<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>:</strong></span>|<span class="bold"><strong>:></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>;</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>:</strong></span>|<span class="bold"><strong>:></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…<span class="bold"><strong>}</strong></span></h3></div></div></div><p><strong class="userinput"><code>record id x y z: S ≝ { f1: T1; …; fn:Tn }</code></strong></p><p>Declares a new record family <span class="command"><strong>id</strong></span> parameterized over
+ <span class="command"><strong>x,y,z</strong></span>.</p><p><span class="command"><strong>S</strong></span> is the type of the record
+ and it must be convertible to a sort.</p><p>Each field <span class="command"><strong>fi</strong></span> is declared by giving its type
+ <span class="command"><strong>Ti</strong></span>. A record without any field is admitted.</p><p>Elimination principles for the record are automatically generated
+ by Matita, if allowed by the typing rules of the calculus according to
+ the sort <span class="command"><strong>S</strong></span>. If generated,
+ they are named <span class="command"><strong>i_ind</strong></span>, <span class="command"><strong>i_rec</strong></span> and
+ <span class="command"><strong>i_rect</strong></span> according to the sort of their induction
+ predicate.</p><p>For each field <span class="command"><strong>fi</strong></span> a record projection
+ <span class="command"><strong>fi</strong></span> is also automatically generated if projection
+ is allowed by the typing rules of the calculus according to the
+ sort <span class="command"><strong>S</strong></span>, the type <span class="command"><strong>T1</strong></span> and
+ the definability of depending record projections.</p><p>If the type of a field is declared with <span class="command"><strong>:></strong></span>,
+ the corresponding record projection becomes an implicit coercion.
+ This is just syntactic sugar and it has the same effect of declaring the
+ record projection as a coercion later on.</p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_terms.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="proofs.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 4. Syntax </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Proofs</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>interpretation</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /><link rel="prev" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /><link rel="next" href="sec_tacticals.html" title="Chapter 6. Tacticals" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">interpretation</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_usernotation.html">Prev</a> </td><th width="60%" align="center">Chapter 5. Extending the syntax</th><td width="20%" align="right"> <a accesskey="n" href="sec_tacticals.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="idm2123"></a>interpretation</h2></div></div></div><p><strong class="userinput"><code>interpretation "description" 'symbol p<sub>1</sub> … p<sub>n</sub> =
+ rhs</code></strong></p><p><a id="interpretation"></a>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>interpretation</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span> [<span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_argument">interpretation_argument</a></em></span>]…
+ <span class="bold"><strong>=</strong></span>
+ <span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span>
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It declares a bi-directional mapping <span class="command"><strong>{…}</strong></span> between the content-level AST <span class="command"><strong>'symbol t<sub>1</sub> … t<sub>n</sub></strong></span> and the semantic term <span class="command"><strong>rhs[{t<sub>1</sub>}/p<sub>1</sub>;…;{t<sub>n</sub>}/p<sub>n</sub>]</strong></span>
+ (the simultaneous substitution in <span class="command"><strong>rhs</strong></span> of the
+ interpretation <span class="command"><strong>{…}</strong></span> of every content-level
+ actual argument <span class="command"><strong>t<sub>i</sub></strong></span> for its
+ corresponding formal parameter
+ <span class="command"><strong>p<sub>i</sub></strong></span>). The
+ <span class="command"><strong>description</strong></span> must be a textual description of the
+ meaning associated to <span class="command"><strong>'symbol</strong></span> by this
+ interpretation, and is used by the user interface of Matita to
+ provide feedback on the interpretation of ambiguous terms.
+ </p></dd><dt><span class="term">Interpretation arguments:</span></dt><dd><div class="table"><a id="idm2170"></a><p class="title"><strong>Table 5.11. interpretation_argument</strong></p><div class="table-contents"><table class="table" summary="interpretation_argument" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.interpretation_argument"></a><span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_argument">interpretation_argument</a></em></span></td><td style="">::=</td><td style="">[<span class="bold"><strong>η</strong></span><span class="bold"><strong>.</strong></span>]… <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">A formal parameter. If the name of the formal parameter is
+ prefixed by n symbols "η", then the mapping performs
+ (multiple) η-expansions to grant that the semantic actual
+ parameter begins with at least n λ-abstractions.</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm2185"></a><p class="title"><strong>Table 5.12. interpretation_rhs</strong></p><div class="table-contents"><table class="table" summary="interpretation_rhs" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.interpretation_rhs"></a><span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span></td><td style="">A constant, specified by its URI</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">A constant, specified by its name, or a bound variable. If
+ the constant name is ambiguous, the one corresponding to the
+ last implicitly or explicitly specified alias is used.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>?</strong></span></td><td style="">An implicit parameter</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span>
+ <span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span>
+ [<span class="emphasis"><em><a class="link" href="ch05s02.html#grammar.interpretation_rhs">interpretation_rhs</a></em></span>]…
+ <span class="bold"><strong>)</strong></span></td><td style="">An application</td></tr></tbody></table></div></div><br class="table-break" /></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_usernotation.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_usernotation.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_tacticals.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 5. Extending the syntax </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 6. Tacticals</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Browsing and searching</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /><link rel="prev" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /><link rel="next" href="authoring.html" title="Authoring" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Browsing and searching</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_gettingstarted.html">Prev</a> </td><th width="60%" align="center">Chapter 3. Getting started</th><td width="20%" align="right"> <a accesskey="n" href="authoring.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="cicbrowser"></a>Browsing and searching</h2></div></div></div><p>The CIC browser is used to browse and search the library.
+ You can open a new CIC browser selecting "New Cic Browser"
+ from the "View" menu of Matita, or by pressing "F3".
+ The CIC browser is similar to a traditional Web browser.</p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="browsinglib"></a>Browsing the library</h3></div></div></div><p>To browse the library, type in the location bar the absolute URI of
+ the theorem, definition or library fragment you are interested in.
+ "cic:/" is the root of the library. Contributions developed
+ in Matita are under "cic:/matita"; all the others are
+ part of the library of Coq.</p><p>Following the hyperlinks it is possible to navigate in the Web
+ of mathematical notions. Proof are rendered in pseudo-natural language
+ and mathematical notation is used for formulae. For now, mathematical
+ notation must be included in the current script to be activated, but we
+ plan to remove this limitation.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="aboutproof"></a>Looking at a proof under development</h3></div></div></div><p>A proof under development is not yet part of the library.
+ The special URI "about:proof" can be used to browse the
+ proof currently under development, if there is one.
+ The "home" button of the CIC browser sets the location bar to
+ "about:proof".
+ </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_gettingstarted.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_gettingstarted.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="authoring.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 3. Getting started </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Authoring</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>check</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="next" href="command_coercion.html" title="coercion" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">check</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_commands.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_coercion.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_check"></a>check</h2></div></div></div><p><strong class="userinput"><code>check t</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>check</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Action:</span></dt><dd><p>Opens a CIC browser window that shows <span class="command"><strong>t</strong></span>
+ together with its type. The command is immediately removed from
+ the script.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_commands.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_coercion.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 9. Other commands </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> coercion</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>coercion</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_check.html" title="check" /><link rel="next" href="command_include.html" title="include" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">coercion</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_check.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_include.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_coercion"></a>coercion</h2></div></div></div><p><strong class="userinput"><code>coercion nocomposites c : ty ≝ u on s : S to T</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>coercion</strong></span>
+ [ <span class="bold"><strong>nocomposites</strong></span> ] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ [ : <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ <span class="bold"><strong>on</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> : <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ <span class="bold"><strong>to</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ]
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>Declares <span class="command"><strong>c</strong></span> as an implicit coercion.
+ If only <span class="command"><strong>c</strong></span> is given, <span class="command"><strong>u</strong></span>
+ is the constant named by <span class="command"><strong>c</strong></span>,
+ <span class="command"><strong>ty</strong></span> its declared type,
+ <span class="command"><strong>s</strong></span> the name of the last variable abstracted in
+ in <span class="command"><strong>ty</strong></span>, <span class="command"><strong>S</strong></span> the type of
+ this last variable and <span class="command"><strong>T</strong></span> the target of
+ <span class="command"><strong>ty</strong></span>. The user can specify all these component to
+ have full control on how the coercion is indexed.
+ The type of the body of the coercion <span class="command"><strong>u</strong></span> must be
+ convertible to the declared one <span class="command"><strong>ty</strong></span>. Let it be
+ <span class="command"><strong>∀x1:T1. … ∀x(n-1):T(n-1).Tn</strong></span>.
+ Then <span class="command"><strong>s</strong></span> must be one of <span class="command"><strong>x1</strong></span> …
+ <span class="command"><strong>xn</strong></span> (possibly prefixed by <span class="command"><strong>_</strong></span>
+ if the product is non dependent). Let <span class="command"><strong>s</strong></span>
+ be <span class="command"><strong>xi</strong></span> in the following.
+ Then <span class="command"><strong>S</strong></span> must be <span class="command"><strong>Ti</strong></span>
+ where all bound variables are replaced by <span class="command"><strong>?</strong></span>,
+ and <span class="command"><strong>T</strong></span> must be <span class="command"><strong>Tn</strong></span>
+ where all bound variable are replaced by <span class="command"><strong>?</strong></span>.
+ For example the following command
+ declares a coercions from vectors of any length to lists of
+ natural numbers.</p><p><strong class="userinput"><code>coercion nocomposites v2l : ∀n:nat.∀v:Vect nat n.
+ List nat ≝ l_of_v on _v : Vect nat ? to List nat</code></strong></p><p>Every time a term <span class="command"><strong>x</strong></span>
+ of a type that matches <span class="command"><strong>S</strong></span>
+ (<span class="command"><strong>Vect nat ?</strong></span> here)
+ is used with an expected
+ type that matches <span class="command"><strong>T</strong></span>
+ (<span class="command"><strong>List nat</strong></span> here), Matita
+ automatically replaces <span class="command"><strong>x</strong></span> with
+ <span class="command"><strong>(u ? … ? x ? … ?)</strong></span> to avoid a typing error.
+ Note that the position of <span class="command"><strong>x</strong></span> is determined by
+ <span class="command"><strong>s</strong></span>.</p><p>Implicit coercions are not displayed to the user:
+ <span class="command"><strong>(u ? … ? x)</strong></span> is rendered simply
+ as <span class="command"><strong>x</strong></span>.</p><p>When a coercion <span class="command"><strong>u</strong></span> is declared
+ from source <span class="command"><strong>s</strong></span> to target <span class="command"><strong>t</strong></span>
+ and there is already a coercion <span class="command"><strong>u'</strong></span> of
+ target <span class="command"><strong>s</strong></span> or source <span class="command"><strong>t</strong></span>,
+ a composite implicit coercion is automatically computed
+ by Matita unless <span class="bold"><strong>nocomposites</strong></span>
+ is specified.</p><p>Note that <span class="command"><strong>Vect nat ?</strong></span> can be replaced with
+ <span class="command"><strong>Vect ? ?</strong></span> to index the coercion is a loose way.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_check.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_include.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">check </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> include</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>include</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_coercion.html" title="coercion" /><link rel="next" href="command_include_alias.html" title="include alias" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">include</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_coercion.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_include_alias.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_include"></a>include</h2></div></div></div><p><strong class="userinput"><code>include "s"</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>include</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span></p></dd><dt><span class="term">Action:</span></dt><dd><p>Every <a class="link" href="command_coercion.html" title="coercion">coercion</a>,
+ <a class="link" href="sec_usernotation.html#notation">notation</a> and
+ <a class="link" href="ch05s02.html#interpretation">interpretation</a> that was active
+ when the file <span class="command"><strong>s</strong></span> was compiled last time
+ is made active. The same happens for declarations of
+ disambiguation
+ hints (<a class="link" href="sec_commands.html#command_alias" title="alias">aliases</a>).
+ On the contrary, theorem and definitions declared in a file can be
+ immediately used without including it.</p><p>The file <span class="command"><strong>s</strong></span> is automatically compiled
+ if it is not compiled yet.
+ </p><p>
+ If the file <span class="command"><strong>s</strong></span> was already included, either
+ directly or recursively, the commands does nothing.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_coercion.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_include_alias.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">coercion </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> include alias</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>include alias</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_include.html" title="include" /><link rel="next" href="command_qed.html" title="qed" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">include alias</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_include.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_qed.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_include_alias"></a>include alias</h2></div></div></div><p><strong class="userinput"><code>include alias "s"</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>include</strong></span> <span class="bold"><strong>alias</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span></p></dd><dt><span class="term">Action:</span></dt><dd><p>Every
+ <a class="link" href="ch05s02.html#interpretation">interpretation</a>
+ declared in the file <span class="command"><strong>s</strong></span> is re-declared
+ so to make it the preferred choice for disambiguation.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_include.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_qed.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">include </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> qed</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>qed</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_include_alias.html" title="include alias" /><link rel="next" href="command_qed_minus.html" title="qed-" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">qed</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_include_alias.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_qed_minus.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_qed"></a>qed</h2></div></div></div><p><strong class="userinput"><code>qed</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>qed</strong></span>
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>Saves and indexes the current interactive theorem or
+ definition.
+ In order to do this, the set of sequents still to be proved
+ must be empty.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_include_alias.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_qed_minus.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">include alias </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> qed-</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>qed-</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_qed.html" title="qed" /><link rel="next" href="command_unification_hint.html" title="unification hint" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">qed-</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_qed.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_unification_hint.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_qed_minus"></a>qed-</h2></div></div></div><p><strong class="userinput"><code>qed-</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>qed-</strong></span>
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>Saves the current interactive theorem or
+ definition without indexing. Therefore automation will ignore
+ it.
+ In order to do this, the set of sequents still to be proved
+ must be empty.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_qed.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_unification_hint.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">qed </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> unification hint</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>unification hint</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_qed_minus.html" title="qed-" /><link rel="next" href="command_universe_constraints.html" title="universe constraint" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">unification hint</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_qed_minus.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="command_universe_constraints.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_unification_hint"></a>unification hint</h2></div></div></div><p><strong class="userinput"><code>unification hint n ≔ v1 : T1,… vi : Ti; h1 ≟ t1, … hn ≟ tn ⊢ tl ≡ tr.</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>unification hint</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>
+ <span class="bold"><strong>≔</strong></span>
+ [ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [ <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ] ,.. ]
+ <span class="bold"><strong>;</strong></span>
+ [ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>≟</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ,.. ]
+ <span class="bold"><strong>⊢</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>≡</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>Declares the hint at precedence <span class="command"><strong>n</strong></span></p><p>The file <span class="command"><strong>hints_declaration.ma</strong></span> must be
+ included to declare hints with that syntax.</p><p>Unification hints are described in the paper
+ "Hints in unification" by
+ Asperti, Ricciotti, Sacerdoti and Tassi.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_qed_minus.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="command_universe_constraints.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">qed- </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> universe constraint</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>universe constraint</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_commands.html" title="Chapter 9. Other commands" /><link rel="prev" href="command_unification_hint.html" title="unification hint" /><link rel="next" href="sec_license.html" title="Chapter 10. License" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">universe constraint</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_unification_hint.html">Prev</a> </td><th width="60%" align="center">Chapter 9. Other commands</th><td width="20%" align="right"> <a accesskey="n" href="sec_license.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_universe_constraints"></a>universe constraint</h2></div></div></div><p>TODO</p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_unification_hint.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_commands.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_license.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">unification hint </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 10. License</td></tr></table></div></body></html>
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+
+body {
+ background: url(../../images/sheetbg.png);
+}
+
+ul.authorgroup {
+ list-style-type: none;
+ padding-left: 1em;
+}
+
+div.titlepage {
+ background: #eaeaea;
+}
+
+div.titlepage hr {
+ display: none;
+}
+
+div.navheader hr {
+ display: none;
+}
+
+div.navfooter hr {
+ display: none;
+}
+
+div.navheader {
+ padding-left: 150px;
+ background: #eaeaea;
+}
+
+div.navfooter {
+ background: #eaeaea;
+}
+
+div.matita_logo {
+ position: absolute;
+ top: 3px;
+ left: 5px;
+}
+
+div.matita_logo img {
+ border-style: none;
+}
+
+div.matita_logo span {
+ position: absolute;
+ top: 13px;
+ left: 65px;
+ text-decoration: underline;
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+ text-align: center;
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+
--- /dev/null
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Matita V0.99.5 User Manual (rev. 0.99.5 )</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="next" href="sec_intro.html" title="Chapter 1. Introduction" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center"><span class="application">Matita</span> V0.99.5
+ User Manual (rev. 0.99.5
+)</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="sec_intro.html">Next</a></td></tr></table><hr /></div><div xml:lang="en" class="book" lang="en"><div class="titlepage"><div><div><h1 class="title"><a id="matita_manual"></a><span class="application">Matita</span> V0.99.5
+ User Manual (rev. 0.99.5
+)</h1></div><div><ul xmlns="" class="authorgroup"><li class="author">Andrea Asperti <<a href="mailto:asperti@cs.unibo.it">asperti@cs.unibo.it</a>></li><li class="author">Claudio Sacerdoti Coen <<a href="mailto:sacerdot@cs.unibo.it">sacerdot@cs.unibo.it</a>></li><li class="author">Ferruccio Guidi <<a href="mailto:fguidi@cs.unibo.it">fguidi@cs.unibo.it</a>></li><li class="author">Enrico Tassi <<a href="mailto:tassi@cs.unibo.it">tassi@cs.unibo.it</a>></li><li class="author">Stefano Zacchiroli <<a href="mailto:zacchiro@cs.unibo.it">zacchiro@cs.unibo.it</a>></li></ul></div><div><p class="copyright">Copyright © 2006 The HELM team.</p></div><div><div class="legalnotice"><a id="idm39"></a><p> Both Matita and this document are free software, you can
+ redistribute them and/or modify them under the terms of the GNU General
+ Public License as published by the Free Software Foundation. See <a class="xref" href="sec_license.html" title="Chapter 10. License">Chapter 10, <em>License</em></a> for more information. </p></div></div><div><div xmlns="" class="revhistory"><span class="revision">Revision: <span class="revnumber">0.99.5
+</span>, <span class="date">12/07/2006</span></span></div></div></div><hr /></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="chapter"><a href="sec_intro.html">1. Introduction</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_intro.html#Features">Features</a></span></dt><dt><span class="sect1"><a href="WrtCoq.html">Matita vs Coq</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_install.html">2. Installation</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_install.html#inst_livecd">Using the LiveCD</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_install.html#make_vmachine">Creating the virtual machine</a></span></dt><dt><span class="sect2"><a href="sec_install.html#idm148">Sharing files with the real PC</a></span></dt></dl></dd><dt><span class="sect1"><a href="inst_from_src.html">Installing from sources</a></span></dt><dd><dl><dt><span class="sect2"><a href="inst_from_src.html#get_source_code">Getting the source code</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_requirements">Requirements</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_instructions">Compiling and installing</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="sec_gettingstarted.html">3. Getting started</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_gettingstarted.html#unicode">How to type Unicode symbols</a></span></dt><dt><span class="sect1"><a href="cicbrowser.html">Browsing and searching</a></span></dt><dd><dl><dt><span class="sect2"><a href="cicbrowser.html#browsinglib">Browsing the library</a></span></dt><dt><span class="sect2"><a href="cicbrowser.html#aboutproof">Looking at a proof under development</a></span></dt></dl></dd><dt><span class="sect1"><a href="authoring.html">Authoring</a></span></dt><dd><dl><dt><span class="sect2"><a href="authoring.html#compilation">How to compile a script</a></span></dt><dt><span class="sect2"><a href="authoring.html#authoringinterface">The authoring interface</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="sec_terms.html">4. Syntax</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_terms.html#terms_and_co">Terms & co.</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_terms.html#lexical">Lexical conventions</a></span></dt><dt><span class="sect2"><a href="sec_terms.html#terms">Terms</a></span></dt></dl></dd><dt><span class="sect1"><a href="axiom_definition_declaration.html">Definitions and declarations</a></span></dt><dd><dl><dt><span class="sect2"><a href="axiom_definition_declaration.html#axiom">axiom</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#definition">definition</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#discriminator">discriminator</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inverter">inverter</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#letrec"><span class="emphasis"><em>TODO</em></span></a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inductive">(co)inductive types declaration</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#record">record</a></span></dt></dl></dd><dt><span class="sect1"><a href="proofs.html">Proofs</a></span></dt><dd><dl><dt><span class="sect2"><a href="proofs.html#theorem">theorem</a></span></dt><dt><span class="sect2"><a href="proofs.html#corollary">corollary</a></span></dt><dt><span class="sect2"><a href="proofs.html#lemma">lemma</a></span></dt><dt><span class="sect2"><a href="proofs.html#fact">fact</a></span></dt><dt><span class="sect2"><a href="proofs.html#example">example</a></span></dt></dl></dd><dt><span class="sect1"><a href="tacticargs.html">Tactic arguments</a></span></dt><dd><dl><dt><span class="sect2"><a href="tacticargs.html#pattern">pattern</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#reduction-kind">reduction-kind</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#auto-params">auto-params</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#justification">justification</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="sec_usernotation.html">5. Extending the syntax</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_usernotation.html#idm1489">notation</a></span></dt><dt><span class="sect1"><a href="ch05s02.html">interpretation</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_tacticals.html">6. Tacticals</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_tacticals.html#idm2224">Interactive proofs and definitions</a></span></dt><dt><span class="sect1"><a href="proofstatus.html">The proof status</a></span></dt><dt><span class="sect1"><a href="tacticals.html">Tacticals</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_tactics.html">7. Tactics</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_tactics.html#tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_apply.html">@</a></span></dt><dt><span class="sect1"><a href="tac_auto.html">//</a></span></dt><dt><span class="sect1"><a href="tac_intro.html">#</a></span></dt><dt><span class="sect1"><a href="tac_intro_clear.html">#_</a></span></dt><dt><span class="sect1"><a href="macro_intro.html">##</a></span></dt><dt><span class="sect1"><a href="tac_clear.html">-</a></span></dt><dt><span class="sect1"><a href="tac_constructor.html">%</a></span></dt><dt><span class="sect1"><a href="tac_decompose.html">*</a></span></dt><dt><span class="sect1"><a href="tac_rewrite.html">></a></span></dt><dt><span class="sect1"><a href="tac_applyS.html">applyS</a></span></dt><dt><span class="sect1"><a href="tac_assumption.html">assumption</a></span></dt><dt><span class="sect1"><a href="tac_cases.html">cases</a></span></dt><dt><span class="sect1"><a href="tac_change.html">change</a></span></dt><dt><span class="sect1"><a href="tac_cut.html">cut</a></span></dt><dt><span class="sect1"><a href="tac_destruct.html">destruct</a></span></dt><dt><span class="sect1"><a href="tac_elim.html">elim</a></span></dt><dt><span class="sect1"><a href="tac_generalize.html">generalize</a></span></dt><dt><span class="sect1"><a href="tac_inversion.html">inversion</a></span></dt><dt><span class="sect1"><a href="tac_lapply.html">lapply</a></span></dt><dt><span class="sect1"><a href="tac_letin.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_normalize.html">normalize</a></span></dt><dt><span class="sect1"><a href="tac_whd.html">whd</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_declarative_tactics.html">8. Declarative Tactics</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_declarative_tactics.html#declarative_tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_assume.html">assume</a></span></dt><dt><span class="sect1"><a href="tac_suppose.html">suppose</a></span></dt><dt><span class="sect1"><a href="tac_let.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_thatisequivalentto.html">that is equivalent to</a></span></dt><dt><span class="sect1"><a href="tac_thesisbecomes.html">the thesis becomes</a></span></dt><dt><span class="sect1"><a href="tac_weneedtoprove.html">we need to prove</a></span></dt><dt><span class="sect1"><a href="tac_bytermweproved.html">we proved</a></span></dt><dt><span class="sect1"><a href="tac_existselim.html">let such that</a></span></dt><dt><span class="sect1"><a href="tac_andelim.html">we have</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbyinduction.html">we proceed by induction on</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbycases.html">we proceed by cases on</a></span></dt><dt><span class="sect1"><a href="tac_case.html">case</a></span></dt><dt><span class="sect1"><a href="tac_byinduction.html">by induction hypothesis we know</a></span></dt><dt><span class="sect1"><a href="tac_conclude.html">conclude</a></span></dt><dt><span class="sect1"><a href="tac_obtain.html">obtain</a></span></dt><dt><span class="sect1"><a href="tac_rewrite_step.html">=</a></span></dt><dt><span class="sect1"><a href="tac_bydone.html">done</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_commands.html">9. Other commands</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_commands.html#command_alias">alias</a></span></dt><dt><span class="sect1"><a href="command_check.html">check</a></span></dt><dt><span class="sect1"><a href="command_coercion.html">coercion</a></span></dt><dt><span class="sect1"><a href="command_include.html">include</a></span></dt><dt><span class="sect1"><a href="command_include_alias.html">include alias</a></span></dt><dt><span class="sect1"><a href="command_qed.html">qed</a></span></dt><dt><span class="sect1"><a href="command_qed_minus.html">qed-</a></span></dt><dt><span class="sect1"><a href="command_unification_hint.html">unification hint</a></span></dt><dt><span class="sect1"><a href="command_universe_constraints.html">universe constraint</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_license.html">10. License</a></span></dt></dl></div><div class="list-of-figures"><p><strong>List of Figures</strong></p><dl><dt>2.1. <a href="sec_install.html#idm116">The brand new virtual machine</a></dt><dt>2.2. <a href="sec_install.html#idm124">Mounting an ISO image</a></dt><dt>2.3. <a href="sec_install.html#idm132">Choosing the ISO image</a></dt><dt>2.4. <a href="sec_install.html#idm140">Choosing the ISO image</a></dt><dt>2.5. <a href="sec_install.html#idm153">Set up a shared folder</a></dt><dt>2.6. <a href="sec_install.html#idm161">Choosing the folder to share</a></dt><dt>2.7. <a href="sec_install.html#idm169">Naming the shared folder</a></dt><dt>2.8. <a href="sec_install.html#idm177">Using it from the virtual machine</a></dt></dl></div><div class="list-of-tables"><p><strong>List of Tables</strong></p><dl><dt>4.1. <a href="sec_terms.html#idm389">qstring</a></dt><dt>4.2. <a href="sec_terms.html#idm402">id</a></dt><dt>4.3. <a href="sec_terms.html#idm414">nat</a></dt><dt>4.4. <a href="sec_terms.html#idm426">char</a></dt><dt>4.5. <a href="sec_terms.html#idm440">uri-step</a></dt><dt>4.6. <a href="sec_terms.html#idm454">uri</a></dt><dt>4.7. <a href="sec_terms.html#idm487">csymbol</a></dt><dt>4.8. <a href="sec_terms.html#idm500">symbol</a></dt><dt>4.9. <a href="sec_terms.html#tbl_terms">Terms</a></dt><dt>4.10. <a href="sec_terms.html#idm665">Simple terms</a></dt><dt>4.11. <a href="sec_terms.html#idm792">Arguments</a></dt><dt>4.12. <a href="sec_terms.html#idm870">Pattern matching</a></dt><dt>4.13. <a href="tacticargs.html#idm1235">pattern</a></dt><dt>4.14. <a href="tacticargs.html#idm1275">path</a></dt><dt>4.15. <a href="tacticargs.html#idm1378">reduction-kind</a></dt><dt>4.16. <a href="tacticargs.html#idm1402">auto-params</a></dt><dt>4.17. <a href="tacticargs.html#idm1423">simple-auto-param</a></dt><dt>4.18. <a href="tacticargs.html#idm1466">justification</a></dt><dt>5.1. <a href="sec_usernotation.html#idm1537">usage</a></dt><dt>5.2. <a href="sec_usernotation.html#idm1555">associativity</a></dt><dt>5.3. <a href="sec_usernotation.html#idm1582">notation_rhs</a></dt><dt>5.4. <a href="sec_usernotation.html#idm1604">unparsed_ast</a></dt><dt>5.5. <a href="sec_usernotation.html#idm1639">enriched_term</a></dt><dt>5.6. <a href="sec_usernotation.html#idm1655">unparsed_meta</a></dt><dt>5.7. <a href="sec_usernotation.html#idm1690">level2_meta</a></dt><dt>5.8. <a href="sec_usernotation.html#idm1806">notation_lhs</a></dt><dt>5.9. <a href="sec_usernotation.html#idm1820">layout</a></dt><dt>5.10. <a href="sec_usernotation.html#idm2094">literal</a></dt><dt>5.11. <a href="ch05s02.html#idm2170">interpretation_argument</a></dt><dt>5.12. <a href="ch05s02.html#idm2185">interpretation_rhs</a></dt><dt>6.1. <a href="tacticals.html#idm2266">proof script</a></dt><dt>6.2. <a href="tacticals.html#idm2281">proof steps</a></dt><dt>6.3. <a href="tacticals.html#idm2377">tactics and LCF tacticals</a></dt><dt>7.1. <a href="sec_tactics.html#idm2483">tactics</a></dt><dt>8.1. <a href="sec_declarative_tactics.html#idm3387">tactics</a></dt></dl></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="sec_intro.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top"> </td><td width="20%" align="center"> </td><td width="40%" align="right" valign="top"> Chapter 1. Introduction</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Installing from sources</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_install.html" title="Chapter 2. Installation" /><link rel="prev" href="sec_install.html" title="Chapter 2. Installation" /><link rel="next" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Installing from sources</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_install.html">Prev</a> </td><th width="60%" align="center">Chapter 2. Installation</th><td width="20%" align="right"> <a accesskey="n" href="sec_gettingstarted.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="inst_from_src"></a>Installing from sources</h2></div></div></div><p>Install Matita from the sources is hard, you have been warned!
+ </p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="get_source_code"></a>Getting the source code</h3></div></div></div><p>You can get the Matita source code in two ways:
+ </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p> go to the <a class="ulink" href="http://matita.cs.unibo.it/download.shtml" target="_top">download
+ page</a> and get the <a class="ulink" href="http://matita.cs.unibo.it/sources/matita-latest.tar.gz" target="_top">latest released source tarball</a>;</p></li><li class="listitem"><p> get the development sources from <a class="ulink" href="http://helm.cs.unibo.it/websvn/listing.php?repname=helm&path=%2F&sc=0" target="_top">our
+ SVN repository</a>. You will need the
+ <span class="application">components/</span> and
+ <span class="application">matita/</span> directories from the
+ <code class="filename">trunk/helm/software/</code> directory, plus the
+ <code class="filename">configure</code> and <code class="filename">Makefile*</code>
+ stuff from the same directory. </p><p>In this case you will need to run
+ <span class="command"><strong>autoconf</strong></span> before proceding with the building
+ instructions below.</p></li></ol></div><p>
+ </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="build_requirements"></a>Requirements</h3></div></div></div><p>In order to build Matita from sources you will need some
+ tools and libraries. They are listed below.
+
+ </p><div class="note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note for Debian (and derivatives) users</h3><p>If you are running a
+ <a class="ulink" href="http://www.debian.org" target="_top">Debian GNU/Linux</a>
+ distribution,
+ or any of its derivative like <a class="ulink" href="http://ubuntu.com" target="_top">Ubuntu</a>,
+ you can use APT to install all the required tools and
+ libraries since they are all part of the Debian archive.
+ </p><p>
+ apt-get install ocaml ocaml-findlib libgdome2-ocaml-dev liblablgtk2-ocaml-dev liblablgtkmathview-ocaml-dev liblablgtksourceview-ocaml-dev libsqlite3-ocaml-dev libocamlnet-ocaml-dev libzip-ocaml-dev libhttp-ocaml-dev ocaml-ulex08 libexpat-ocaml-dev libmysql-ocaml-dev camlp5
+ </p><p>
+ An official debian package is going to be added to the
+ archive too.
+ </p></div><p>
+
+ </p><div class="variablelist"><p class="title"><strong>Required tools and libraries</strong></p><dl class="variablelist"><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://caml.inria.fr" target="_top">OCaml</a> </span>
+ </span></dt><dd><p> the Objective Caml compiler, version 3.09 or above </p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://www.ocaml-programming.de/packages/" target="_top">Findlib</a>
+ </span>
+ </span></dt><dd><p> OCaml package manager, version 1.1.1 or above</p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://www.xs4all.nl/~mmzeeman/ocaml/" target="_top">OCaml
+ Expat</a> </span>
+ </span></dt><dd><p>OCaml bindings for the <span class="application"><a class="ulink" href="http://expat.sourceforge.net/" target="_top">expat</a>
+ library</span> </p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://wwwfun.kurims.kyoto-u.ac.jp/soft/lsl/lablgtk.html" target="_top">LablGTK</a>
+ </span>
+ </span></dt><dd><p> OCaml bindings for the <span class="application"> <a class="ulink" href="http://www.gtk.org" target="_top"> GTK+</a> library
+ </span>, version 2.6.0 or above </p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://gtksourceview.sourceforge.net/" target="_top">GtkSourceView</a>
+ </span>
+ , </span><span class="term">
+ <span class="application"> <a class="ulink" href="http://helm.cs.unibo.it/software/lablgtksourceview/" target="_top">LablGtkSourceView</a>
+ </span>
+ </span></dt><dd><p> extension for the GTK+ text widget (adding the typical
+ features of source code editors) and its OCaml bindings </p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://ocamlnet.sourceforge.net/" target="_top">Ocamlnet</a>
+ </span>
+ </span></dt><dd><p> collection of OCaml libraries to deal with
+ application-level Internet protocols and conventions </p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://www.cduce.org/download.html" target="_top">ulex</a>
+ </span>
+ </span></dt><dd><p> Unicode lexer generator for OCaml </p></dd><dt><span class="term">
+ <span class="application"> <a class="ulink" href="http://cristal.inria.fr/~xleroy/software.html" target="_top">CamlZip</a>
+ </span>
+ </span></dt><dd><p> OCaml library to access <code class="filename">.gz</code> files
+ </p></dd></dl></div><p> </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="build_instructions"></a>Compiling and installing</h3></div></div></div><p> Once you get the source code the installations steps should be
+ quite familiar.</p><p> First of all you need to configure the build process executing
+ <strong class="userinput"><code>./configure</code></strong>. This will check that all needed
+ tools and library are installed and prepare the sources for compilation
+ and installation. </p><p> Quite a few (optional) arguments may be passed to the
+ <span class="application">configure</span> command line to change build time
+ parameters. They are listed below, together with their
+ default values: </p><div class="variablelist"><p class="title"><strong> <span class="application">configure</span> command line
+ arguments</strong></p><dl class="variablelist"><dt><span class="term">
+ <strong class="userinput"><code>--with-runtime-dir=<em class="replaceable"><code>dir</code></em></code></strong>
+ </span></dt><dd><p>
+ (<span class="emphasis"><em>Default:</em></span>
+ <code class="filename">/usr/local/matita</code>) Runtime base directory
+ where all Matita stuff (executables, configuration files,
+ standard library, ...) will be installed
+ </p></dd><dt><span class="term">
+ <strong class="userinput"><code>--enable-debug</code></strong>
+ </span></dt><dd><p>
+ (<span class="emphasis"><em>Default:</em></span> disabled) Enable debugging code.
+ Not for the casual user.
+ </p></dd></dl></div><p> Then you will manage the build and install process using
+ <span class="application"><a class="ulink" href="http://www.gnu.org/software/make/" target="_top">make</a></span>
+ as usual. Below are reported the targets you have to invoke in sequence
+ to build and install:
+ </p><div class="variablelist"><p class="title"><strong><span class="application">make</span> targets</strong></p><dl class="variablelist"><dt><span class="term"><strong class="userinput"><code>world</code></strong></span></dt><dd><p>builds components needed by Matita and Matita itself
+ (in bytecode or native code depending
+ on the availability of the OCaml native code compiler) </p></dd><dt><span class="term"><strong class="userinput"><code>install</code></strong></span></dt><dd><p>installs Matita related tools, standard library and the
+ needed runtime stuff in the proper places on the filesystem.
+ </p></dd></dl></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_install.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_install.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_gettingstarted.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 2. Installation </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 3. Getting started</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>macro_input</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_intro_clear.html" title="intro_clear" /><link rel="next" href="tac_clear.html" title="clear" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">macro_input</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_intro_clear.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_clear.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="macro_intro"></a>macro_input</h2></div></div></div><p><strong class="userinput"><code>##</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>##</strong></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>This macro expands to the longest possible list of
+ <span class="command"><strong>#H<sub>i</sub></strong></span> tactics. The
+ names of the introduced hypotheses are automatically
+ generated.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_intro_clear.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_clear.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">intro_clear </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> clear</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Proofs</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="axiom_definition_declaration.html" title="Definitions and declarations" /><link rel="next" href="tacticargs.html" title="Tactic arguments" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Proofs</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="axiom_definition_declaration.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="tacticargs.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="proofs"></a>Proofs</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="theorem"></a><span class="bold"><strong>theorem</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>theorem f: P ≝ p</code></strong></p><p>Proves a new theorem <span class="command"><strong>f</strong></span> whose thesis is
+ <span class="command"><strong>P</strong></span>.</p><p>If <span class="command"><strong>p</strong></span> is provided, it must be a proof term for
+ <span class="command"><strong>P</strong></span>. Otherwise an interactive proof is started.</p><p><span class="command"><strong>P</strong></span> can be omitted only if the proof is not
+ interactive.</p><p>A warning is raised if the name of the theorem cannot be obtained
+ by mangling the name of the constants in its thesis.</p><p>Notice that the command is equivalent to <span class="command"><strong>definition f: T ≝ t</strong></span>.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="corollary"></a><span class="bold"><strong>corollary</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>corollary f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="lemma"></a><span class="bold"><strong>lemma</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>lemma f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="fact"></a><span class="bold"><strong>fact</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>fact f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="example"></a><span class="bold"><strong>example</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>example f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span>, but the example
+ is not indexed nor used by automation.</p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="axiom_definition_declaration.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tacticargs.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Definitions and declarations </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Tactic arguments</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>The proof status</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tacticals.html" title="Chapter 6. Tacticals" /><link rel="prev" href="sec_tacticals.html" title="Chapter 6. Tacticals" /><link rel="next" href="tacticals.html" title="Tacticals" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">The proof status</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_tacticals.html">Prev</a> </td><th width="60%" align="center">Chapter 6. Tacticals</th><td width="20%" align="right"> <a accesskey="n" href="tacticals.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="proofstatus"></a>The proof status</h2></div></div></div><p>
+ During an interactive proof, the proof status is made of
+ the set of sequents to prove and the partial proof built so far.
+ </p><p>The partial proof can be <a class="link" href="cicbrowser.html#aboutproof" title="Looking at a proof under development">inspected</a>
+ on demand in the CIC browser. It will be shown in pseudo-natural language
+ produced on the fly from the proof term.</p><p>The set of sequents to prove is shown in the notebook of the
+ <a class="link" href="authoring.html#authoringinterface" title="The authoring interface">authoring interface</a>, in the
+ top-right corner of the main window of Matita. Each tab shows a different
+ sequent, named with a question mark followed by a number. The current
+ role of the sequent, according to the following description, is also
+ shown in the tab tag.
+ </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p><a id="selectedsequents"></a>
+ <span class="bold"><strong>Selected sequents</strong></span>
+ (name in boldface, e.g. <span class="bold"><strong>?3</strong></span>).
+ The next tactic will be applied to every selected sequent, producing
+ new selected sequents. <a class="link" href="tacticals.html" title="Tacticals">Tacticals</a>
+ such as branching ("<span class="bold"><strong>[</strong></span>")
+ or "<span class="bold"><strong>focus</strong></span>" can be used
+ to change the set of selected sequents.
+ </p></li><li class="listitem"><p><a id="siblingsequents"></a>
+ <span class="bold"><strong>Sibling sequents</strong></span>
+ (name prefixed by a vertical bar and their position, e.g.
+ |<sub>3</sub>?2). When the set of selected sequents
+ has more than one element, the user can decide to focus in turn on each
+ of them. The branching <a class="link" href="tacticals.html" title="Tacticals">tactical</a>
+ ("<span class="bold"><strong>[</strong></span>") selects the first
+ sequent only, marking every previously selected sequent as a sibling
+ sequent. Each sibling sequent is given a different position. The
+ tactical "<span class="bold"><strong>2,3:</strong></span>" can be used to
+ select one or more sibling sequents, different from the one proposed,
+ according to their position. Once the user starts to work on the
+ selected sibling sequents it becomes impossible to select a new
+ set of siblings until the ("<span class="bold"><strong>|</strong></span>")
+ tactical is used to end work on the current one.
+ </p></li><li class="listitem"><p><a id="solvedsequents"></a>
+ <span class="bold"><strong>Automatically solved sibling sequents</strong></span>
+ (name strokethrough, e.g. |<sub>3</sub><span class="strikethrough">?2</span>).
+ Sometimes a tactic can close by side effects a sibling sequent the
+ user has not selected yet. The sequent is left in the automatically
+ solved status in order for the user to explicitly accept
+ (using the "<span class="bold"><strong>skip</strong></span>"
+ <a class="link" href="tacticals.html" title="Tacticals">tactical</a>) the automatic
+ instantiation in the proof script. This way the correspondence between
+ the number of branches in the proof script and the number of sequents
+ generated in the proof is preserved.
+ </p></li></ol></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_tacticals.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tacticals.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tacticals.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 6. Tacticals </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Tacticals</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 9. Other commands</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tac_bydone.html" title="done" /><link rel="next" href="command_check.html" title="check" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 9. Other commands</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_bydone.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="command_check.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_commands"></a>Chapter 9. Other commands</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_commands.html#command_alias">alias</a></span></dt><dt><span class="sect1"><a href="command_check.html">check</a></span></dt><dt><span class="sect1"><a href="command_coercion.html">coercion</a></span></dt><dt><span class="sect1"><a href="command_include.html">include</a></span></dt><dt><span class="sect1"><a href="command_include_alias.html">include alias</a></span></dt><dt><span class="sect1"><a href="command_qed.html">qed</a></span></dt><dt><span class="sect1"><a href="command_qed_minus.html">qed-</a></span></dt><dt><span class="sect1"><a href="command_unification_hint.html">unification hint</a></span></dt><dt><span class="sect1"><a href="command_universe_constraints.html">universe constraint</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_alias"></a>alias</h2></div></div></div><p><strong class="userinput"><code>alias id "s" = "def"</code></strong></p><p><strong class="userinput"><code>alias symbol "s" (instance n) = "def"</code></strong></p><p><strong class="userinput"><code>alias num (instance n) = "def"</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>alias</strong></span>
+ [<span class="bold"><strong>id</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span>
+ | <span class="bold"><strong>symbol</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> [<span class="bold"><strong>(instance</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span><span class="bold"><strong>)</strong></span>] <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span>
+ | <span class="bold"><strong>num</strong></span> [<span class="bold"><strong>(instance</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span><span class="bold"><strong>)</strong></span>] <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span>
+ ]
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>Used to give an hint to the disambiguating parser.
+ When the parser is faced to the identifier (or symbol)
+ <span class="command"><strong>s</strong></span> or to any number, it will prefer
+ interpretations that "map <span class="command"><strong>s</strong></span> (or the
+ number) to <span class="command"><strong>def</strong></span>". For identifiers,
+ "def" is the URI of the interpretation.
+ E.g.: <span class="command"><strong>cic:/matita/nat/nat.ind#xpointer(1/1/1)</strong></span>
+ for the first constructor of the first inductive type defined
+ in the block of inductive type(s)
+ <span class="command"><strong>cic:/matita/nat/nat.ind</strong></span>.
+ For symbols and numbers, "def" is the label used to
+ mark the wanted
+ <a class="link" href="ch05s02.html#interpretation">interpretation</a>.
+ </p><p>When a symbol or a number occurs several times in the
+ term to be parsed, it is possible to give an hint only for the
+ instance <span class="command"><strong>n</strong></span>. When the instance is omitted,
+ the hint is valid for every occurrence.
+ </p><p>
+ Hints are automatically inserted in the script by Matita every
+ time the user is interactively asked a question to disambiguate
+ a term. This way the user won't be posed the same question twice
+ when the script will be executed again.</p></dd></dl></div><p>
+ </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_bydone.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="command_check.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">done </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> check</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 8. Declarative Tactics</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tac_whd.html" title="whd" /><link rel="next" href="tac_assume.html" title="assume" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 8. Declarative Tactics</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_whd.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="tac_assume.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_declarative_tactics"></a>Chapter 8. Declarative Tactics</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_declarative_tactics.html#declarative_tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_assume.html">assume</a></span></dt><dt><span class="sect1"><a href="tac_suppose.html">suppose</a></span></dt><dt><span class="sect1"><a href="tac_let.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_thatisequivalentto.html">that is equivalent to</a></span></dt><dt><span class="sect1"><a href="tac_thesisbecomes.html">the thesis becomes</a></span></dt><dt><span class="sect1"><a href="tac_weneedtoprove.html">we need to prove</a></span></dt><dt><span class="sect1"><a href="tac_bytermweproved.html">we proved</a></span></dt><dt><span class="sect1"><a href="tac_existselim.html">let such that</a></span></dt><dt><span class="sect1"><a href="tac_andelim.html">we have</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbyinduction.html">we proceed by induction on</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbycases.html">we proceed by cases on</a></span></dt><dt><span class="sect1"><a href="tac_case.html">case</a></span></dt><dt><span class="sect1"><a href="tac_byinduction.html">by induction hypothesis we know</a></span></dt><dt><span class="sect1"><a href="tac_conclude.html">conclude</a></span></dt><dt><span class="sect1"><a href="tac_obtain.html">obtain</a></span></dt><dt><span class="sect1"><a href="tac_rewrite_step.html">=</a></span></dt><dt><span class="sect1"><a href="tac_bydone.html">done</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="declarative_tactics_quickref"></a>Quick reference card</h2></div></div></div><p>
+ </p><div class="table"><a id="idm3387"></a><p class="title"><strong>Table 8.1. tactics</strong></p><div class="table-contents"><table class="table" summary="tactics" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.declarative_tactic"></a><span class="emphasis"><em><a class="link" href="sec_tactics.html#grammar.tactic">tactic</a></em></span></td><td style="">::=</td><td style="">
+ <a class="link" href="tac_rewrite_step.html" title="="><span class="bold"><strong>=</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> [<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span> | <span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>using once</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>proof</strong></span>] [<span class="bold"><strong>done</strong></span>]
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_assume.html" title="assume"><span class="bold"><strong>assume</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> : </strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_byinduction.html" title="by induction hypothesis we know"><span class="bold"><strong>by induction hypothesis we know</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_case.html" title="case"><span class="bold"><strong>case</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>] … [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_conclude.html" title="conclude"><span class="bold"><strong>conclude</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <a class="link" href="tac_bydone.html" title="done"><span class="bold"><strong>done</strong></span></a></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>such that</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> = </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_obtain.html" title="obtain"><span class="bold"><strong>obtain</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_suppose.html" title="suppose"><span class="bold"><strong>suppose</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>) </strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <a class="link" href="tac_thatisequivalentto.html" title="that is equivalent to"><span class="bold"><strong>that is equivalent to</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_thesisbecomes.html" title="the thesis becomes"><span class="bold"><strong>the thesis becomes</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_weneedtoprove.html" title="we need to prove"><span class="bold"><strong>we need to prove</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>)</strong></span>]
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_weproceedbycases.html" title="we proceed by cases on"><span class="bold"><strong>we proceed by cases on</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_weproceedbyinduction.html" title="we proceed by induction on"><span class="bold"><strong>we proceed by induction on</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> to prove </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <a class="link" href="tac_bytermweproved.html" title="we proved"><span class="bold"><strong>we proved</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>)</strong></span>]
+ </td></tr></tbody></table></div></div><p><br class="table-break" />
+
+ </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_whd.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="tac_assume.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">whd </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> assume</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 3. Getting started</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="inst_from_src.html" title="Installing from sources" /><link rel="next" href="cicbrowser.html" title="Browsing and searching" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 3. Getting started</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="inst_from_src.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="cicbrowser.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_gettingstarted"></a>Chapter 3. Getting started</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_gettingstarted.html#unicode">How to type Unicode symbols</a></span></dt><dt><span class="sect1"><a href="cicbrowser.html">Browsing and searching</a></span></dt><dd><dl><dt><span class="sect2"><a href="cicbrowser.html#browsinglib">Browsing the library</a></span></dt><dt><span class="sect2"><a href="cicbrowser.html#aboutproof">Looking at a proof under development</a></span></dt></dl></dd><dt><span class="sect1"><a href="authoring.html">Authoring</a></span></dt><dd><dl><dt><span class="sect2"><a href="authoring.html#compilation">How to compile a script</a></span></dt><dt><span class="sect2"><a href="authoring.html#authoringinterface">The authoring interface</a></span></dt></dl></dd></dl></div><p> If you are already familiar with the Calculus of (Co)Inductive
+ Constructions (CIC) and with interactive theorem provers with procedural
+ proof languages (expecially Coq), getting started with Matita is relatively
+ easy. You just need to learn how to type Unicode symbols, how to browse
+ and search the library and how to author a proof script.</p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="unicode"></a>How to type Unicode symbols</h2></div></div></div><p>Unicode characters can be typed in several ways:</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>Using the "Ctrl+Shift+Unicode code" standard Gnome shortcut. E.g. Ctrl+Shift+3a9 generates "Ω".</p></li><li class="listitem"><p>Typing the ligature "\name" where "name"
+ is a standard Unicode or LaTeX name for the character or an
+ ASCII art resembling the shape of the character. Pressing
+ "Alt+L" or Space or Enter just after the last character
+ of the name converts
+ the ligature to the Unicode symbol.
+ E.g. "\Delta" followed by Alt+L generates
+ "Δ", while pressing Alt-L after "=>" generates
+ "⇒"</p></li><li class="listitem"><p>Typing a symbol and rotating trough its equivalence class
+ with Alt-L. E.g. pressing Alt-L after an "l"
+ generates a "λ", while pressing Alt-L after an
+ "→" once generates "⇉" and pressing
+ Alt-L again generates "⇒".
+ </p></li></ul></div><p>
+ The comprehensive list of symbols names or shortcuts and their equivalence
+ classes is available clicking on the "TeX/UTF-8 table" item
+ of the "View" menu.
+ </p><p>
+ There is a memory mechanism related to equivalence classes that
+ remembers your last choice, making it the default one. For example,
+ if you use "_" to generate "⎻"
+ (that is the third choice, after "⎽" and "⎼"),
+ the next time you type Alt-L
+ after "_" you immediately get "⎻".
+ </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="inst_from_src.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="cicbrowser.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Installing from sources </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Browsing and searching</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 2. Installation</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="WrtCoq.html" title="Matita vs Coq" /><link rel="next" href="inst_from_src.html" title="Installing from sources" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 2. Installation</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="WrtCoq.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="inst_from_src.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_install"></a>Chapter 2. Installation</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_install.html#inst_livecd">Using the LiveCD</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_install.html#make_vmachine">Creating the virtual machine</a></span></dt><dt><span class="sect2"><a href="sec_install.html#idm148">Sharing files with the real PC</a></span></dt></dl></dd><dt><span class="sect1"><a href="inst_from_src.html">Installing from sources</a></span></dt><dd><dl><dt><span class="sect2"><a href="inst_from_src.html#get_source_code">Getting the source code</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_requirements">Requirements</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_instructions">Compiling and installing</a></span></dt></dl></dd></dl></div><p>
+ Matita is a quite complex piece of software, we thus recommend
+ you to either install al precompiled version or use the LiveCD.
+ If you are running Debian GNU/Linux (or one of its derivatives
+ like Ubuntu), you can install matita typing
+ </p><pre class="programlisting"> aptitude install matita matita-standard-library </pre><p>
+ If you are running MacOSX or Windows, give the LiveCD a try before
+ trying to compile Matita from its sources.
+ </p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="inst_livecd"></a>Using the LiveCD</h2></div></div></div><p>
+ In the following, we will assume you have installed
+ <a class="ulink" href="http://www.virtualbox.org" target="_top">virtualbox</a>
+ for your platform and downloaded the .iso image of the LiveCD
+ </p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="make_vmachine"></a>Creating the virtual machine</h3></div></div></div><p>
+ Click on the New button, a wizard will popup, you should ask to
+ its questions as follows
+ </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>
+ The name should be something like Matita, but can
+ be any meaningful string.
+ </p></li><li class="listitem"><p>
+ The OS type should be Debian
+ </p></li><li class="listitem"><p>
+ The base memory size can be 256 mega bytes, but you may
+ want to increase it if you are going to work with huge
+ formalizations.
+ </p></li><li class="listitem"><p>
+ The boot hard disk should be no hard disk. It may complain
+ that this choice is not common, but it is right, since you
+ will run a LiveCD you do not need to emulate an hard drive.
+ </p></li></ol></div><p>
+ Now that you are done with the creation of the virtual machine,
+ you need to insert the LiveCD in the virtual cd reader unit.
+ </p><div class="figure"><a id="idm116"></a><p class="title"><strong>Figure 2.1. The brand new virtual machine</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox1.png" alt="The breand new virtual machine" /></div></div></div><br class="figure-break" /><p>
+ Click on CD/DVD-ROM (that should display something like: Not mouted).
+ Then click on mount CD/DVD drive and select the ISO image
+ option. The combo-box should display no available image, you need to
+ add the ISO image you downloaded from the Matita website clicking on
+ the button near the combo-box.
+ to start the virtual machine.
+ </p><div class="figure"><a id="idm124"></a><p class="title"><strong>Figure 2.2. Mounting an ISO image</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox2.png" alt="Mounting an ISO image" /></div></div></div><br class="figure-break" /><p>
+ In the newely opened window click
+ the Add button
+ </p><div class="figure"><a id="idm132"></a><p class="title"><strong>Figure 2.3. Choosing the ISO image</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox3.png" alt="Choosing the ISO image" /></div></div></div><br class="figure-break" /><p>
+ A new windows will pop-up: choose the file you downloaded
+ (usually matita-version.iso) and click open.
+ </p><div class="figure"><a id="idm140"></a><p class="title"><strong>Figure 2.4. Choosing the ISO image</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox35.png" alt="Choosing the ISO image" /></div></div></div><br class="figure-break" /><p>
+ Now select the new entry you just added as the CD image
+ you want to insert in the virtual CD drive.
+ You are now ready to start the virtual machine.
+ </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="idm148"></a>Sharing files with the real PC</h3></div></div></div><p>
+ The virtual machine Matita will run on, has its own file
+ system, that is completely separated from the one of your
+ real PC (thus your files are not available in the
+ emulated environment) and moreover it is a non-presistent
+ file system (thus you data is lost every time you
+ turn off the virtual machine).
+ </p><p>
+ Virtualbox allows you to share a real folder (beloging
+ to your real PC) with the emulated computer. Since this
+ folder is persistent, you are encouraged to put
+ your work there, so that it is not lost when the virtual
+ machine is powered off.
+ </p><p>
+ The first step to set up a shared folder is to click
+ on the shared folder configuration entry
+ of the virtual machine.
+ </p><div class="figure"><a id="idm153"></a><p class="title"><strong>Figure 2.5. Set up a shared folder</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox4.png" alt="Shared folder" /></div></div></div><br class="figure-break" /><p>
+ Then you shuld add a shared folder clicking on the
+ plus icon on the right
+ </p><div class="figure"><a id="idm161"></a><p class="title"><strong>Figure 2.6. Choosing the folder to share</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox5.png" alt="Shared folder" /></div></div></div><br class="figure-break" /><p>
+ Then you have to specify the real PC folder you want to share
+ and name it. A reasonable folder to share is /home on
+ a standard Unix system, while /Users on MaxOSX.
+ The name you give to the share is important, you should
+ remember it.
+ </p><div class="figure"><a id="idm169"></a><p class="title"><strong>Figure 2.7. Naming the shared folder</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox6.png" alt="Shared folder" /></div></div></div><br class="figure-break" /><p>
+ Once your virtual machine is up and running, you can
+ mount (that meand have access to) the shared folder
+ by clicking on the Mount VirtualBox share icon, and typing
+ the name of the share.
+ </p><div class="figure"><a id="idm177"></a><p class="title"><strong>Figure 2.8. Using it from the virtual machine</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox7.png" alt="Shared folder at work" /></div></div></div><br class="figure-break" /><p>
+ A window will then pop-up, and its content will be the
+ the content of the real PC folder.
+ </p></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="WrtCoq.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="inst_from_src.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Matita vs Coq </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Installing from sources</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 1. Introduction</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="next" href="WrtCoq.html" title="Matita vs Coq" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 1. Introduction</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="index.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="WrtCoq.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_intro"></a>Chapter 1. Introduction</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_intro.html#Features">Features</a></span></dt><dt><span class="sect1"><a href="WrtCoq.html">Matita vs Coq</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="Features"></a>Features</h2></div></div></div><p><span class="application">Matita</span> is an interactive theorem prover
+ (or proof assistant) with the following characteristics:</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>It is based on a variant of the Calculus of (Co)Inductive Constructions (CIC). CIC is also the logic of the Coq proof assistant.</p></li><li class="listitem"><p>It adopts a procedural proof language, but it has a new set of small step tacticals that improve proof structuring and debugging.</p></li><li class="listitem"><p>It has a stand-alone graphical user interface (GUI) inspired by
+CtCoq/Proof General. The GUI is implemented according to the state
+of the art. In particular:</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "><li class="listitem"><p>It is based and fully integrated with Gtk/Gnome.</p></li><li class="listitem"><p>An on-line help can be browsed via the Gnome documentation browser.</p></li><li class="listitem"><p>Mathematical formulae are rendered via Unicode.</p></li></ul></div></li><li class="listitem"><p>It allows the use of the typical ambiguous mathematical notation by means of a disambiguating parser.</p></li></ul></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="index.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="WrtCoq.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top"><span class="application">Matita</span> V0.99.5
+ User Manual (rev. 0.99.5
+) </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Matita vs Coq</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 10. License</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="command_universe_constraints.html" title="universe constraint" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 10. License</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_universe_constraints.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> </td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_license"></a>Chapter 10. License</h1></div></div></div><p> Both Matita and this document are part of HELM, an Hypertextual,
+ Electronic Library of Mathematics, developed at the Computer Science
+ Department, University of Bologna, Italy. </p><p> HELM is free software; you can redistribute it and/or modify it under
+ the terms of the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any later
+ version. </p><p> HELM is distributed in the hope that it will be useful, but WITHOUT ANY
+ WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
+ A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+</p><p> You should have received a copy of the GNU General Public License along
+ with HELM; if not, write to the Free Software Foundation, Inc., 51 Franklin
+ St, Fifth Floor, Boston, MA 02110-1301 USA. A copy of the GNU General
+ Public License is available at <a class="ulink" href="http://www.gnu.org/copyleft/gpl.html" target="_top">this link</a>. </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_universe_constraints.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> </td></tr><tr><td width="40%" align="left" valign="top">universe constraint </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> </td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 6. Tacticals</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="ch05s02.html" title="interpretation" /><link rel="next" href="proofstatus.html" title="The proof status" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 6. Tacticals</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch05s02.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="proofstatus.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_tacticals"></a>Chapter 6. Tacticals</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_tacticals.html#idm2224">Interactive proofs and definitions</a></span></dt><dt><span class="sect1"><a href="proofstatus.html">The proof status</a></span></dt><dt><span class="sect1"><a href="tacticals.html">Tacticals</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="idm2224"></a>Interactive proofs and definitions</h2></div></div></div><p>
+ An interactive definition is started by giving a
+ <a class="link" href="axiom_definition_declaration.html#definition" title="definition id[: term] [≝ term]">definition</a> command omitting
+ the definiens.
+ An interactive proof is started by using one of the
+ <a class="link" href="proofs.html" title="Proofs">proof commands</a> omitting
+ an explicit proof term.
+ </p><p>An interactive proof or definition can and must be terminated by
+ a <a class="link" href="command_qed.html" title="qed">qed</a> command when no more sequents are
+ left to prove. Between the command that starts the interactive session and
+ the qed command the user must provide a procedural proof script made
+ of <a class="link" href="sec_tactics.html" title="Chapter 7. Tactics">tactics</a> structured by means of
+ <a class="link" href="tacticals.html" title="Tacticals">tacticals</a>.</p><p>In the tradition of the LCF system, tacticals can be considered
+ higher order tactics. Their syntax is structured and they are executed
+ atomically. On the contrary, in Matita the syntax of several tacticals is
+ destructured into a sequence of tokens and tactics in such a way that is
+ is possible to stop execution after every single token or tactic.
+ The original semantics is preserved: the execution of the whole sequence
+ yields the result expected by the original LCF-like tactical.</p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch05s02.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="proofstatus.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">interpretation </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> The proof status</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 7. Tactics</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tacticals.html" title="Tacticals" /><link rel="next" href="tac_apply.html" title="apply" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 7. Tactics</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tacticals.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="tac_apply.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_tactics"></a>Chapter 7. Tactics</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_tactics.html#tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_apply.html">@</a></span></dt><dt><span class="sect1"><a href="tac_auto.html">//</a></span></dt><dt><span class="sect1"><a href="tac_intro.html">#</a></span></dt><dt><span class="sect1"><a href="tac_intro_clear.html">#_</a></span></dt><dt><span class="sect1"><a href="macro_intro.html">##</a></span></dt><dt><span class="sect1"><a href="tac_clear.html">-</a></span></dt><dt><span class="sect1"><a href="tac_constructor.html">%</a></span></dt><dt><span class="sect1"><a href="tac_decompose.html">*</a></span></dt><dt><span class="sect1"><a href="tac_rewrite.html">></a></span></dt><dt><span class="sect1"><a href="tac_applyS.html">applyS</a></span></dt><dt><span class="sect1"><a href="tac_assumption.html">assumption</a></span></dt><dt><span class="sect1"><a href="tac_cases.html">cases</a></span></dt><dt><span class="sect1"><a href="tac_change.html">change</a></span></dt><dt><span class="sect1"><a href="tac_cut.html">cut</a></span></dt><dt><span class="sect1"><a href="tac_destruct.html">destruct</a></span></dt><dt><span class="sect1"><a href="tac_elim.html">elim</a></span></dt><dt><span class="sect1"><a href="tac_generalize.html">generalize</a></span></dt><dt><span class="sect1"><a href="tac_inversion.html">inversion</a></span></dt><dt><span class="sect1"><a href="tac_lapply.html">lapply</a></span></dt><dt><span class="sect1"><a href="tac_letin.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_normalize.html">normalize</a></span></dt><dt><span class="sect1"><a href="tac_whd.html">whd</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tactics_quickref"></a>Quick reference card</h2></div></div></div><p>
+ </p><div class="table"><a id="idm2483"></a><p class="title"><strong>Table 7.1. tactics</strong></p><div class="table-contents"><table class="table" summary="tactics" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.tactic"></a><span class="emphasis"><em><a class="link" href="sec_tactics.html#grammar.tactic">tactic</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>@</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_applyS.html" title="applyS"><span class="bold"><strong>applyS</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <a class="link" href="tac_assumption.html" title="assumption">
+ <span class="bold"><strong>assumption</strong></span>
+ </a>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span><span class="bold"><strong>/</strong></span>. </td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <a class="link" href="tac_cases.html" title="cases"><span class="bold"><strong>cases</strong></span></a>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_change.html" title="change"><span class="bold"><strong>change</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> <span class="bold"><strong>with</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>-</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>%</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] [<span class="bol">{</span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>…<span class="bol">}</span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_cut.html" title="cut"><span class="bold"><strong>cut</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>*</strong></span>
+ [<span class="bold"><strong>as</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_destruct.html" title="destruct"><span class="bold"><strong>destruct</strong></span></a>
+ [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>] [<span class="bold"><strong>skip</strong></span> <span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_elim.html" title="elim"><span class="bold"><strong>elim</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_generalize.html" title="generalize"><span class="bold"><strong>generalize</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>#</strong></span>
+ <span class="emphasis"><em>
+ <a class="link" href="sec_terms.html#grammar.id">id</a>
+ </em></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>#_</strong></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_inversion.html" title="inversion"><span class="bold"><strong>inversion</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <a class="link" href="tac_lapply.html" title="lapply"><span class="bold"><strong>lapply</strong></span></a>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_letin.html" title="letin"><span class="bold"><strong>letin</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>##</strong></span>
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_normalize.html" title="normalize"><span class="bold"><strong>normalize</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
+ [<span class="bold"><strong>nodelta</strong></span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style="">[<span class="bold"><strong><</strong></span>|<span class="bold"><strong>></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_whd.html" title="whd"><span class="bold"><strong>whd</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> [<span class="bold"><strong>nodelta</strong></span>]</td></tr></tbody></table></div></div><p><br class="table-break" />
+
+ </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tacticals.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="tac_apply.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Tacticals </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> apply</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 4. Syntax</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="authoring.html" title="Authoring" /><link rel="next" href="axiom_definition_declaration.html" title="Definitions and declarations" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 4. Syntax</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="authoring.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="axiom_definition_declaration.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_terms"></a>Chapter 4. Syntax</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_terms.html#terms_and_co">Terms & co.</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_terms.html#lexical">Lexical conventions</a></span></dt><dt><span class="sect2"><a href="sec_terms.html#terms">Terms</a></span></dt></dl></dd><dt><span class="sect1"><a href="axiom_definition_declaration.html">Definitions and declarations</a></span></dt><dd><dl><dt><span class="sect2"><a href="axiom_definition_declaration.html#axiom">axiom</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#definition">definition</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#discriminator">discriminator</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inverter">inverter</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#letrec"><span class="emphasis"><em>TODO</em></span></a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inductive">(co)inductive types declaration</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#record">record</a></span></dt></dl></dd><dt><span class="sect1"><a href="proofs.html">Proofs</a></span></dt><dd><dl><dt><span class="sect2"><a href="proofs.html#theorem">theorem</a></span></dt><dt><span class="sect2"><a href="proofs.html#corollary">corollary</a></span></dt><dt><span class="sect2"><a href="proofs.html#lemma">lemma</a></span></dt><dt><span class="sect2"><a href="proofs.html#fact">fact</a></span></dt><dt><span class="sect2"><a href="proofs.html#example">example</a></span></dt></dl></dd><dt><span class="sect1"><a href="tacticargs.html">Tactic arguments</a></span></dt><dd><dl><dt><span class="sect2"><a href="tacticargs.html#pattern">pattern</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#reduction-kind">reduction-kind</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#auto-params">auto-params</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#justification">justification</a></span></dt></dl></dd></dl></div><p>To describe syntax in this manual we use the following conventions:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Non terminal symbols are emphasized and have a link to their
+ definition. E.g.: <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></li><li class="listitem"><p>Terminal symbols are in bold. E.g.:
+ <span class="bold"><strong>theorem</strong></span></p></li><li class="listitem"><p>Optional sequences of elements are put in square brackets.
+ E.g.: [<span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</p></li><li class="listitem"><p>Alternatives are put in square brakets and they are
+ separated by vertical bars. E.g.: [<span class="bold"><strong><</strong></span>|<span class="bold"><strong>></strong></span>]</p></li><li class="listitem"><p>Repetitions of a sequence of elements are given by putting the
+ sequence in square brackets, that are followed by three dots. The empty
+ sequence is a valid repetition.
+ E.g.: [<span class="bold"><strong>and</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…</p></li><li class="listitem"><p>Characters belonging to a set of characters are given
+ by listing the set elements in square brackets. Hyphens are used to
+ specify ranges of characters in the set.
+ E.g.: [<span class="bold"><strong>a</strong></span>-<span class="bold"><strong>zA</strong></span>-<span class="bold"><strong>Z0</strong></span>-<span class="bold"><strong>9_-</strong></span>]</p></li></ol></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="terms_and_co"></a>Terms & co.</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="lexical"></a>Lexical conventions</h3></div></div></div><div class="table"><a id="idm389"></a><p class="title"><strong>Table 4.1. qstring</strong></p><div class="table-contents"><table class="table" summary="qstring" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.qstring"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>"</strong></span><span class="emphasis"><em>〈〈any sequence of characters excluded "〉〉</em></span><span class="bold"><strong>"</strong></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm402"></a><p class="title"><strong>Table 4.2. id</strong></p><div class="table-contents"><table class="table" summary="id" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.id"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em>〈〈any sequence of letters, underscores or valid <a class="ulink" href="http://www.w3.org/TR/2004/REC-xml-20040204/#NT-Digit" target="_top">XML digits</a> prefixed by a latin letter ([a-zA-Z]) and post-fixed by a possible empty sequence of decorators ([?'`])〉〉</em></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm414"></a><p class="title"><strong>Table 4.3. nat</strong></p><div class="table-contents"><table class="table" summary="nat" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.nat"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em>〈〈any sequence of valid <a class="ulink" href="http://www.w3.org/TR/2004/REC-xml-20040204/#NT-Digit" target="_top">XML digits</a>〉〉</em></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm426"></a><p class="title"><strong>Table 4.4. char</strong></p><div class="table-contents"><table class="table" summary="char" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.char"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.char">char</a></em></span></td><td style="">::=</td><td style="">[<span class="bold"><strong>a</strong></span>-<span class="bold"><strong>zA</strong></span>-<span class="bold"><strong>Z0</strong></span>-<span class="bold"><strong>9_-</strong></span>]</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm440"></a><p class="title"><strong>Table 4.5. uri-step</strong></p><div class="table-contents"><table class="table" summary="uri-step" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.uri-step"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri-step">uri-step</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.char">char</a></em></span>[<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.char">char</a></em></span>]…</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm454"></a><p class="title"><strong>Table 4.6. uri</strong></p><div class="table-contents"><table class="table" summary="uri" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.uri"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span></td><td style="">::=</td><td style="">[<span class="bold"><strong>cic:/</strong></span>|<span class="bold"><strong>theory:/</strong></span>]<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri-step">uri-step</a></em></span>[<span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri-step">uri-step</a></em></span>]…<span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…[<span class="bold"><strong>#xpointer(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span><span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>[<span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>]…<span class="bold"><strong>)</strong></span>]</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm487"></a><p class="title"><strong>Table 4.7. csymbol</strong></p><div class="table-contents"><table class="table" summary="csymbol" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.csymbol"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>'</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm500"></a><p class="title"><strong>Table 4.8. symbol</strong></p><div class="table-contents"><table class="table" summary="symbol" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.symbol"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.symbol">symbol</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>〈〈None of the above〉〉</strong></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="terms"></a>Terms</h3></div></div></div><p>
+ </p><div class="table"><a id="tbl_terms"></a><p class="title"><strong>Table 4.9. Terms</strong></p><div class="table-contents"><table class="table" summary="Terms" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.term"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td><td style="">simple or delimited term</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">application</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>λ</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span><span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">λ-abstraction</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Π</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span><span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">dependent product meant to define a datatype</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>∀</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span><span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">dependent product meant to define a proposition</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>→</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">non-dependent product (logical implication or function space)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>let</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>|(<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>)] <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">local definition</td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>let</strong></span>
+ [<span class="bold"><strong>co</strong></span>]<span class="bold"><strong>rec</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.rec_def">rec_def</a></em></span>
+ </td><td style="">(co)recursive definitions</td></tr><tr><td style=""> </td><td style=""> </td><td style="">
+ [<span class="bold"><strong>and</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.rec_def">rec_def</a></em></span>]…
+ </td><td style=""> </td></tr><tr><td style=""> </td><td style=""> </td><td style="">
+ <span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ </td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style="">…</td><td style="">user provided notation</td></tr><tr><td style=""><a id="grammar.rec_def"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.rec_def">rec_def</a></em></span></td><td style="">::=</td><td style="">
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>|<span class="bold"><strong>_</strong></span>|<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]… <span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span>]…
+ </td><td style=""> </td></tr><tr><td style=""> </td><td style=""> </td><td style="">
+ [<span class="bold"><strong>on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]
+ [<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]
+ <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]
+ </td><td style=""> </td></tr></tbody></table></div></div><p><br class="table-break" />
+
+ </p><div class="table"><a id="idm665"></a><p class="title"><strong>Table 4.10. Simple terms</strong></p><div class="table-contents"><table class="table" summary="Simple terms" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.sterm"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>\subst[</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>≔</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ [<span class="bold"><strong>;</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>≔</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…
+ <span class="bold"><strong>]</strong></span>]
+ </td><td style="">identifier with optional explicit named substitution</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span></td><td style="">a qualified reference</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Prop</strong></span></td><td style="">the impredicative sort of propositions</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Set</strong></span></td><td style="">the impredicate sort of datatypes</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>CProp</strong></span></td><td style="">one fixed predicative sort of constructive propositions</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Type</strong></span></td><td style="">one predicative sort of datatypes</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>?</strong></span></td><td style="">implicit argument</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>?n</strong></span>
+ [<span class="bold"><strong>[</strong></span>
+ [<span class="bold"><strong>_</strong></span>|<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…
+ <span class="bold"><strong>]</strong></span>]</td><td style="">metavariable</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>match</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ [ <span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> ]
+ [ <span class="bold"><strong>return</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ]
+ <span class="bold"><strong>with</strong></span>
+ </td><td style="">case analysis</td></tr><tr><td style=""> </td><td style=""> </td><td style="">
+ <span class="bold"><strong>[</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_branch">match_branch</a></em></span>[<span class="bold"><strong>|</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_branch">match_branch</a></em></span>]…
+ <span class="bold"><strong>]</strong></span>
+ </td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span></td><td style="">cast</td></tr><tr><td style=""> </td><td style="">|</td><td style="">…</td><td style="">user provided notation at precedence 90</td></tr></tbody></table></div></div><p><br class="table-break" />
+
+ </p><div class="table"><a id="idm792"></a><p class="title"><strong>Table 4.11. Arguments</strong></p><div class="table-contents"><table class="table" summary="Arguments" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.args"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span></td><td style="">::=</td><td style="">
+ <span class="bold"><strong>_</strong></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]
+ </td><td style="">ignored argument</td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>(</strong></span><span class="bold"><strong>_</strong></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]<span class="bold"><strong>)</strong></span>
+ </td><td style="">ignored argument</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]<span class="bold"><strong>)</strong></span></td><td style=""> </td></tr><tr><td style=""><a id="grammar.args2"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args2">args2</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span></td><td style=""> </td></tr></tbody></table></div></div><p><br class="table-break" />
+
+ </p><div class="table"><a id="idm870"></a><p class="title"><strong>Table 4.12. Pattern matching</strong></p><div class="table-contents"><table class="table" summary="Pattern matching" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.match_branch"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_branch">match_branch</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_pattern">match_pattern</a></em></span> <span class="bold"><strong>⇒</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style=""> </td></tr><tr><td style=""><a id="grammar.match_pattern"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_pattern">match_pattern</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">0-ary constructor</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…<span class="bold"><strong>)</strong></span></td><td style="">n-ary constructor (binds the n arguments)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…</td><td style="">n-ary constructor (binds the n arguments)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>_</strong></span></td><td style="">any remaining constructor (ignoring its arguments)</td></tr></tbody></table></div></div><p><br class="table-break" />
+ </p></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="authoring.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="axiom_definition_declaration.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Authoring </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Definitions and declarations</td></tr></table></div></body></html>
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 5. Extending the syntax</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tacticargs.html" title="Tactic arguments" /><link rel="next" href="ch05s02.html" title="interpretation" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 5. Extending the syntax</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tacticargs.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="ch05s02.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_usernotation"></a>Chapter 5. Extending the syntax</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_usernotation.html#idm1489">notation</a></span></dt><dt><span class="sect1"><a href="ch05s02.html">interpretation</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="idm1489"></a>notation</h2></div></div></div><p><strong class="userinput"><code>notation usage "presentation" associativity with precedence p for content</code></strong></p><p><a id="notation"></a>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>notation</strong></span>
+ [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.usage">usage</a></em></span>] <span class="bold"><strong>"</strong></span><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_lhs">notation_lhs</a></em></span><span class="bold"><strong>"</strong></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.associativity">associativity</a></em></span>] <span class="bold"><strong>with</strong></span> <span class="bold"><strong>precedence</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>
+ <span class="bold"><strong>for</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_rhs">notation_rhs</a></em></span>
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>Declares a mapping between the presentation
+ AST <span class="command"><strong>presentation</strong></span> and the content AST
+ <span class="command"><strong>content</strong></span>. The declared presentation AST fragment
+ <span class="command"><strong>presentation</strong></span> is at precedence level
+ <span class="command"><strong>p</strong></span>. The precedence level is used to determine where
+ parentheses must be inserted. In particular, the content AST fragment
+ <span class="command"><strong>content</strong></span> is actually a pattern, since it contains
+ placeholders (variables) for sub-ASTs. Every placeholder for a term
+ is given an expected precedence level. Parentheses must be inserted
+ around sub-ASTs having a precedence level strictly smaller than the
+ expected one.</p><p>If <span class="command"><strong>presentation</strong></span> describes a binary
+ infix operator and if no precedence level is explicitly given for the
+ operator arguments, an <span class="command"><strong>associativity</strong></span> declaration
+ can be given to automatically choose the right level for the operands.
+ Otherwise, no <span class="command"><strong>associativity</strong></span> can be given.</p><p>If <span class="command"><strong>direction</strong></span> is
+ omitted, the mapping is bi-directional and is used both during
+ parsing and pretty-printing of terms. If <span class="command"><strong>direction</strong></span>
+ is <span class="command"><strong>></strong></span>, the mapping is used only during parsing;
+ if it is <span class="command"><strong><</strong></span>, it is used only during
+ pretty-printing. Thus it is possible to use simple notations to type
+ for writing the term, and nicer ones for rendering it.</p></dd><dt><span class="term">Notation arguments:</span></dt><dd><div class="table"><a id="idm1537"></a><p class="title"><strong>Table 5.1. usage</strong></p><div class="table-contents"><table class="table" summary="usage" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.usage"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.usage">usage</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong><</strong></span></td><td style="">Only for pretty-printing</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>></strong></span></td><td style="">Only for parsing</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1555"></a><p class="title"><strong>Table 5.2. associativity</strong></p><div class="table-contents"><table class="table" summary="associativity" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.associativity"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.associativity">associativity</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>left</strong></span> <span class="bold"><strong>associative</strong></span></td><td style="">Left associative</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>right</strong></span> <span class="bold"><strong>associative</strong></span></td><td style="">Right associative</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>non</strong></span> <span class="bold"><strong>associative</strong></span></td><td style="">Non associative (default)</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1582"></a><p class="title"><strong>Table 5.3. notation_rhs</strong></p><div class="table-contents"><table class="table" summary="notation_rhs" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.notation_rhs"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_rhs">notation_rhs</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_ast">unparsed_ast</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_meta">unparsed_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1604"></a><p class="title"><strong>Table 5.4. unparsed_ast</strong></p><div class="table-contents"><table class="table" summary="unparsed_ast" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.unparsed_ast"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_ast">unparsed_ast</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>@{</strong></span><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.enriched_term">enriched_term</a></em></span><span class="bold"><strong>}</strong></span></td><td style="">A content level AST (a term which is parsed, but not disambiguated).</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>@</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="command"><strong>@id</strong></span> is just an abbreviation for <span class="command"><strong>@{id}</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>@</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span></td><td style=""><span class="command"><strong>@'symbol</strong></span> is just an abbreviation for <span class="command"><strong>@{'symbol}</strong></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1639"></a><p class="title"><strong>Table 5.5. enriched_term</strong></p><div class="table-contents"><table class="table" summary="enriched_term" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.enriched_term"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.enriched_term">enriched_term</a></em></span></td><td style="">::=</td><td style="">〈〈A term that may contain occurrences of <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_meta">unparsed_meta</a></em></span>, even as variable names in binders, and occurrences of <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span>〉〉</td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1655"></a><p class="title"><strong>Table 5.6. unparsed_meta</strong></p><div class="table-contents"><table class="table" summary="unparsed_meta" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.unparsed_meta"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_meta">unparsed_meta</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>${</strong></span><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span><span class="bold"><strong>}</strong></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>$</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="command"><strong>$id</strong></span> is just an abbreviation for <span class="command"><strong>${id}</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>$</strong></span><span class="bold"><strong>_</strong></span></td><td style=""><span class="command"><strong>$_</strong></span> is just an abbreviation for <span class="command"><strong>${_}</strong></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1690"></a><p class="title"><strong>Table 5.7. level2_meta</strong></p><div class="table-contents"><table class="table" summary="level2_meta" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.level2_meta"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_ast">unparsed_ast</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>term</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>number</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>ident</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fresh</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>anonymous</strong></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fold</strong></span> [<span class="bold"><strong>left</strong></span>|<span class="bold"><strong>right</strong></span>] <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="bold"><strong>rec</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>default</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>if</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="bold"><strong>then</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="bold"><strong>else</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fail</strong></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1806"></a><p class="title"><strong>Table 5.8. notation_lhs</strong></p><div class="table-contents"><table class="table" summary="notation_lhs" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.notation_lhs"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_lhs">notation_lhs</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]…</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1820"></a><p class="title"><strong>Table 5.9. layout</strong></p><div class="table-contents"><table class="table" summary="layout" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.layout"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\sub</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Subscript</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\sup</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Superscript</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\below</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\above</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\over</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\atop</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\frac</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Fraction</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>\infrule</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Inference rule (premises, conclusion, rule name)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>\sqrt</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Square root</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>\root</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\of</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Generalized root</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>hbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Horizontal box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>vbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Vertical box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>hvbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Horizontal and vertical box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>hovbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Horizontal or vertical box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>break</strong></span></td><td style="">Breakable space</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Group</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for a term with no explicit precedence</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>term</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for a term with explicit expected precedence</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>number</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for a natural number</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>ident</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for an identifier</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span></td><td style="">Literal</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>opt</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Optional layout (it can be omitted for parsing)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>list0</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>
+ [<span class="bold"><strong>sep</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span>]</td><td style="">List of layouts separated by <span class="command"><strong>sep</strong></span> (default:
+ any blank)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>list1</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>
+ [<span class="bold"><strong>sep</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span>]</td><td style="">Non empty list of layouts separated by <span class="command"><strong>sep</strong></span>
+ (default: any blank)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>mstyle</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> value (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>)
+ </td><td style="">Style attributes like color #ff0000</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>mpadded</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> value (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>)
+ </td><td style="">padding attributes like width -150%</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>maction</strong></span> (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>)
+ [ (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>) … ]
+ </td><td style="">Alternative notations (output only)</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm2094"></a><p class="title"><strong>Table 5.10. literal</strong></p><div class="table-contents"><table class="table" summary="literal" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.literal"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.symbol">symbol</a></em></span></td><td style="">Unicode symbol</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></td><td style="">Natural number (a constant)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>'</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>'</strong></span></td><td style="">New keyword for the lexer</td></tr></tbody></table></div></div><br class="table-break" /></dd></dl></div><p>
+ </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tacticargs.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="ch05s02.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Tactic arguments </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> interpretation</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we have</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_existselim.html" title="let such that" /><link rel="next" href="tac_weproceedbyinduction.html" title="we proceed by induction on" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we have</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_existselim.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weproceedbyinduction.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_andelim"></a>we have</h2></div></div></div><p><strong class="userinput"><code>justification we have A (H1) and B (H2)</code></strong>
+ </p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>we have</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ <span class="bold"><strong>( </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> ) and </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ <span class="bold"><strong> ( </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ None.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It applies the left multiplicative introduction rule for the conjunction on the formula <span class="command"><strong>A ∧ B</strong></span> (in Natural Deduction this corresponds to the elimination rule for the conjunction).
+ </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent with <span class="command"><strong>A ∧ B</strong></span> as the conclusion is opened and then immediately closed using the given justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and two new hypotheses <span class="command"><strong>H1 : A</strong></span> and <span class="command"><strong>H2 : B</strong></span> are added to the context.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_existselim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weproceedbyinduction.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">let such that </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proceed by induction on</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>apply</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="next" href="tac_auto.html" title="auto" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">apply</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_tactics.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_auto.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_apply"></a>apply</h2></div></div></div><p><strong class="userinput"><code>@t</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>@</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must have type
+ <span class="command"><strong>T<sub>1</sub> → … →
+ T<sub>n</sub> → G</strong></span>
+ where <span class="command"><strong>G</strong></span> can be unified with the conclusion
+ of the current sequent.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent by applying <span class="command"><strong>t</strong></span> to <span class="command"><strong>n</strong></span> implicit arguments (that become new sequents).</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each premise
+ <span class="command"><strong>T<sub>i</sub></strong></span> that is not
+ instantiated by unification. <span class="command"><strong>T<sub>i</sub></strong></span> is
+ the conclusion of the <span class="command"><strong>i</strong></span>-th new sequent to
+ prove.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_tactics.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_auto.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 7. Tactics </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> auto</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>applyS</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_rewrite.html" title="rewrite" /><link rel="next" href="tac_assumption.html" title="assumption" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">applyS</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_rewrite.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_assumption.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_applyS"></a>applyS</h2></div></div></div><p><strong class="userinput"><code>applyS t auto_params</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>applyS</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must have type
+ <span class="command"><strong>T<sub>1</sub> → ... →
+ T<sub>n</sub> → G</strong></span>.</p></dd><dt><span class="term">Action:</span></dt><dd><p><span class="command"><strong>applyS</strong></span> is useful when
+ <span class="command"><strong>apply</strong></span> fails because the current goal
+ and the conclusion of the applied theorems are extensionally
+ equivalent up to instantiation of metavariables, but cannot
+ be unified. E.g. the goal is <span class="command"><strong>P(n*O+m)</strong></span> and
+ the theorem to be applied proves <span class="command"><strong>∀m.P(m+O)</strong></span>.
+ </p><p>
+ It tries to automatically rewrite the current goal using
+ <a class="link" href="tac_auto.html" title="auto">auto paramodulation</a>
+ to make it unifiable with <span class="command"><strong>G</strong></span>.
+ Then it closes the current sequent by applying
+ <span class="command"><strong>t</strong></span> to <span class="command"><strong>n</strong></span>
+ implicit arguments (that become new sequents).
+ The <span class="command"><strong>auto_params</strong></span> parameters are passed
+ directly to <span class="command"><strong>auto paramodulation</strong></span>.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each premise
+ <span class="command"><strong>T<sub>i</sub></strong></span> that is not
+ instantiated by unification. <span class="command"><strong>T<sub>i</sub></strong></span> is
+ the conclusion of the <span class="command"><strong>i</strong></span>-th new sequent to
+ prove.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_rewrite.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_assumption.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">rewrite </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> assumption</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>assume</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="next" href="tac_suppose.html" title="suppose" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">assume</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_declarative_tactics.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_suppose.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_assume"></a>assume</h2></div></div></div><p><strong class="userinput"><code>assume x : T</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>assume</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> : </strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>
+ The conclusion of the sequent to prove must be a universal quantification.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It applies the right introduction rule for the universal quantifier, closing the current sequent (in Natural Deduction this corresponds to the introduction rule for the quantifier).
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
+ It opens a new sequent to prove the quantified subformula adding <span class="command"><strong>x : T</strong></span> to the hypotheses.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_declarative_tactics.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_suppose.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 8. Declarative Tactics </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> suppose</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>assumption</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_applyS.html" title="applyS" /><link rel="next" href="tac_cases.html" title="cases" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">assumption</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_applyS.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_cases.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_assumption"></a>assumption</h2></div></div></div><p><strong class="userinput"><code>assumption </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>assumption</strong></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>There must exist an hypothesis whose type can be unified with
+ the conclusion of the current sequent.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent exploiting an hypothesis.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_applyS.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_cases.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">applyS </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> cases</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>auto</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_apply.html" title="apply" /><link rel="next" href="tac_intro.html" title="intro" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">auto</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_apply.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_intro.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_auto"></a>auto</h2></div></div></div><p><strong class="userinput"><code>/params/</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span><span class="bold"><strong>/</strong></span>. </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None, but the tactic may fail finding a proof if every
+ proof is in the search space that is pruned away. Pruning is
+ controlled by the optional <span class="command"><strong>params</strong></span>.
+ Moreover, only lemmas whose type signature is a subset of the
+ signature of the current sequent are considered. The signature of
+ a sequent is essentially the set of constats appearing in it.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent by repeated application of
+ rewriting steps (unless <span class="command"><strong>paramodulation</strong></span> is
+ omitted), hypothesis and lemmas in the library.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_apply.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_intro.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">apply </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> intro</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>done</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_rewrite_step.html" title="=" /><link rel="next" href="sec_commands.html" title="Chapter 9. Other commands" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">done</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_rewrite_step.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="sec_commands.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_bydone"></a>done</h2></div></div></div><p><strong class="userinput"><code>justification done</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>done</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The user is proving a sequent which was opened with the tactic <span class="bold"><strong>we need to prove</strong></span>, or the user is proving a sequent which was opened with the tactic <span class="bold"><strong>we proceed by induction/cases on</strong></span>, or the user is proving a chain of equalities that was started with either the tactic <span class="bold"><strong>conclude</strong></span> or <span class="bold"><strong>obtain</strong></span>.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent with the given justification.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_rewrite_step.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_commands.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">= </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 9. Other commands</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>by induction hypothesis we know</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_case.html" title="case" /><link rel="next" href="tac_conclude.html" title="conclude" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">by induction hypothesis we know</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_case.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_conclude.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_byinduction"></a>by induction hypothesis we know</h2></div></div></div><p><strong class="userinput"><code>by induction hypothesis we know P (id)</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>by induction hypothesis we know</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The user must have started proving a case for a proof by induction/case-analysis.</p></dd><dt><span class="term">Action:</span></dt><dd><p> It introduces the inductive hypothesis. </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_case.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_conclude.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">case </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> conclude</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proved</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_weneedtoprove.html" title="we need to prove" /><link rel="next" href="tac_existselim.html" title="let such that" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proved</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_weneedtoprove.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_existselim.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_bytermweproved"></a>we proved</h2></div></div></div><p><strong class="userinput"><code>justification we proved T [(id)]</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>we proved</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>)</strong></span>]
+ </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ None.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ If <span class="command"><strong>id</strong></span> is supplied, a logical cut on <span class="command"><strong>T</strong></span> is made. Otherwise, if <span class="command"><strong>T</strong></span> is identical to the current conclusion, it allows the user to start a chain of reductions on the conclusion with the tactic <span class="bold"><strong>that is equivalent to</strong></span>.
+ </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>
+ If <span class="command"><strong>id</strong></span> is supplied, a new sequent with <span class="command"><strong>T</strong></span> as the conclusion is opened and then immediately closed using the supplied justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and a new hypotesis <span class="command"><strong>T</strong></span> is added to the context, with name <span class="command"><strong>id</strong></span>.
+ If <span class="command"><strong>id</strong></span> is not supplied, no new sequents are opened.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_weneedtoprove.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_existselim.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we need to prove </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> let such that</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>case</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_weproceedbycases.html" title="we proceed by cases on" /><link rel="next" href="tac_byinduction.html" title="by induction hypothesis we know" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">case</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_weproceedbycases.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_byinduction.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_case"></a>case</h2></div></div></div><p><strong class="userinput"><code>case id (id1:T1) … (idn:Tn)</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>case</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>] … [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>]</p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The user must have started a proof by induction/cases that has not been concluded yet, <span class="command"><strong>id</strong></span> must be a constructor for the inductive type of the term under induction/case-analysis, and the case must not have already been proved.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It starts the proof for the case <span class="command"><strong>id</strong></span>, where <span class="command"><strong>id1:T1</strong></span>,…,<span class="command"><strong>idn:Tn</strong></span> are the arguments of the constructor, each declared with its type.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>The sequent for the case <span class="command"><strong>id</strong></span>.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_weproceedbycases.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_byinduction.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we proceed by cases on </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> by induction hypothesis we know</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>cases</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_assumption.html" title="assumption" /><link rel="next" href="tac_change.html" title="change" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">cases</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_assumption.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_change.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_cases"></a>cases</h2></div></div></div><p><strong class="userinput"><code>
+ cases t pattern
+ </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>cases</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
+ </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>
+ <span class="command"><strong>t</strong></span> must inhabit an inductive type
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It proceed by cases on <span class="command"><strong>t</strong></span>. The new generated
+ hypothesis in each branch are named according to
+ <span class="command"><strong>hyps</strong></span>.
+ The elimintation predicate is restricted by
+ <span class="command"><strong>pattern</strong></span>. In particular, if some hypothesis
+ is listed in <span class="command"><strong>pattern</strong></span>, the hypothesis is
+ generalized and cleared before proceeding by cases on
+ <span class="command"><strong>t</strong></span>. Currently, we only support patterns of the
+ form <span class="command"><strong>H<sub>1</sub> … H<sub>n</sub> ⊢ %</strong></span>. This limitation will be lifted in the future.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>One new sequent for each constructor of the type of
+ <span class="command"><strong>t</strong></span>. Each sequent has a new hypothesis for
+ each argument of the constructor.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_assumption.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_change.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">assumption </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> change</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>change</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_cases.html" title="cases" /><link rel="next" href="tac_cut.html" title="cut" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">change</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_cases.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_cut.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_change"></a>change</h2></div></div></div><p><strong class="userinput"><code>change patt with t</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>change</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> <span class="bold"><strong>with</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>Each subterm matched by the pattern must be convertible
+ with the term <span class="command"><strong>t</strong></span> disambiguated in the context
+ of the matched subterm.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It replaces the subterms of the current sequent matched by
+ <span class="command"><strong>patt</strong></span> with the new term <span class="command"><strong>t</strong></span>.
+ For each subterm matched by the pattern, <span class="command"><strong>t</strong></span> is
+ disambiguated in the context of the subterm.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_cases.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_cut.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">cases </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> cut</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>clear</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="macro_intro.html" title="macro_input" /><link rel="next" href="tac_constructor.html" title="constructor" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">clear</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="macro_intro.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_constructor.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_clear"></a>clear</h2></div></div></div><p><strong class="userinput"><code>-H</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>-</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>
+ <span class="command"><strong>H</strong></span> must be an hypothesis of the
+ current sequent to prove.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It hides the hypothesis <span class="command"><strong>H</strong></span>
+ from the current sequent.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="macro_intro.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_constructor.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">macro_input </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> constructor</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>conclude</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_byinduction.html" title="by induction hypothesis we know" /><link rel="next" href="tac_obtain.html" title="obtain" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">conclude</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_byinduction.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_obtain.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_conclude"></a>conclude</h2></div></div></div><p><strong class="userinput"><code>conclude t1 </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>conclude</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ The current conclusion must be an equality <span class="command"><strong>t1 = tk</strong></span>
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It starts an equality chain on the conclusion. It allows the user to apply the tactic <span class="bold"><strong>=</strong></span> to continue the chain.</p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_byinduction.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_obtain.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">by induction hypothesis we know </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> obtain</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>constructor</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_clear.html" title="clear" /><link rel="next" href="tac_decompose.html" title="decompose" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">constructor</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_clear.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_decompose.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_constructor"></a>constructor</h2></div></div></div><p><strong class="userinput"><code>%n {args}</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>%</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] [<span class="bol">{</span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>…<span class="bol">}</span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The conclusion of the current sequent must be
+ an inductive type or the application of an inductive type with
+ at least <span class="command"><strong>n</strong></span> constructors.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the <span class="command"><strong>n</strong></span>-th constructor of the
+ inductive type of the conclusion of the current sequent to
+ the arguments <span class="command"><strong>args</strong></span>.
+ If <span class="command"><strong>n</strong></span> is omitted, it defaults to 1.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each premise of the constructor
+ that can not be inferred by unification. For more details,
+ see the <span class="command"><strong>apply</strong></span> tactic.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_clear.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_decompose.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">clear </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> decompose</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>cut</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_change.html" title="change" /><link rel="next" href="tac_destruct.html" title="destruct" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">cut</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_change.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_destruct.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_cut"></a>cut</h2></div></div></div><p><strong class="userinput"><code>cut P</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>cut</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>P</strong></span> must be a type.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens two new sequents. The first one has conclusion
+ <span class="command"><strong>P → G</strong></span> where <span class="command"><strong>G</strong></span> is the
+ old conclusion.
+ The second sequent has conclusion <span class="command"><strong>P</strong></span> and
+ hypotheses the hypotheses of the current sequent to prove.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_change.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_destruct.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">change </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> destruct</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>decompose</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_constructor.html" title="constructor" /><link rel="next" href="tac_rewrite.html" title="rewrite" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">decompose</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_constructor.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_rewrite.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_decompose"></a>decompose</h2></div></div></div><p><strong class="userinput"><code>
+ * as H
+ </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>*</strong></span>
+ [<span class="bold"><strong>as</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]
+ </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The current conclusion must be of the form
+ <span class="command"><strong>T → G</strong></span> where <span class="command"><strong>I</strong></span> is
+ an inductive type applied to its arguments, if any.</p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It introduces a new hypothesis <span class="command"><strong>H</strong></span> of type
+ <span class="command"><strong>T</strong></span>. Then it proceeds by cases over
+ <span class="command"><strong>H</strong></span>. Finally, if the name <span class="command"><strong>H</strong></span>
+ is not specified, it clears the new hypothesis from all contexts.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
+ The ones generated by case analysis.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_constructor.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_rewrite.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">constructor </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> rewrite</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>destruct</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_cut.html" title="cut" /><link rel="next" href="tac_elim.html" title="elim" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">destruct</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_cut.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_elim.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_destruct"></a>destruct</h2></div></div></div><p><strong class="userinput"><code>destruct (H<sub>0</sub> ... H<sub>n</sub>) skip (K<sub>0</sub> ... K<sub>m</sub>)</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>destruct</strong></span>
+ [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>] [<span class="bold"><strong>skip</strong></span> <span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>Each hypothesis <span class="command"><strong>H<sub>i</sub></strong></span> must be either a Leibniz or a John Major equality where the two sides of the equality are possibly applied constructors of an inductive type.</p></dd><dt><span class="term">Action:</span></dt><dd><p>The tactic recursively compare the two sides of each equality
+ looking for different constructors in corresponding position.
+ If two of them are found, the tactic closes the current sequent
+ by proving the absurdity of <span class="command"><strong>p</strong></span>. Otherwise
+ it adds a new hypothesis for each leaf of the formula that
+ states the equality of the subformulae in the corresponding
+ positions on the two sides of the equality. If the newly
+ added hypothesis is an equality between a variable and a term,
+ the variable is substituted for the term everywhere in the
+ sequent, except for the hypotheses <span class="command"><strong>K<sub>j</sub></strong></span>, and it is then cleared from the list of hypotheses.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_cut.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_elim.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">cut </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> elim</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>elim</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_destruct.html" title="destruct" /><link rel="next" href="tac_generalize.html" title="generalize" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">elim</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_destruct.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_generalize.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_elim"></a>elim</h2></div></div></div><p><strong class="userinput"><code>elim t pattern</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>elim</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must inhabit an inductive type.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It proceeds by cases on the values of <span class="command"><strong>t</strong></span>,
+ according to the most appropriate elimination principle for
+ the current goal.
+ The induction predicate is restricted by
+ <span class="command"><strong>pattern</strong></span>. In particular, if some hypothesis
+ is listed in <span class="command"><strong>pattern</strong></span>, the hypothesis is
+ generalized and cleared before eliminating <span class="command"><strong>t</strong></span>
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each case.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_destruct.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_generalize.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">destruct </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> generalize</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>let such that</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_bytermweproved.html" title="we proved" /><link rel="next" href="tac_andelim.html" title="we have" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">let such that</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_bytermweproved.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_andelim.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_existselim"></a>let such that</h2></div></div></div><p><strong class="userinput"><code>justification let x:T such that P (H)</code></strong>
+ </p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>such that</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ None.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It applies the left introduction rule of the existential quantifier on the formula <span class="command"><strong>∃ x. P(x)</strong></span> (in Natural Deduction this corresponds to the elimination rule for the quantifier).
+ </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent with <span class="command"><strong>∃ x. P(x)</strong></span> as the conclusion is opened and then immediately closed using the given justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and two new hypotheses <span class="command"><strong>x : T</strong></span> and <span class="command"><strong>H : P</strong></span> are added to the context.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_bytermweproved.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_andelim.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we proved </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we have</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>generalize</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_elim.html" title="elim" /><link rel="next" href="tac_inversion.html" title="inversion" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">generalize</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_elim.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_inversion.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_generalize"></a>generalize</h2></div></div></div><p><strong class="userinput"><code>generalize patt</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>generalize</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>All the terms matched by <span class="command"><strong>patt</strong></span> must be
+ convertible and close in the context of the current sequent.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent by applying a stronger
+ lemma that is proved using the new generated sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent where the current sequent conclusion
+ <span class="command"><strong>G</strong></span> is generalized to
+ <span class="command"><strong>∀x.G{x/t}</strong></span> where <span class="command"><strong>{x/t}</strong></span>
+ is a notation for the replacement with <span class="command"><strong>x</strong></span> of all
+ the occurrences of the term <span class="command"><strong>t</strong></span> matched by
+ <span class="command"><strong>patt</strong></span>. If <span class="command"><strong>patt</strong></span> matches no
+ subterm then <span class="command"><strong>t</strong></span> is defined as the
+ <span class="command"><strong>wanted</strong></span> part of the pattern.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_elim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_inversion.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">elim </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> inversion</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>intro</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_auto.html" title="auto" /><link rel="next" href="tac_intro_clear.html" title="intro_clear" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">intro</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_auto.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_intro_clear.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_intro"></a>intro</h2></div></div></div><p><strong class="userinput"><code>#H</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>#</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The conclusion of the sequent to prove must be an implication
+ or a universal quantification.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the right introduction rule for implication,
+ closing the current sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent to prove adding to the hypothesis
+ the antecedent of the implication and setting the conclusion
+ to the consequent of the implicaiton. The name of the new
+ hypothesis is <span class="command"><strong>H</strong></span>.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_auto.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_intro_clear.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">auto </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> intro_clear</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>intro_clear</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_intro.html" title="intro" /><link rel="next" href="macro_intro.html" title="macro_input" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">intro_clear</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_intro.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="macro_intro.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_intro_clear"></a>intro_clear</h2></div></div></div><p><strong class="userinput"><code>#_</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>#_</strong></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The conclusion of the sequent to prove must be an implication.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the ``a fortiori'' rule for implication,
+ closing the current sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent whose conclusion is the conclusion
+ of the implication of the original sequent.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_intro.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="macro_intro.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">intro </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> macro_input</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>inversion</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_generalize.html" title="generalize" /><link rel="next" href="tac_lapply.html" title="lapply" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">inversion</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_generalize.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_lapply.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_inversion"></a>inversion</h2></div></div></div><p><strong class="userinput"><code>inversion t</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>inversion</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The type of the term <span class="command"><strong>t</strong></span> must be an inductive
+ type or the application of an inductive type.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It proceeds by cases on <span class="command"><strong>t</strong></span> paying attention
+ to the constraints imposed by the actual "right arguments"
+ of the inductive type.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent to prove for each case in the
+ definition of the type of <span class="command"><strong>t</strong></span>. With respect to
+ a simple elimination, each new sequent has additional hypotheses
+ that states the equalities of the "right parameters"
+ of the inductive type with terms originally present in the
+ sequent to prove. It uses either Leibniz or John Major equality
+ for the new hypotheses, according to the included files.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_generalize.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_lapply.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">generalize </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> lapply</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>lapply</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_inversion.html" title="inversion" /><link rel="next" href="tac_letin.html" title="letin" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">lapply</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_inversion.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_letin.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_lapply"></a>lapply</h2></div></div></div><p><strong class="userinput"><code>
+ lapply t
+ </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>lapply</strong></span>
+ <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>
+ </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It generalizes the conclusion of the current goal
+ adding as a premise the type of <span class="command"><strong>t</strong></span>,
+ closing the current goal.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
+ The new sequent has conclusion <span class="command"><strong>T → G</strong></span> where
+ <span class="command"><strong>T</strong></span> is the type of <span class="command"><strong>t</strong></span>
+ and <span class="command"><strong>G</strong></span> the old conclusion.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_inversion.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_letin.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">inversion </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> letin</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>letin</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_suppose.html" title="suppose" /><link rel="next" href="tac_thatisequivalentto.html" title="that is equivalent to" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">letin</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_suppose.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_thatisequivalentto.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_let"></a>letin</h2></div></div></div><p><strong class="userinput"><code>let x := T </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> = </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>None</p></dd><dt><span class="term">Action:</span></dt><dd><p>It adds a new local definition <span class="command"><strong>x := T</strong></span> to the context of the sequent to prove.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_suppose.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_thatisequivalentto.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">suppose </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> that is equivalent to</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>letin</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_lapply.html" title="lapply" /><link rel="next" href="tac_normalize.html" title="normalize" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">letin</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_lapply.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_normalize.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_letin"></a>letin</h2></div></div></div><p><strong class="userinput"><code>letin x ≝ t</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>letin</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It adds to the context of the current sequent to prove a new
+ definition <span class="command"><strong>x ≝ t</strong></span>.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_lapply.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_normalize.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">lapply </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> normalize</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>normalize</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_letin.html" title="letin" /><link rel="next" href="tac_whd.html" title="whd" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">normalize</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_letin.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_whd.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_normalize"></a>normalize</h2></div></div></div><p><strong class="userinput"><code>normalize patt nodelta</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>normalize</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
+ [<span class="bold"><strong>nodelta</strong></span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It replaces all the terms matched by <span class="command"><strong>patt</strong></span>
+ with their βδιζ-normal form. If <span class="command"><strong>nodelta</strong></span> is
+ specified, δ-expansions are not performed.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_letin.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_whd.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">letin </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> whd</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>obtain</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_conclude.html" title="conclude" /><link rel="next" href="tac_rewrite_step.html" title="=" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">obtain</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_conclude.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_rewrite_step.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_obtain"></a>obtain</h2></div></div></div><p><strong class="userinput"><code>obtain H t1 </code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>obtain</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ None.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It starts an equality chain <span class="command"><strong>t1 = ?</strong></span>, which, when concluded, will be added to hypoteses of the current sequent. It allows the user to apply the tactic <span class="bold"><strong>=</strong></span> to continue the chain.</p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent for <span class="command"><strong>t1 = ?</strong></span> is opened, a new sequent for <span class="command"><strong>?</strong></span> is opened, and a new sequent with the conclusion of the sequent on which this tactic was applied is opened, with <span class="command"><strong>H: t1 = ?</strong></span> added to its hypotheses. This hypotesis will be changed when the equality chain is concluded with <span class="command"><strong>H: t1 = tk</strong></span>, where <span class="command"><strong>tk</strong></span> is the last term of the equality chain. The goal for <span class="command"><strong>?</strong></span> can be safely ignored, as it will be automatically closed when the equality chain is concluded.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_conclude.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_rewrite_step.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">conclude </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> =</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>rewrite</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_decompose.html" title="decompose" /><link rel="next" href="tac_applyS.html" title="applyS" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">rewrite</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_decompose.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_applyS.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_rewrite"></a>rewrite</h2></div></div></div><p><strong class="userinput"><code>> p patt</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>[<span class="bold"><strong><</strong></span>|<span class="bold"><strong>></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>p</strong></span> must be the proof of an equality,
+ possibly under some hypotheses.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It looks in every term matched by <span class="command"><strong>patt</strong></span>
+ for all the occurrences of the
+ left hand side of the equality that <span class="command"><strong>p</strong></span> proves
+ (resp. the right hand side if <span class="command"><strong><</strong></span> is used).
+ Every occurence found is replaced with
+ the opposite side of the equality.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each hypothesis of the
+ equality proved by <span class="command"><strong>p</strong></span> that is not closed
+ by unification.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_decompose.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_applyS.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">decompose </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> applyS</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>=</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_obtain.html" title="obtain" /><link rel="next" href="tac_bydone.html" title="done" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">=</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_obtain.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_bydone.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_rewrite_step"></a>=</h2></div></div></div><p><strong class="userinput"><code>= t2 justification</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> [<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span> | <span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>using once</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>proof</strong></span>] [<span class="bold"><strong>done</strong></span>]
+ </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ The user must have started an equality chain with <span class="bold"><strong>conclude</strong></span> or <span class="bold"><strong>obtain</strong></span> that has not been concluded yet.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It applies the transitivity of <span class="command"><strong>=</strong></span> on the left-hand-side of the current conclusion, <span class="command"><strong>t2</strong></span>, and the right-hand-side of the current conclusion, using the given justification. If <span class="bold"><strong>done</strong></span> is supplied, this represents the last step in the equality chain.
+ </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>
+ A new sequent for <span class="command"><strong>lhs = t2</strong></span> is opened and then immediately closed using the given justification. A new sequent with the conclusion <span class="command"><strong>t2 = rhs</strong></span> is opened.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_obtain.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_bydone.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">obtain </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> done</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>suppose</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_assume.html" title="assume" /><link rel="next" href="tac_let.html" title="letin" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">suppose</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_assume.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_let.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_suppose"></a>suppose</h2></div></div></div><p><strong class="userinput"><code>suppose A (H)</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>suppose</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>) </strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ The conclusion of the sequent to prove must be an implication.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ It applies the right introduction rule for the implication, closing the current sequent (in Natural Deduction this corresponds to the introduction rule for the implication).
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
+ It opens a new sequent to prove the consequent of the implication adding the antecedent <span class="command"><strong>A</strong></span> to the hypotheses. The name of the new hypothesis is <span class="command"><strong>H</strong></span>.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_assume.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_let.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">assume </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> letin</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>that is equivalent to</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_let.html" title="letin" /><link rel="next" href="tac_thesisbecomes.html" title="the thesis becomes" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">that is equivalent to</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_let.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_thesisbecomes.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_thatisequivalentto"></a>that is equivalent to</h2></div></div></div><p><strong class="userinput"><code>that is equivalent to t</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
+ <span class="bold"><strong>that is equivalent to</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
+ The user must have applied one of the following tactics immediately before applying this tactic: <span class="bold"><strong>assume</strong></span>, <span class="bold"><strong>suppose</strong></span>, <span class="bold"><strong>we need to prove</strong></span>, <span class="bold"><strong>by just we proved</strong></span>,<span class="bold"><strong>the thesis becomes</strong></span>, <span class="bold"><strong>that is equivalent to</strong></span>.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>
+ If the tactic that was applied before this introduced a new hypothesis in the context, this tactic works on this hypothesis; otherwise, it works on the conclusion. Either way, if the term <span class="command"><strong>t</strong></span> is beta-equivalent to the term <span class="command"><strong>t1</strong></span> on which this tactic is working (i.e. they can be reduced to a common term), <span class="command"><strong>t1</strong></span> is changed with <span class="command"><strong>t</strong></span>.
+
+ If the tactic that was applied before this tactic was <span class="bold"><strong>that is equivalent to</strong></span>, and that tactic was working on a term <span class="command"><strong>t1</strong></span>, this tactic keeps working on <span class="command"><strong>t1</strong></span>.
+ </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>
+ If this tactic is working on the conclusion, a new sequent with the same hypotheses and the conclusion changed to <span class="command"><strong>t</strong></span> is opened. If this tactic is working on the last introduced hypotesis, a new sequent with the same conclusion is opened. The hypotheses of this sequent are the same, except for the one on which the tactic is working on, which is changed with <span class="command"><strong>t</strong></span>.
+ </p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_let.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_thesisbecomes.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">letin </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> the thesis becomes</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>the thesis becomes</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_thatisequivalentto.html" title="that is equivalent to" /><link rel="next" href="tac_weneedtoprove.html" title="we need to prove" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">the thesis becomes</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_thatisequivalentto.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weneedtoprove.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_thesisbecomes"></a>the thesis becomes</h2></div></div></div><p><strong class="userinput"><code>the thesis becomes P</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>the thesis becomes</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The provided term <span class="command"><strong>P</strong></span> must be identical to the current conclusion.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It allows the user to start a chain of reductions on the conclusion with the tactic <span class="bold"><strong>that is equivalent to</strong></span>, after stating the current conclusion.</p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_thatisequivalentto.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weneedtoprove.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">that is equivalent to </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we need to prove</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we need to prove</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_thesisbecomes.html" title="the thesis becomes" /><link rel="next" href="tac_bytermweproved.html" title="we proved" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we need to prove</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_thesisbecomes.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_bytermweproved.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weneedtoprove"></a>we need to prove</h2></div></div></div><p><strong class="userinput"><code>we need to prove T [(H)]</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we need to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
+ [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
+ <span class="bold"><strong>)</strong></span>]
+ </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>If <span class="command"><strong>id</strong></span> is provided, it applies a logical cut on <span class="command"><strong>T</strong></span>. Otherwise, it allows the user to start a chain of reductions on the conclusion with the tactic <span class="bold"><strong>that is equivalent to</strong></span>.
+ </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>If <span class="command"><strong>id</strong></span> is supplied, a new sequent with <span class="command"><strong>T</strong></span> as the conclusion is opened, and a new sequent with the conclusion of the sequent on which this tactic was applied is opened, with <span class="command"><strong>H:T</strong></span> added to the hypotheses.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_thesisbecomes.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_bytermweproved.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">the thesis becomes </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proved</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proceed by cases on</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_weproceedbyinduction.html" title="we proceed by induction on" /><link rel="next" href="tac_case.html" title="case" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proceed by cases on</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_weproceedbyinduction.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_case.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weproceedbycases"></a>we proceed by cases on</h2></div></div></div><p><strong class="userinput"><code>we proceed by cases on t to prove P</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we proceed by cases on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The type of <span class="command"><strong>t</strong></span> must be an inductive type and <span class="command"><strong>P</strong></span> must be identical to the current conclusion.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p> It proceeds by case-analysis on <span class="command"><strong>t</strong></span> </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each constructor of the
+ type of <span class="command"><strong>t</strong></span>, each with the conclusion <span class="command"><strong>P</strong></span> instantiated for the constructor.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_weproceedbyinduction.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_case.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we proceed by induction on </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> case</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proceed by induction on</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_andelim.html" title="we have" /><link rel="next" href="tac_weproceedbycases.html" title="we proceed by cases on" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proceed by induction on</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_andelim.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weproceedbycases.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weproceedbyinduction"></a>we proceed by induction on</h2></div></div></div><p><strong class="userinput"><code>we proceed by induction on t to prove P</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we proceed by induction on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> to prove </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The type of <span class="command"><strong>t</strong></span> must be an inductive type and <span class="command"><strong>P</strong></span> must be identical to the current conclusion.
+ </p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the induction principle on <span class="command"><strong>t</strong></span> to prove <span class="command"><strong>P</strong></span>.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each constructor of the type of <span class="command"><strong>t</strong></span>, each with the conclusion <span class="command"><strong>P</strong></span> instantiated for the constructor. For the inductive constructors (i.e. if the inductive type is <span class="command"><strong>T</strong></span>, constructors with an argument of type <span class="command"><strong>T</strong></span>), the conclusion is a logical implication, where the antecedent is the inductive hypothesis for the constructor, and the consequent is <span class="command"><strong>P</strong></span>.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_andelim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weproceedbycases.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we have </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proceed by cases on</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>whd</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_normalize.html" title="normalize" /><link rel="next" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">whd</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_normalize.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="sec_declarative_tactics.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_whd"></a>whd</h2></div></div></div><p><strong class="userinput"><code>whd patt nodelta</code></strong></p><p>
+ </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>whd</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> [<span class="bold"><strong>nodelta</strong></span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It replaces all the terms matched by <span class="command"><strong>patt</strong></span>
+ with their βδιζ-weak-head normal form. If <span class="command"><strong>nodelta</strong></span> is specified, δ-expansions are not performed.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
+ </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_normalize.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_declarative_tactics.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">normalize </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 8. Declarative Tactics</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Tacticals</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tacticals.html" title="Chapter 6. Tacticals" /><link rel="prev" href="proofstatus.html" title="The proof status" /><link rel="next" href="sec_tactics.html" title="Chapter 7. Tactics" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Tacticals</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="proofstatus.html">Prev</a> </td><th width="60%" align="center">Chapter 6. Tacticals</th><td width="20%" align="right"> <a accesskey="n" href="sec_tactics.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tacticals"></a>Tacticals</h2></div></div></div><div class="table"><a id="idm2266"></a><p class="title"><strong>Table 6.1. proof script</strong></p><div class="table-contents"><table class="table" summary="proof script" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.proofscript"></a><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofscript">proof-script</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofstep">proof-step</a></em></span> [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofstep">proof-step</a></em></span>]…</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><p>Every proof step can be immediately executed.</p><div class="table"><a id="idm2281"></a><p class="title"><strong>Table 6.2. proof steps</strong></p><div class="table-contents"><table class="table" summary="proof steps" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.proofstep"></a><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofstep">proof-step</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style="">The tactical is applied to each
+ <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>.
+ Each new sequent becomes a selected sequent.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>.</strong></span></td><td style="">The first
+ <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a> becomes
+ the only one selected. All the remaining previously selected sequents
+ are proposed to the user one at a time when the next
+ "<span class="bold"><strong>.</strong></span>" is used.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>;</strong></span></td><td style="">Nothing changes. Use this proof step as a separator in
+ concrete syntax.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>[</strong></span></td><td style="">Every <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>
+ becomes a <a class="link" href="proofstatus.html#siblingsequents">sibling sequent</a>
+ that constitute a branch in the proof.
+ Moreover, the first sequent is also selected.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>|</strong></span></td><td style="">Stop working on the current branch of the innermost branching
+ proof.
+ The sibling branches become the <a class="link" href="proofstatus.html#siblingsequents">sibling
+ sequents</a> and the first one is also selected.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>]…<span class="bold"><strong>:</strong></span></td><td style="">The <a class="link" href="proofstatus.html#siblingsequents">sibling sequents</a>
+ specified by the user become the next
+ <a class="link" href="proofstatus.html#selectedsequents">selected sequents</a>.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>*:</strong></span></td><td style="">Every sibling branch not considered yet in the innermost
+ branching proof becomes a
+ <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>skip</strong></span></td><td style="">Accept the automatically provided instantiation (not shown
+ to the user) for the currently selected
+ <a class="link" href="proofstatus.html#solvedsequents">automatically closed sibling sequent</a>.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>]</strong></span></td><td style="">Stop analyzing branches for the innermost branching proof.
+ Every sequent opened during the branching proof and not closed yet
+ becomes a <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>focus</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>]…</td><td style="">
+ Selects the sequents specified by the user. The selected sequents
+ must be completely closed (no new sequents left open) before doing an
+ "<span class="bold"><strong>unfocus</strong></span> that restores
+ the current set of sibling branches.
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>unfocus</strong></span></td><td style="">
+ Used to match the innermost
+ "<span class="bold"><strong>focus</strong></span>" tactical
+ when all the sequents selected by it have been closed.
+ Until "<span class="bold"><strong>unfocus</strong></span>" is
+ performed, it is not possible to progress in the rest of the
+ proof.
+ </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm2377"></a><p class="title"><strong>Table 6.3. tactics and LCF tacticals</strong></p><div class="table-contents"><table class="table" summary="tactics and LCF tacticals" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.LCFtactical"></a><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_tactics.html#grammar.tactic">tactic</a></em></span></td><td style="">Applies the specified tactic.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span> <span class="bold"><strong>;</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style="">Applies the first tactical first and the second tactical
+ to each sequent opened by the first one.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>
+ <span class="bold"><strong>[</strong></span>
+ [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]
+ [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]…
+ <span class="bold"><strong>]</strong></span>
+ </td><td style="">Applies the first tactical first and each tactical in the
+ list of tacticals to the corresponding sequent opened by the
+ first one. The number of tacticals provided in the list must be
+ equal to the number of sequents opened by the first tactical.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>do</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>
+ <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>
+ </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>repeat</strong></span>
+ <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>
+ </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>first [</strong></span>
+ [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]
+ [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]…
+ <span class="bold"><strong>]</strong></span>
+ </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>try</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
+ <span class="bold"><strong>solve [</strong></span>
+ [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]
+ [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]…
+ <span class="bold"><strong>]</strong></span>
+ </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span><span class="bold"><strong>)</strong></span></td><td style="">Used for grouping during parsing.</td></tr></tbody></table></div></div><br class="table-break" /></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="proofstatus.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tacticals.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_tactics.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">The proof status </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 7. Tactics</td></tr></table></div></body></html>
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Tactic arguments</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="proofs.html" title="Proofs" /><link rel="next" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Tactic arguments</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="proofs.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="sec_usernotation.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tacticargs"></a>Tactic arguments</h2></div></div></div><p>This section documents the syntax of some recurring arguments for
+ tactics.</p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="pattern"></a>pattern</h3></div></div></div><div class="table"><a id="idm1235"></a><p class="title"><strong>Table 4.13. pattern</strong></p><div class="table-contents"><table class="table" summary="pattern" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.pattern"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>in</strong></span>
+ [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]…
+ [<span class="bold"><strong>⊢</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]<span class="bold"><strong>;</strong></span></td><td style="">simple pattern</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>in</strong></span> <span class="bold"><strong>match</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
+ [<span class="bold"><strong>in</strong></span>
+ [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]…
+ [<span class="bold"><strong>⊢</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]<span class="bold"><strong>;</strong></span></td><td style="">full pattern</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1275"></a><p class="title"><strong>Table 4.14. path</strong></p><div class="table-contents"><table class="table" summary="path" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.path"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em>〈〈any <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> without occurrences of <span class="bold"><strong>Set</strong></span>, <span class="bold"><strong>Prop</strong></span>, <span class="bold"><strong>CProp</strong></span>, <span class="bold"><strong>Type</strong></span>, <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>, <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span> and user provided notation; however, <span class="bold"><strong>%</strong></span> is now an additional production for <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>〉〉</em></span></td></tr></tbody></table></div></div><br class="table-break" /><p>A <span class="emphasis"><em>path</em></span> locates zero or more subterms of a given term by mimicking the term structure up to:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Occurrences of the subterms to locate that are
+ represented by <span class="bold"><strong>%</strong></span>.</p></li><li class="listitem"><p>Subterms without any occurrence of subterms to locate
+ that can be represented by <span class="bold"><strong>?</strong></span>.
+ </p></li></ol></div><p>Warning: the format for a path for a <span class="bold"><strong>match</strong></span> … <span class="bold"><strong>with</strong></span>
+ expression is restricted to: <span class="bold"><strong>match</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
+ <span class="bold"><strong>with</strong></span>
+ <span class="bold"><strong>[</strong></span>
+ <span class="bold"><strong>_</strong></span>
+ <span class="bold"><strong>⇒</strong></span>
+ <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
+ <span class="bold"><strong>|</strong></span> …
+ <span class="bold"><strong>|</strong></span>
+ <span class="bold"><strong>_</strong></span>
+ <span class="bold"><strong>⇒</strong></span>
+ <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
+ <span class="bold"><strong>]</strong></span>
+ Its semantics is the following: the n-th
+ "<span class="bold"><strong>_</strong></span>
+ <span class="bold"><strong>⇒</strong></span>
+ <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>" branch is matched against the n-th constructor of the
+ inductive data type. The head λ-abstractions of <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span> are matched
+ against the corresponding constructor arguments.
+ </p><p>For instance, the path
+ <strong class="userinput"><code>∀_,_:?.(? ? % ?)→(? ? ? %)</code></strong>
+ locates at once the subterms
+ <strong class="userinput"><code>x+y</code></strong> and <strong class="userinput"><code>x*y</code></strong> in the
+ term <strong class="userinput"><code>∀x,y:nat.x+y=1→0=x*y</code></strong>
+ (where the notation <strong class="userinput"><code>A=B</code></strong> hides the term
+ <strong class="userinput"><code>(eq T A B)</code></strong> for some type <strong class="userinput"><code>T</code></strong>).
+ </p><p>A <span class="emphasis"><em>simple pattern</em></span> extends paths to locate
+ subterms in a whole sequent. In particular, the pattern
+ <strong class="userinput"><code>{ H: p K: q ⊢ r }</code></strong> locates at once all the subterms
+ located by the pattern <strong class="userinput"><code>r</code></strong> in the conclusion of the
+ sequent and by the patterns <strong class="userinput"><code>p</code></strong> and
+ <strong class="userinput"><code>q</code></strong> in the hypotheses <strong class="userinput"><code>H</code></strong>
+ and <strong class="userinput"><code>K</code></strong> of the sequent.
+ </p><p>If no list of hypotheses is provided in a simple pattern, no subterm
+ is selected in the hypothesis. If the <strong class="userinput"><code>⊢ p</code></strong>
+ part of the pattern is not provided, no subterm will be matched in the
+ conclusion if at least one hypothesis is provided; otherwise the whole
+ conclusion is selected.
+ </p><p>Finally, a <span class="emphasis"><em>full pattern</em></span> is interpreted in three
+ steps. In the first step the <strong class="userinput"><code>match T in</code></strong>
+ part is ignored and a set <span class="emphasis"><em>S</em></span> of subterms is
+ located as for the case of
+ simple patterns. In the second step the term <strong class="userinput"><code>T</code></strong>
+ is parsed and interpreted in the context of each subterm
+ <span class="emphasis"><em>s ∈ S</em></span>. In the last term for each
+ <span class="emphasis"><em>s ∈ S</em></span> the interpreted term <strong class="userinput"><code>T</code></strong>
+ computed in the previous step is looked for. The final set of subterms
+ located by the full pattern is the set of occurrences of
+ the interpreted <strong class="userinput"><code>T</code></strong> in the subterms <span class="emphasis"><em>s</em></span>.
+ </p><p>A full pattern can always be replaced by a simple pattern,
+ often at the cost of increased verbosity or decreased readability.</p><p>Example: the pattern
+ <strong class="userinput"><code>{ match x+y in ⊢ ∀_,_:?.(? ? % ?) }</code></strong>
+ locates only the first occurrence of <strong class="userinput"><code>x+y</code></strong>
+ in the sequent <strong class="userinput"><code>x,y: nat ⊢ ∀z,w:nat. (x+y) * (z+w) =
+ z * (x+y) + w * (x+y)</code></strong>. The corresponding simple pattern
+ is <strong class="userinput"><code>{ ⊢ ∀_,_:?.(? ? (? % ?) ?) }</code></strong>.
+ </p><p>Every tactic that acts on subterms of the selected sequents have
+ a pattern argument for uniformity. To automatically generate a simple
+ pattern:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Select in the current goal the subterms to pass to the
+ tactic by using the mouse. In order to perform a multiple selection of
+ subterms, hold the Ctrl key while selecting every subterm after the
+ first one.</p></li><li class="listitem"><p>From the contextual menu select "Copy".</p></li><li class="listitem"><p>From the "Edit" or the contextual menu select
+ "Paste as pattern"</p></li></ol></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="reduction-kind"></a>reduction-kind</h3></div></div></div><p>Reduction kinds are normalization functions that transform a term
+ to a convertible but simpler one. Each reduction kind can be used both
+ as a tactic argument and as a stand-alone tactic.</p><div class="table"><a id="idm1378"></a><p class="title"><strong>Table 4.15. reduction-kind</strong></p><div class="table-contents"><table class="table" summary="reduction-kind" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.reduction-kind"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.reduction-kind">reduction-kind</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>normalize</strong></span> [<span class="bold"><strong>nodelta</strong></span>]</td><td style="">Computes the βδιζ-normal form. If <strong class="userinput"><code>nodelta</code></strong>
+ is specified, δ-expansions are not performed.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>whd</strong></span> [<span class="bold"><strong>nodelta</strong></span>]</td><td style="">Computes the βδιζ-weak-head normal form. If <strong class="userinput"><code>nodelta</code></strong>
+ is specified, δ-expansions are not performed.</td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="auto-params"></a>auto-params</h3></div></div></div><div class="table"><a id="idm1402"></a><p class="title"><strong>Table 4.16. auto-params</strong></p><div class="table-contents"><table class="table" summary="auto-params" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.autoparams"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></td><td style="">::=</td><td style="">[<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] [<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.simpleautoparam">simple_auto_param</a></em></span>]…
+ [<span class="bold"><strong>by</strong></span>
+ [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>… | <span class="bold"><strong>_</strong></span>]]
+ </td><td style="">The natural number, which defaults to 1, gives a bound to
+ the depth of the search tree. The terms listed is the only
+ knowledge base used by automation together with all indexed factual
+ and equational theorems in the included library. If the list of terms
+ is empty, only equational theorems and facts in the library are
+ used. If the list is omitted, it defaults to all indexed theorems
+ in the library. Finally, if the list is <span class="command"><strong>_</strong></span>,
+ the automation command becomes a macro that is expanded in a new
+ automation command where <span class="command"><strong>_</strong></span> is replaced with the
+ list of theorems required to prove the sequent.
+ </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1423"></a><p class="title"><strong>Table 4.17. simple-auto-param</strong></p><div class="table-contents"><table class="table" summary="simple-auto-param" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.simpleautoparam"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.simpleautoparam">simple_auto_param</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>width=<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></strong></span></td><td style="">The maximal width of the search tree</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>size=<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></strong></span></td><td style="">The maximal number of nodes in the proof</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>demod</strong></span></td><td style="">Simplifies the current sequent using the current set of
+ equations known to automation
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>paramod</strong></span></td><td style="">Try to close the goal performing unit-equality paramodulation
+ </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fast_paramod</strong></span></td><td style="">A bounded version of <span class="command"><strong>paramod</strong></span> that is granted to terminate quickly
+ </td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="justification"></a>justification</h3></div></div></div><div class="table"><a id="idm1466"></a><p class="title"><strong>Table 4.18. justification</strong></p><div class="table-contents"><table class="table" summary="justification" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.justification"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">Proof term manually provided</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></td><td style="">Call automation</td></tr></tbody></table></div></div><br class="table-break" /></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="proofs.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_usernotation.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Proofs </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 5. Extending the syntax</td></tr></table></div></body></html>
\ No newline at end of file
+++ /dev/null
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Matita V0.99.5 User Manual (rev. 0.99.5 )</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="next" href="sec_intro.html" title="Chapter 1. Introduction" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center"><span class="application">Matita</span> V0.99.5
- User Manual (rev. 0.99.5
-)</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="sec_intro.html">Next</a></td></tr></table><hr /></div><div xml:lang="en" class="book" lang="en"><div class="titlepage"><div><div><h1 class="title"><a id="matita_manual"></a><span class="application">Matita</span> V0.99.5
- User Manual (rev. 0.99.5
-)</h1></div><div><ul xmlns="" class="authorgroup"><li class="author">Andrea Asperti <<a href="mailto:asperti@cs.unibo.it">asperti@cs.unibo.it</a>></li><li class="author">Claudio Sacerdoti Coen <<a href="mailto:sacerdot@cs.unibo.it">sacerdot@cs.unibo.it</a>></li><li class="author">Ferruccio Guidi <<a href="mailto:fguidi@cs.unibo.it">fguidi@cs.unibo.it</a>></li><li class="author">Enrico Tassi <<a href="mailto:tassi@cs.unibo.it">tassi@cs.unibo.it</a>></li><li class="author">Stefano Zacchiroli <<a href="mailto:zacchiro@cs.unibo.it">zacchiro@cs.unibo.it</a>></li></ul></div><div><p class="copyright">Copyright © 2006 The HELM team.</p></div><div><div class="legalnotice"><a id="idm39"></a><p> Both Matita and this document are free software, you can
- redistribute them and/or modify them under the terms of the GNU General
- Public License as published by the Free Software Foundation. See <a class="xref" href="sec_license.html" title="Chapter 10. License">Chapter 10, <em>License</em></a> for more information. </p></div></div><div><div xmlns="" class="revhistory"><span class="revision">Revision: <span class="revnumber">0.99.5
-</span>, <span class="date">12/07/2006</span></span></div></div></div><hr /></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="chapter"><a href="sec_intro.html">1. Introduction</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_intro.html#Features">Features</a></span></dt><dt><span class="sect1"><a href="WrtCoq.html">Matita vs Coq</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_install.html">2. Installation</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_install.html#inst_livecd">Using the LiveCD</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_install.html#make_vmachine">Creating the virtual machine</a></span></dt><dt><span class="sect2"><a href="sec_install.html#idm148">Sharing files with the real PC</a></span></dt></dl></dd><dt><span class="sect1"><a href="inst_from_src.html">Installing from sources</a></span></dt><dd><dl><dt><span class="sect2"><a href="inst_from_src.html#get_source_code">Getting the source code</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_requirements">Requirements</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_instructions">Compiling and installing</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="sec_gettingstarted.html">3. Getting started</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_gettingstarted.html#unicode">How to type Unicode symbols</a></span></dt><dt><span class="sect1"><a href="cicbrowser.html">Browsing and searching</a></span></dt><dd><dl><dt><span class="sect2"><a href="cicbrowser.html#browsinglib">Browsing the library</a></span></dt><dt><span class="sect2"><a href="cicbrowser.html#aboutproof">Looking at a proof under development</a></span></dt></dl></dd><dt><span class="sect1"><a href="authoring.html">Authoring</a></span></dt><dd><dl><dt><span class="sect2"><a href="authoring.html#compilation">How to compile a script</a></span></dt><dt><span class="sect2"><a href="authoring.html#authoringinterface">The authoring interface</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="sec_terms.html">4. Syntax</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_terms.html#terms_and_co">Terms & co.</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_terms.html#lexical">Lexical conventions</a></span></dt><dt><span class="sect2"><a href="sec_terms.html#terms">Terms</a></span></dt></dl></dd><dt><span class="sect1"><a href="axiom_definition_declaration.html">Definitions and declarations</a></span></dt><dd><dl><dt><span class="sect2"><a href="axiom_definition_declaration.html#axiom">axiom</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#definition">definition</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#discriminator">discriminator</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inverter">inverter</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#letrec"><span class="emphasis"><em>TODO</em></span></a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inductive">(co)inductive types declaration</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#record">record</a></span></dt></dl></dd><dt><span class="sect1"><a href="proofs.html">Proofs</a></span></dt><dd><dl><dt><span class="sect2"><a href="proofs.html#theorem">theorem</a></span></dt><dt><span class="sect2"><a href="proofs.html#corollary">corollary</a></span></dt><dt><span class="sect2"><a href="proofs.html#lemma">lemma</a></span></dt><dt><span class="sect2"><a href="proofs.html#fact">fact</a></span></dt><dt><span class="sect2"><a href="proofs.html#example">example</a></span></dt></dl></dd><dt><span class="sect1"><a href="tacticargs.html">Tactic arguments</a></span></dt><dd><dl><dt><span class="sect2"><a href="tacticargs.html#pattern">pattern</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#reduction-kind">reduction-kind</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#auto-params">auto-params</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#justification">justification</a></span></dt></dl></dd></dl></dd><dt><span class="chapter"><a href="sec_usernotation.html">5. Extending the syntax</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_usernotation.html#idm1489">notation</a></span></dt><dt><span class="sect1"><a href="ch05s02.html">interpretation</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_tacticals.html">6. Tacticals</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_tacticals.html#idm2224">Interactive proofs and definitions</a></span></dt><dt><span class="sect1"><a href="proofstatus.html">The proof status</a></span></dt><dt><span class="sect1"><a href="tacticals.html">Tacticals</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_tactics.html">7. Tactics</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_tactics.html#tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_apply.html">@</a></span></dt><dt><span class="sect1"><a href="tac_auto.html">//</a></span></dt><dt><span class="sect1"><a href="tac_intro.html">#</a></span></dt><dt><span class="sect1"><a href="tac_intro_clear.html">#_</a></span></dt><dt><span class="sect1"><a href="macro_intro.html">##</a></span></dt><dt><span class="sect1"><a href="tac_clear.html">-</a></span></dt><dt><span class="sect1"><a href="tac_constructor.html">%</a></span></dt><dt><span class="sect1"><a href="tac_decompose.html">*</a></span></dt><dt><span class="sect1"><a href="tac_rewrite.html">></a></span></dt><dt><span class="sect1"><a href="tac_applyS.html">applyS</a></span></dt><dt><span class="sect1"><a href="tac_assumption.html">assumption</a></span></dt><dt><span class="sect1"><a href="tac_cases.html">cases</a></span></dt><dt><span class="sect1"><a href="tac_change.html">change</a></span></dt><dt><span class="sect1"><a href="tac_cut.html">cut</a></span></dt><dt><span class="sect1"><a href="tac_destruct.html">destruct</a></span></dt><dt><span class="sect1"><a href="tac_elim.html">elim</a></span></dt><dt><span class="sect1"><a href="tac_generalize.html">generalize</a></span></dt><dt><span class="sect1"><a href="tac_inversion.html">inversion</a></span></dt><dt><span class="sect1"><a href="tac_lapply.html">lapply</a></span></dt><dt><span class="sect1"><a href="tac_letin.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_normalize.html">normalize</a></span></dt><dt><span class="sect1"><a href="tac_whd.html">whd</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_declarative_tactics.html">8. Declarative Tactics</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_declarative_tactics.html#declarative_tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_assume.html">assume</a></span></dt><dt><span class="sect1"><a href="tac_suppose.html">suppose</a></span></dt><dt><span class="sect1"><a href="tac_let.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_thatisequivalentto.html">that is equivalent to</a></span></dt><dt><span class="sect1"><a href="tac_thesisbecomes.html">the thesis becomes</a></span></dt><dt><span class="sect1"><a href="tac_weneedtoprove.html">we need to prove</a></span></dt><dt><span class="sect1"><a href="tac_bytermweproved.html">we proved</a></span></dt><dt><span class="sect1"><a href="tac_existselim.html">let such that</a></span></dt><dt><span class="sect1"><a href="tac_andelim.html">we have</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbyinduction.html">we proceed by induction on</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbycases.html">we proceed by cases on</a></span></dt><dt><span class="sect1"><a href="tac_case.html">case</a></span></dt><dt><span class="sect1"><a href="tac_byinduction.html">by induction hypothesis we know</a></span></dt><dt><span class="sect1"><a href="tac_conclude.html">conclude</a></span></dt><dt><span class="sect1"><a href="tac_obtain.html">obtain</a></span></dt><dt><span class="sect1"><a href="tac_rewrite_step.html">=</a></span></dt><dt><span class="sect1"><a href="tac_bydone.html">done</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_commands.html">9. Other commands</a></span></dt><dd><dl><dt><span class="sect1"><a href="sec_commands.html#command_alias">alias</a></span></dt><dt><span class="sect1"><a href="command_check.html">check</a></span></dt><dt><span class="sect1"><a href="command_coercion.html">coercion</a></span></dt><dt><span class="sect1"><a href="command_include.html">include</a></span></dt><dt><span class="sect1"><a href="command_include_alias.html">include alias</a></span></dt><dt><span class="sect1"><a href="command_qed.html">qed</a></span></dt><dt><span class="sect1"><a href="command_qed_minus.html">qed-</a></span></dt><dt><span class="sect1"><a href="command_unification_hint.html">unification hint</a></span></dt><dt><span class="sect1"><a href="command_universe_constraints.html">universe constraint</a></span></dt></dl></dd><dt><span class="chapter"><a href="sec_license.html">10. License</a></span></dt></dl></div><div class="list-of-figures"><p><strong>List of Figures</strong></p><dl><dt>2.1. <a href="sec_install.html#idm116">The brand new virtual machine</a></dt><dt>2.2. <a href="sec_install.html#idm124">Mounting an ISO image</a></dt><dt>2.3. <a href="sec_install.html#idm132">Choosing the ISO image</a></dt><dt>2.4. <a href="sec_install.html#idm140">Choosing the ISO image</a></dt><dt>2.5. <a href="sec_install.html#idm153">Set up a shared folder</a></dt><dt>2.6. <a href="sec_install.html#idm161">Choosing the folder to share</a></dt><dt>2.7. <a href="sec_install.html#idm169">Naming the shared folder</a></dt><dt>2.8. <a href="sec_install.html#idm177">Using it from the virtual machine</a></dt></dl></div><div class="list-of-tables"><p><strong>List of Tables</strong></p><dl><dt>4.1. <a href="sec_terms.html#idm389">qstring</a></dt><dt>4.2. <a href="sec_terms.html#idm402">id</a></dt><dt>4.3. <a href="sec_terms.html#idm414">nat</a></dt><dt>4.4. <a href="sec_terms.html#idm426">char</a></dt><dt>4.5. <a href="sec_terms.html#idm440">uri-step</a></dt><dt>4.6. <a href="sec_terms.html#idm454">uri</a></dt><dt>4.7. <a href="sec_terms.html#idm487">csymbol</a></dt><dt>4.8. <a href="sec_terms.html#idm500">symbol</a></dt><dt>4.9. <a href="sec_terms.html#tbl_terms">Terms</a></dt><dt>4.10. <a href="sec_terms.html#idm665">Simple terms</a></dt><dt>4.11. <a href="sec_terms.html#idm792">Arguments</a></dt><dt>4.12. <a href="sec_terms.html#idm870">Pattern matching</a></dt><dt>4.13. <a href="tacticargs.html#idm1235">pattern</a></dt><dt>4.14. <a href="tacticargs.html#idm1275">path</a></dt><dt>4.15. <a href="tacticargs.html#idm1378">reduction-kind</a></dt><dt>4.16. <a href="tacticargs.html#idm1402">auto-params</a></dt><dt>4.17. <a href="tacticargs.html#idm1423">simple-auto-param</a></dt><dt>4.18. <a href="tacticargs.html#idm1466">justification</a></dt><dt>5.1. <a href="sec_usernotation.html#idm1537">usage</a></dt><dt>5.2. <a href="sec_usernotation.html#idm1555">associativity</a></dt><dt>5.3. <a href="sec_usernotation.html#idm1582">notation_rhs</a></dt><dt>5.4. <a href="sec_usernotation.html#idm1604">unparsed_ast</a></dt><dt>5.5. <a href="sec_usernotation.html#idm1639">enriched_term</a></dt><dt>5.6. <a href="sec_usernotation.html#idm1655">unparsed_meta</a></dt><dt>5.7. <a href="sec_usernotation.html#idm1690">level2_meta</a></dt><dt>5.8. <a href="sec_usernotation.html#idm1806">notation_lhs</a></dt><dt>5.9. <a href="sec_usernotation.html#idm1820">layout</a></dt><dt>5.10. <a href="sec_usernotation.html#idm2094">literal</a></dt><dt>5.11. <a href="ch05s02.html#idm2170">interpretation_argument</a></dt><dt>5.12. <a href="ch05s02.html#idm2185">interpretation_rhs</a></dt><dt>6.1. <a href="tacticals.html#idm2266">proof script</a></dt><dt>6.2. <a href="tacticals.html#idm2281">proof steps</a></dt><dt>6.3. <a href="tacticals.html#idm2377">tactics and LCF tacticals</a></dt><dt>7.1. <a href="sec_tactics.html#idm2483">tactics</a></dt><dt>8.1. <a href="sec_declarative_tactics.html#idm3387">tactics</a></dt></dl></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="sec_intro.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top"> </td><td width="20%" align="center"> </td><td width="40%" align="right" valign="top"> Chapter 1. Introduction</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Installing from sources</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_install.html" title="Chapter 2. Installation" /><link rel="prev" href="sec_install.html" title="Chapter 2. Installation" /><link rel="next" href="sec_gettingstarted.html" title="Chapter 3. Getting started" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Installing from sources</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_install.html">Prev</a> </td><th width="60%" align="center">Chapter 2. Installation</th><td width="20%" align="right"> <a accesskey="n" href="sec_gettingstarted.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="inst_from_src"></a>Installing from sources</h2></div></div></div><p>Install Matita from the sources is hard, you have been warned!
- </p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="get_source_code"></a>Getting the source code</h3></div></div></div><p>You can get the Matita source code in two ways:
- </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p> go to the <a class="ulink" href="http://matita.cs.unibo.it/download.shtml" target="_top">download
- page</a> and get the <a class="ulink" href="http://matita.cs.unibo.it/sources/matita-latest.tar.gz" target="_top">latest released source tarball</a>;</p></li><li class="listitem"><p> get the development sources from <a class="ulink" href="http://helm.cs.unibo.it/websvn/listing.php?repname=helm&path=%2F&sc=0" target="_top">our
- SVN repository</a>. You will need the
- <span class="application">components/</span> and
- <span class="application">matita/</span> directories from the
- <code class="filename">trunk/helm/software/</code> directory, plus the
- <code class="filename">configure</code> and <code class="filename">Makefile*</code>
- stuff from the same directory. </p><p>In this case you will need to run
- <span class="command"><strong>autoconf</strong></span> before proceding with the building
- instructions below.</p></li></ol></div><p>
- </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="build_requirements"></a>Requirements</h3></div></div></div><p>In order to build Matita from sources you will need some
- tools and libraries. They are listed below.
-
- </p><div class="note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note for Debian (and derivatives) users</h3><p>If you are running a
- <a class="ulink" href="http://www.debian.org" target="_top">Debian GNU/Linux</a>
- distribution,
- or any of its derivative like <a class="ulink" href="http://ubuntu.com" target="_top">Ubuntu</a>,
- you can use APT to install all the required tools and
- libraries since they are all part of the Debian archive.
- </p><p>
- apt-get install ocaml ocaml-findlib libgdome2-ocaml-dev liblablgtk2-ocaml-dev liblablgtkmathview-ocaml-dev liblablgtksourceview-ocaml-dev libsqlite3-ocaml-dev libocamlnet-ocaml-dev libzip-ocaml-dev libhttp-ocaml-dev ocaml-ulex08 libexpat-ocaml-dev libmysql-ocaml-dev camlp5
- </p><p>
- An official debian package is going to be added to the
- archive too.
- </p></div><p>
-
- </p><div class="variablelist"><p class="title"><strong>Required tools and libraries</strong></p><dl class="variablelist"><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://caml.inria.fr" target="_top">OCaml</a> </span>
- </span></dt><dd><p> the Objective Caml compiler, version 3.09 or above </p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://www.ocaml-programming.de/packages/" target="_top">Findlib</a>
- </span>
- </span></dt><dd><p> OCaml package manager, version 1.1.1 or above</p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://www.xs4all.nl/~mmzeeman/ocaml/" target="_top">OCaml
- Expat</a> </span>
- </span></dt><dd><p>OCaml bindings for the <span class="application"><a class="ulink" href="http://expat.sourceforge.net/" target="_top">expat</a>
- library</span> </p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://wwwfun.kurims.kyoto-u.ac.jp/soft/lsl/lablgtk.html" target="_top">LablGTK</a>
- </span>
- </span></dt><dd><p> OCaml bindings for the <span class="application"> <a class="ulink" href="http://www.gtk.org" target="_top"> GTK+</a> library
- </span>, version 2.6.0 or above </p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://gtksourceview.sourceforge.net/" target="_top">GtkSourceView</a>
- </span>
- , </span><span class="term">
- <span class="application"> <a class="ulink" href="http://helm.cs.unibo.it/software/lablgtksourceview/" target="_top">LablGtkSourceView</a>
- </span>
- </span></dt><dd><p> extension for the GTK+ text widget (adding the typical
- features of source code editors) and its OCaml bindings </p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://ocamlnet.sourceforge.net/" target="_top">Ocamlnet</a>
- </span>
- </span></dt><dd><p> collection of OCaml libraries to deal with
- application-level Internet protocols and conventions </p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://www.cduce.org/download.html" target="_top">ulex</a>
- </span>
- </span></dt><dd><p> Unicode lexer generator for OCaml </p></dd><dt><span class="term">
- <span class="application"> <a class="ulink" href="http://cristal.inria.fr/~xleroy/software.html" target="_top">CamlZip</a>
- </span>
- </span></dt><dd><p> OCaml library to access <code class="filename">.gz</code> files
- </p></dd></dl></div><p> </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="build_instructions"></a>Compiling and installing</h3></div></div></div><p> Once you get the source code the installations steps should be
- quite familiar.</p><p> First of all you need to configure the build process executing
- <strong class="userinput"><code>./configure</code></strong>. This will check that all needed
- tools and library are installed and prepare the sources for compilation
- and installation. </p><p> Quite a few (optional) arguments may be passed to the
- <span class="application">configure</span> command line to change build time
- parameters. They are listed below, together with their
- default values: </p><div class="variablelist"><p class="title"><strong> <span class="application">configure</span> command line
- arguments</strong></p><dl class="variablelist"><dt><span class="term">
- <strong class="userinput"><code>--with-runtime-dir=<em class="replaceable"><code>dir</code></em></code></strong>
- </span></dt><dd><p>
- (<span class="emphasis"><em>Default:</em></span>
- <code class="filename">/usr/local/matita</code>) Runtime base directory
- where all Matita stuff (executables, configuration files,
- standard library, ...) will be installed
- </p></dd><dt><span class="term">
- <strong class="userinput"><code>--enable-debug</code></strong>
- </span></dt><dd><p>
- (<span class="emphasis"><em>Default:</em></span> disabled) Enable debugging code.
- Not for the casual user.
- </p></dd></dl></div><p> Then you will manage the build and install process using
- <span class="application"><a class="ulink" href="http://www.gnu.org/software/make/" target="_top">make</a></span>
- as usual. Below are reported the targets you have to invoke in sequence
- to build and install:
- </p><div class="variablelist"><p class="title"><strong><span class="application">make</span> targets</strong></p><dl class="variablelist"><dt><span class="term"><strong class="userinput"><code>world</code></strong></span></dt><dd><p>builds components needed by Matita and Matita itself
- (in bytecode or native code depending
- on the availability of the OCaml native code compiler) </p></dd><dt><span class="term"><strong class="userinput"><code>install</code></strong></span></dt><dd><p>installs Matita related tools, standard library and the
- needed runtime stuff in the proper places on the filesystem.
- </p></dd></dl></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_install.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_install.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_gettingstarted.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 2. Installation </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 3. Getting started</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>macro_input</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_intro_clear.html" title="intro_clear" /><link rel="next" href="tac_clear.html" title="clear" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">macro_input</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_intro_clear.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_clear.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="macro_intro"></a>macro_input</h2></div></div></div><p><strong class="userinput"><code>##</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>##</strong></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>This macro expands to the longest possible list of
- <span class="command"><strong>#H<sub>i</sub></strong></span> tactics. The
- names of the introduced hypotheses are automatically
- generated.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_intro_clear.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_clear.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">intro_clear </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> clear</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Proofs</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="axiom_definition_declaration.html" title="Definitions and declarations" /><link rel="next" href="tacticargs.html" title="Tactic arguments" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Proofs</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="axiom_definition_declaration.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="tacticargs.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="proofs"></a>Proofs</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="theorem"></a><span class="bold"><strong>theorem</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>theorem f: P ≝ p</code></strong></p><p>Proves a new theorem <span class="command"><strong>f</strong></span> whose thesis is
- <span class="command"><strong>P</strong></span>.</p><p>If <span class="command"><strong>p</strong></span> is provided, it must be a proof term for
- <span class="command"><strong>P</strong></span>. Otherwise an interactive proof is started.</p><p><span class="command"><strong>P</strong></span> can be omitted only if the proof is not
- interactive.</p><p>A warning is raised if the name of the theorem cannot be obtained
- by mangling the name of the constants in its thesis.</p><p>Notice that the command is equivalent to <span class="command"><strong>definition f: T ≝ t</strong></span>.</p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="corollary"></a><span class="bold"><strong>corollary</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>corollary f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="lemma"></a><span class="bold"><strong>lemma</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>lemma f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="fact"></a><span class="bold"><strong>fact</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>fact f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span></p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="example"></a><span class="bold"><strong>example</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>] [<span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</h3></div></div></div><p><strong class="userinput"><code>example f: T ≝ t</code></strong></p><p>Same as <span class="command"><strong>theorem f: T ≝ t</strong></span>, but the example
- is not indexed nor used by automation.</p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="axiom_definition_declaration.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tacticargs.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Definitions and declarations </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Tactic arguments</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>The proof status</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tacticals.html" title="Chapter 6. Tacticals" /><link rel="prev" href="sec_tacticals.html" title="Chapter 6. Tacticals" /><link rel="next" href="tacticals.html" title="Tacticals" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">The proof status</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_tacticals.html">Prev</a> </td><th width="60%" align="center">Chapter 6. Tacticals</th><td width="20%" align="right"> <a accesskey="n" href="tacticals.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="proofstatus"></a>The proof status</h2></div></div></div><p>
- During an interactive proof, the proof status is made of
- the set of sequents to prove and the partial proof built so far.
- </p><p>The partial proof can be <a class="link" href="cicbrowser.html#aboutproof" title="Looking at a proof under development">inspected</a>
- on demand in the CIC browser. It will be shown in pseudo-natural language
- produced on the fly from the proof term.</p><p>The set of sequents to prove is shown in the notebook of the
- <a class="link" href="authoring.html#authoringinterface" title="The authoring interface">authoring interface</a>, in the
- top-right corner of the main window of Matita. Each tab shows a different
- sequent, named with a question mark followed by a number. The current
- role of the sequent, according to the following description, is also
- shown in the tab tag.
- </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p><a id="selectedsequents"></a>
- <span class="bold"><strong>Selected sequents</strong></span>
- (name in boldface, e.g. <span class="bold"><strong>?3</strong></span>).
- The next tactic will be applied to every selected sequent, producing
- new selected sequents. <a class="link" href="tacticals.html" title="Tacticals">Tacticals</a>
- such as branching ("<span class="bold"><strong>[</strong></span>")
- or "<span class="bold"><strong>focus</strong></span>" can be used
- to change the set of selected sequents.
- </p></li><li class="listitem"><p><a id="siblingsequents"></a>
- <span class="bold"><strong>Sibling sequents</strong></span>
- (name prefixed by a vertical bar and their position, e.g.
- |<sub>3</sub>?2). When the set of selected sequents
- has more than one element, the user can decide to focus in turn on each
- of them. The branching <a class="link" href="tacticals.html" title="Tacticals">tactical</a>
- ("<span class="bold"><strong>[</strong></span>") selects the first
- sequent only, marking every previously selected sequent as a sibling
- sequent. Each sibling sequent is given a different position. The
- tactical "<span class="bold"><strong>2,3:</strong></span>" can be used to
- select one or more sibling sequents, different from the one proposed,
- according to their position. Once the user starts to work on the
- selected sibling sequents it becomes impossible to select a new
- set of siblings until the ("<span class="bold"><strong>|</strong></span>")
- tactical is used to end work on the current one.
- </p></li><li class="listitem"><p><a id="solvedsequents"></a>
- <span class="bold"><strong>Automatically solved sibling sequents</strong></span>
- (name strokethrough, e.g. |<sub>3</sub><span class="strikethrough">?2</span>).
- Sometimes a tactic can close by side effects a sibling sequent the
- user has not selected yet. The sequent is left in the automatically
- solved status in order for the user to explicitly accept
- (using the "<span class="bold"><strong>skip</strong></span>"
- <a class="link" href="tacticals.html" title="Tacticals">tactical</a>) the automatic
- instantiation in the proof script. This way the correspondence between
- the number of branches in the proof script and the number of sequents
- generated in the proof is preserved.
- </p></li></ol></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_tacticals.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tacticals.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tacticals.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 6. Tacticals </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Tacticals</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 9. Other commands</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tac_bydone.html" title="done" /><link rel="next" href="command_check.html" title="check" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 9. Other commands</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_bydone.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="command_check.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_commands"></a>Chapter 9. Other commands</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_commands.html#command_alias">alias</a></span></dt><dt><span class="sect1"><a href="command_check.html">check</a></span></dt><dt><span class="sect1"><a href="command_coercion.html">coercion</a></span></dt><dt><span class="sect1"><a href="command_include.html">include</a></span></dt><dt><span class="sect1"><a href="command_include_alias.html">include alias</a></span></dt><dt><span class="sect1"><a href="command_qed.html">qed</a></span></dt><dt><span class="sect1"><a href="command_qed_minus.html">qed-</a></span></dt><dt><span class="sect1"><a href="command_unification_hint.html">unification hint</a></span></dt><dt><span class="sect1"><a href="command_universe_constraints.html">universe constraint</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="command_alias"></a>alias</h2></div></div></div><p><strong class="userinput"><code>alias id "s" = "def"</code></strong></p><p><strong class="userinput"><code>alias symbol "s" (instance n) = "def"</code></strong></p><p><strong class="userinput"><code>alias num (instance n) = "def"</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>alias</strong></span>
- [<span class="bold"><strong>id</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span>
- | <span class="bold"><strong>symbol</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span> [<span class="bold"><strong>(instance</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span><span class="bold"><strong>)</strong></span>] <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span>
- | <span class="bold"><strong>num</strong></span> [<span class="bold"><strong>(instance</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span><span class="bold"><strong>)</strong></span>] <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span>
- ]
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>Used to give an hint to the disambiguating parser.
- When the parser is faced to the identifier (or symbol)
- <span class="command"><strong>s</strong></span> or to any number, it will prefer
- interpretations that "map <span class="command"><strong>s</strong></span> (or the
- number) to <span class="command"><strong>def</strong></span>". For identifiers,
- "def" is the URI of the interpretation.
- E.g.: <span class="command"><strong>cic:/matita/nat/nat.ind#xpointer(1/1/1)</strong></span>
- for the first constructor of the first inductive type defined
- in the block of inductive type(s)
- <span class="command"><strong>cic:/matita/nat/nat.ind</strong></span>.
- For symbols and numbers, "def" is the label used to
- mark the wanted
- <a class="link" href="ch05s02.html#interpretation">interpretation</a>.
- </p><p>When a symbol or a number occurs several times in the
- term to be parsed, it is possible to give an hint only for the
- instance <span class="command"><strong>n</strong></span>. When the instance is omitted,
- the hint is valid for every occurrence.
- </p><p>
- Hints are automatically inserted in the script by Matita every
- time the user is interactively asked a question to disambiguate
- a term. This way the user won't be posed the same question twice
- when the script will be executed again.</p></dd></dl></div><p>
- </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_bydone.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="command_check.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">done </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> check</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 8. Declarative Tactics</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tac_whd.html" title="whd" /><link rel="next" href="tac_assume.html" title="assume" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 8. Declarative Tactics</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_whd.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="tac_assume.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_declarative_tactics"></a>Chapter 8. Declarative Tactics</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_declarative_tactics.html#declarative_tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_assume.html">assume</a></span></dt><dt><span class="sect1"><a href="tac_suppose.html">suppose</a></span></dt><dt><span class="sect1"><a href="tac_let.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_thatisequivalentto.html">that is equivalent to</a></span></dt><dt><span class="sect1"><a href="tac_thesisbecomes.html">the thesis becomes</a></span></dt><dt><span class="sect1"><a href="tac_weneedtoprove.html">we need to prove</a></span></dt><dt><span class="sect1"><a href="tac_bytermweproved.html">we proved</a></span></dt><dt><span class="sect1"><a href="tac_existselim.html">let such that</a></span></dt><dt><span class="sect1"><a href="tac_andelim.html">we have</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbyinduction.html">we proceed by induction on</a></span></dt><dt><span class="sect1"><a href="tac_weproceedbycases.html">we proceed by cases on</a></span></dt><dt><span class="sect1"><a href="tac_case.html">case</a></span></dt><dt><span class="sect1"><a href="tac_byinduction.html">by induction hypothesis we know</a></span></dt><dt><span class="sect1"><a href="tac_conclude.html">conclude</a></span></dt><dt><span class="sect1"><a href="tac_obtain.html">obtain</a></span></dt><dt><span class="sect1"><a href="tac_rewrite_step.html">=</a></span></dt><dt><span class="sect1"><a href="tac_bydone.html">done</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="declarative_tactics_quickref"></a>Quick reference card</h2></div></div></div><p>
- </p><div class="table"><a id="idm3387"></a><p class="title"><strong>Table 8.1. tactics</strong></p><div class="table-contents"><table class="table" summary="tactics" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.declarative_tactic"></a><span class="emphasis"><em><a class="link" href="sec_tactics.html#grammar.tactic">tactic</a></em></span></td><td style="">::=</td><td style="">
- <a class="link" href="tac_rewrite_step.html" title="="><span class="bold"><strong>=</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> [<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span> | <span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>using once</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>proof</strong></span>] [<span class="bold"><strong>done</strong></span>]
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_assume.html" title="assume"><span class="bold"><strong>assume</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> : </strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_byinduction.html" title="by induction hypothesis we know"><span class="bold"><strong>by induction hypothesis we know</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_case.html" title="case"><span class="bold"><strong>case</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>] … [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_conclude.html" title="conclude"><span class="bold"><strong>conclude</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <a class="link" href="tac_bydone.html" title="done"><span class="bold"><strong>done</strong></span></a></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>such that</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> = </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_obtain.html" title="obtain"><span class="bold"><strong>obtain</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_suppose.html" title="suppose"><span class="bold"><strong>suppose</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>) </strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <a class="link" href="tac_thatisequivalentto.html" title="that is equivalent to"><span class="bold"><strong>that is equivalent to</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_thesisbecomes.html" title="the thesis becomes"><span class="bold"><strong>the thesis becomes</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_weneedtoprove.html" title="we need to prove"><span class="bold"><strong>we need to prove</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>)</strong></span>]
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_weproceedbycases.html" title="we proceed by cases on"><span class="bold"><strong>we proceed by cases on</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_weproceedbyinduction.html" title="we proceed by induction on"><span class="bold"><strong>we proceed by induction on</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> to prove </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <a class="link" href="tac_bytermweproved.html" title="we proved"><span class="bold"><strong>we proved</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>)</strong></span>]
- </td></tr></tbody></table></div></div><p><br class="table-break" />
-
- </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_whd.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="tac_assume.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">whd </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> assume</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 3. Getting started</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="inst_from_src.html" title="Installing from sources" /><link rel="next" href="cicbrowser.html" title="Browsing and searching" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 3. Getting started</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="inst_from_src.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="cicbrowser.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_gettingstarted"></a>Chapter 3. Getting started</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_gettingstarted.html#unicode">How to type Unicode symbols</a></span></dt><dt><span class="sect1"><a href="cicbrowser.html">Browsing and searching</a></span></dt><dd><dl><dt><span class="sect2"><a href="cicbrowser.html#browsinglib">Browsing the library</a></span></dt><dt><span class="sect2"><a href="cicbrowser.html#aboutproof">Looking at a proof under development</a></span></dt></dl></dd><dt><span class="sect1"><a href="authoring.html">Authoring</a></span></dt><dd><dl><dt><span class="sect2"><a href="authoring.html#compilation">How to compile a script</a></span></dt><dt><span class="sect2"><a href="authoring.html#authoringinterface">The authoring interface</a></span></dt></dl></dd></dl></div><p> If you are already familiar with the Calculus of (Co)Inductive
- Constructions (CIC) and with interactive theorem provers with procedural
- proof languages (expecially Coq), getting started with Matita is relatively
- easy. You just need to learn how to type Unicode symbols, how to browse
- and search the library and how to author a proof script.</p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="unicode"></a>How to type Unicode symbols</h2></div></div></div><p>Unicode characters can be typed in several ways:</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>Using the "Ctrl+Shift+Unicode code" standard Gnome shortcut. E.g. Ctrl+Shift+3a9 generates "Ω".</p></li><li class="listitem"><p>Typing the ligature "\name" where "name"
- is a standard Unicode or LaTeX name for the character or an
- ASCII art resembling the shape of the character. Pressing
- "Alt+L" or Space or Enter just after the last character
- of the name converts
- the ligature to the Unicode symbol.
- E.g. "\Delta" followed by Alt+L generates
- "Δ", while pressing Alt-L after "=>" generates
- "⇒"</p></li><li class="listitem"><p>Typing a symbol and rotating trough its equivalence class
- with Alt-L. E.g. pressing Alt-L after an "l"
- generates a "λ", while pressing Alt-L after an
- "→" once generates "⇉" and pressing
- Alt-L again generates "⇒".
- </p></li></ul></div><p>
- The comprehensive list of symbols names or shortcuts and their equivalence
- classes is available clicking on the "TeX/UTF-8 table" item
- of the "View" menu.
- </p><p>
- There is a memory mechanism related to equivalence classes that
- remembers your last choice, making it the default one. For example,
- if you use "_" to generate "⎻"
- (that is the third choice, after "⎽" and "⎼"),
- the next time you type Alt-L
- after "_" you immediately get "⎻".
- </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="inst_from_src.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="cicbrowser.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Installing from sources </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Browsing and searching</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 2. Installation</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="WrtCoq.html" title="Matita vs Coq" /><link rel="next" href="inst_from_src.html" title="Installing from sources" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 2. Installation</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="WrtCoq.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="inst_from_src.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_install"></a>Chapter 2. Installation</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_install.html#inst_livecd">Using the LiveCD</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_install.html#make_vmachine">Creating the virtual machine</a></span></dt><dt><span class="sect2"><a href="sec_install.html#idm148">Sharing files with the real PC</a></span></dt></dl></dd><dt><span class="sect1"><a href="inst_from_src.html">Installing from sources</a></span></dt><dd><dl><dt><span class="sect2"><a href="inst_from_src.html#get_source_code">Getting the source code</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_requirements">Requirements</a></span></dt><dt><span class="sect2"><a href="inst_from_src.html#build_instructions">Compiling and installing</a></span></dt></dl></dd></dl></div><p>
- Matita is a quite complex piece of software, we thus recommend
- you to either install al precompiled version or use the LiveCD.
- If you are running Debian GNU/Linux (or one of its derivatives
- like Ubuntu), you can install matita typing
- </p><pre class="programlisting"> aptitude install matita matita-standard-library </pre><p>
- If you are running MacOSX or Windows, give the LiveCD a try before
- trying to compile Matita from its sources.
- </p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="inst_livecd"></a>Using the LiveCD</h2></div></div></div><p>
- In the following, we will assume you have installed
- <a class="ulink" href="http://www.virtualbox.org" target="_top">virtualbox</a>
- for your platform and downloaded the .iso image of the LiveCD
- </p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="make_vmachine"></a>Creating the virtual machine</h3></div></div></div><p>
- Click on the New button, a wizard will popup, you should ask to
- its questions as follows
- </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>
- The name should be something like Matita, but can
- be any meaningful string.
- </p></li><li class="listitem"><p>
- The OS type should be Debian
- </p></li><li class="listitem"><p>
- The base memory size can be 256 mega bytes, but you may
- want to increase it if you are going to work with huge
- formalizations.
- </p></li><li class="listitem"><p>
- The boot hard disk should be no hard disk. It may complain
- that this choice is not common, but it is right, since you
- will run a LiveCD you do not need to emulate an hard drive.
- </p></li></ol></div><p>
- Now that you are done with the creation of the virtual machine,
- you need to insert the LiveCD in the virtual cd reader unit.
- </p><div class="figure"><a id="idm116"></a><p class="title"><strong>Figure 2.1. The brand new virtual machine</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox1.png" alt="The breand new virtual machine" /></div></div></div><br class="figure-break" /><p>
- Click on CD/DVD-ROM (that should display something like: Not mouted).
- Then click on mount CD/DVD drive and select the ISO image
- option. The combo-box should display no available image, you need to
- add the ISO image you downloaded from the Matita website clicking on
- the button near the combo-box.
- to start the virtual machine.
- </p><div class="figure"><a id="idm124"></a><p class="title"><strong>Figure 2.2. Mounting an ISO image</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox2.png" alt="Mounting an ISO image" /></div></div></div><br class="figure-break" /><p>
- In the newely opened window click
- the Add button
- </p><div class="figure"><a id="idm132"></a><p class="title"><strong>Figure 2.3. Choosing the ISO image</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox3.png" alt="Choosing the ISO image" /></div></div></div><br class="figure-break" /><p>
- A new windows will pop-up: choose the file you downloaded
- (usually matita-version.iso) and click open.
- </p><div class="figure"><a id="idm140"></a><p class="title"><strong>Figure 2.4. Choosing the ISO image</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox35.png" alt="Choosing the ISO image" /></div></div></div><br class="figure-break" /><p>
- Now select the new entry you just added as the CD image
- you want to insert in the virtual CD drive.
- You are now ready to start the virtual machine.
- </p></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="idm148"></a>Sharing files with the real PC</h3></div></div></div><p>
- The virtual machine Matita will run on, has its own file
- system, that is completely separated from the one of your
- real PC (thus your files are not available in the
- emulated environment) and moreover it is a non-presistent
- file system (thus you data is lost every time you
- turn off the virtual machine).
- </p><p>
- Virtualbox allows you to share a real folder (beloging
- to your real PC) with the emulated computer. Since this
- folder is persistent, you are encouraged to put
- your work there, so that it is not lost when the virtual
- machine is powered off.
- </p><p>
- The first step to set up a shared folder is to click
- on the shared folder configuration entry
- of the virtual machine.
- </p><div class="figure"><a id="idm153"></a><p class="title"><strong>Figure 2.5. Set up a shared folder</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox4.png" alt="Shared folder" /></div></div></div><br class="figure-break" /><p>
- Then you shuld add a shared folder clicking on the
- plus icon on the right
- </p><div class="figure"><a id="idm161"></a><p class="title"><strong>Figure 2.6. Choosing the folder to share</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox5.png" alt="Shared folder" /></div></div></div><br class="figure-break" /><p>
- Then you have to specify the real PC folder you want to share
- and name it. A reasonable folder to share is /home on
- a standard Unix system, while /Users on MaxOSX.
- The name you give to the share is important, you should
- remember it.
- </p><div class="figure"><a id="idm169"></a><p class="title"><strong>Figure 2.7. Naming the shared folder</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox6.png" alt="Shared folder" /></div></div></div><br class="figure-break" /><p>
- Once your virtual machine is up and running, you can
- mount (that meand have access to) the shared folder
- by clicking on the Mount VirtualBox share icon, and typing
- the name of the share.
- </p><div class="figure"><a id="idm177"></a><p class="title"><strong>Figure 2.8. Using it from the virtual machine</strong></p><div class="figure-contents"><div class="mediaobject"><img src="figures/vbox7.png" alt="Shared folder at work" /></div></div></div><br class="figure-break" /><p>
- A window will then pop-up, and its content will be the
- the content of the real PC folder.
- </p></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="WrtCoq.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="inst_from_src.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Matita vs Coq </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Installing from sources</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 1. Introduction</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="next" href="WrtCoq.html" title="Matita vs Coq" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 1. Introduction</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="index.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="WrtCoq.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_intro"></a>Chapter 1. Introduction</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_intro.html#Features">Features</a></span></dt><dt><span class="sect1"><a href="WrtCoq.html">Matita vs Coq</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="Features"></a>Features</h2></div></div></div><p><span class="application">Matita</span> is an interactive theorem prover
- (or proof assistant) with the following characteristics:</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem"><p>It is based on a variant of the Calculus of (Co)Inductive Constructions (CIC). CIC is also the logic of the Coq proof assistant.</p></li><li class="listitem"><p>It adopts a procedural proof language, but it has a new set of small step tacticals that improve proof structuring and debugging.</p></li><li class="listitem"><p>It has a stand-alone graphical user interface (GUI) inspired by
-CtCoq/Proof General. The GUI is implemented according to the state
-of the art. In particular:</p><div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "><li class="listitem"><p>It is based and fully integrated with Gtk/Gnome.</p></li><li class="listitem"><p>An on-line help can be browsed via the Gnome documentation browser.</p></li><li class="listitem"><p>Mathematical formulae are rendered via Unicode.</p></li></ul></div></li><li class="listitem"><p>It allows the use of the typical ambiguous mathematical notation by means of a disambiguating parser.</p></li></ul></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="index.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="WrtCoq.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top"><span class="application">Matita</span> V0.99.5
- User Manual (rev. 0.99.5
-) </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Matita vs Coq</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 10. License</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="command_universe_constraints.html" title="universe constraint" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 10. License</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="command_universe_constraints.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> </td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_license"></a>Chapter 10. License</h1></div></div></div><p> Both Matita and this document are part of HELM, an Hypertextual,
- Electronic Library of Mathematics, developed at the Computer Science
- Department, University of Bologna, Italy. </p><p> HELM is free software; you can redistribute it and/or modify it under
- the terms of the GNU General Public License as published by the Free Software
- Foundation; either version 2 of the License, or (at your option) any later
- version. </p><p> HELM is distributed in the hope that it will be useful, but WITHOUT ANY
- WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
- A PARTICULAR PURPOSE. See the GNU General Public License for more details.
-</p><p> You should have received a copy of the GNU General Public License along
- with HELM; if not, write to the Free Software Foundation, Inc., 51 Franklin
- St, Fifth Floor, Boston, MA 02110-1301 USA. A copy of the GNU General
- Public License is available at <a class="ulink" href="http://www.gnu.org/copyleft/gpl.html" target="_top">this link</a>. </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="command_universe_constraints.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> </td></tr><tr><td width="40%" align="left" valign="top">universe constraint </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> </td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 6. Tacticals</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="ch05s02.html" title="interpretation" /><link rel="next" href="proofstatus.html" title="The proof status" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 6. Tacticals</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch05s02.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="proofstatus.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_tacticals"></a>Chapter 6. Tacticals</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_tacticals.html#idm2224">Interactive proofs and definitions</a></span></dt><dt><span class="sect1"><a href="proofstatus.html">The proof status</a></span></dt><dt><span class="sect1"><a href="tacticals.html">Tacticals</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="idm2224"></a>Interactive proofs and definitions</h2></div></div></div><p>
- An interactive definition is started by giving a
- <a class="link" href="axiom_definition_declaration.html#definition" title="definition id[: term] [≝ term]">definition</a> command omitting
- the definiens.
- An interactive proof is started by using one of the
- <a class="link" href="proofs.html" title="Proofs">proof commands</a> omitting
- an explicit proof term.
- </p><p>An interactive proof or definition can and must be terminated by
- a <a class="link" href="command_qed.html" title="qed">qed</a> command when no more sequents are
- left to prove. Between the command that starts the interactive session and
- the qed command the user must provide a procedural proof script made
- of <a class="link" href="sec_tactics.html" title="Chapter 7. Tactics">tactics</a> structured by means of
- <a class="link" href="tacticals.html" title="Tacticals">tacticals</a>.</p><p>In the tradition of the LCF system, tacticals can be considered
- higher order tactics. Their syntax is structured and they are executed
- atomically. On the contrary, in Matita the syntax of several tacticals is
- destructured into a sequence of tokens and tactics in such a way that is
- is possible to stop execution after every single token or tactic.
- The original semantics is preserved: the execution of the whole sequence
- yields the result expected by the original LCF-like tactical.</p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch05s02.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="proofstatus.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">interpretation </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> The proof status</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 7. Tactics</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tacticals.html" title="Tacticals" /><link rel="next" href="tac_apply.html" title="apply" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 7. Tactics</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tacticals.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="tac_apply.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_tactics"></a>Chapter 7. Tactics</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_tactics.html#tactics_quickref">Quick reference card</a></span></dt><dt><span class="sect1"><a href="tac_apply.html">@</a></span></dt><dt><span class="sect1"><a href="tac_auto.html">//</a></span></dt><dt><span class="sect1"><a href="tac_intro.html">#</a></span></dt><dt><span class="sect1"><a href="tac_intro_clear.html">#_</a></span></dt><dt><span class="sect1"><a href="macro_intro.html">##</a></span></dt><dt><span class="sect1"><a href="tac_clear.html">-</a></span></dt><dt><span class="sect1"><a href="tac_constructor.html">%</a></span></dt><dt><span class="sect1"><a href="tac_decompose.html">*</a></span></dt><dt><span class="sect1"><a href="tac_rewrite.html">></a></span></dt><dt><span class="sect1"><a href="tac_applyS.html">applyS</a></span></dt><dt><span class="sect1"><a href="tac_assumption.html">assumption</a></span></dt><dt><span class="sect1"><a href="tac_cases.html">cases</a></span></dt><dt><span class="sect1"><a href="tac_change.html">change</a></span></dt><dt><span class="sect1"><a href="tac_cut.html">cut</a></span></dt><dt><span class="sect1"><a href="tac_destruct.html">destruct</a></span></dt><dt><span class="sect1"><a href="tac_elim.html">elim</a></span></dt><dt><span class="sect1"><a href="tac_generalize.html">generalize</a></span></dt><dt><span class="sect1"><a href="tac_inversion.html">inversion</a></span></dt><dt><span class="sect1"><a href="tac_lapply.html">lapply</a></span></dt><dt><span class="sect1"><a href="tac_letin.html">letin</a></span></dt><dt><span class="sect1"><a href="tac_normalize.html">normalize</a></span></dt><dt><span class="sect1"><a href="tac_whd.html">whd</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tactics_quickref"></a>Quick reference card</h2></div></div></div><p>
- </p><div class="table"><a id="idm2483"></a><p class="title"><strong>Table 7.1. tactics</strong></p><div class="table-contents"><table class="table" summary="tactics" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.tactic"></a><span class="emphasis"><em><a class="link" href="sec_tactics.html#grammar.tactic">tactic</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>@</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_applyS.html" title="applyS"><span class="bold"><strong>applyS</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <a class="link" href="tac_assumption.html" title="assumption">
- <span class="bold"><strong>assumption</strong></span>
- </a>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span><span class="bold"><strong>/</strong></span>. </td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <a class="link" href="tac_cases.html" title="cases"><span class="bold"><strong>cases</strong></span></a>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_change.html" title="change"><span class="bold"><strong>change</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> <span class="bold"><strong>with</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>-</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>%</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] [<span class="bol">{</span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>…<span class="bol">}</span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_cut.html" title="cut"><span class="bold"><strong>cut</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>*</strong></span>
- [<span class="bold"><strong>as</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_destruct.html" title="destruct"><span class="bold"><strong>destruct</strong></span></a>
- [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>] [<span class="bold"><strong>skip</strong></span> <span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_elim.html" title="elim"><span class="bold"><strong>elim</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_generalize.html" title="generalize"><span class="bold"><strong>generalize</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>#</strong></span>
- <span class="emphasis"><em>
- <a class="link" href="sec_terms.html#grammar.id">id</a>
- </em></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>#_</strong></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_inversion.html" title="inversion"><span class="bold"><strong>inversion</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <a class="link" href="tac_lapply.html" title="lapply"><span class="bold"><strong>lapply</strong></span></a>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_letin.html" title="letin"><span class="bold"><strong>letin</strong></span></a> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>##</strong></span>
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_normalize.html" title="normalize"><span class="bold"><strong>normalize</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
- [<span class="bold"><strong>nodelta</strong></span>]</td></tr><tr><td style=""> </td><td style="">|</td><td style="">[<span class="bold"><strong><</strong></span>|<span class="bold"><strong>></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><a class="link" href="tac_whd.html" title="whd"><span class="bold"><strong>whd</strong></span></a> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> [<span class="bold"><strong>nodelta</strong></span>]</td></tr></tbody></table></div></div><p><br class="table-break" />
-
- </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tacticals.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="tac_apply.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Tacticals </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> apply</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 4. Syntax</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="authoring.html" title="Authoring" /><link rel="next" href="axiom_definition_declaration.html" title="Definitions and declarations" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 4. Syntax</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="authoring.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="axiom_definition_declaration.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_terms"></a>Chapter 4. Syntax</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_terms.html#terms_and_co">Terms & co.</a></span></dt><dd><dl><dt><span class="sect2"><a href="sec_terms.html#lexical">Lexical conventions</a></span></dt><dt><span class="sect2"><a href="sec_terms.html#terms">Terms</a></span></dt></dl></dd><dt><span class="sect1"><a href="axiom_definition_declaration.html">Definitions and declarations</a></span></dt><dd><dl><dt><span class="sect2"><a href="axiom_definition_declaration.html#axiom">axiom</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#definition">definition</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#discriminator">discriminator</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inverter">inverter</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#letrec"><span class="emphasis"><em>TODO</em></span></a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#inductive">(co)inductive types declaration</a></span></dt><dt><span class="sect2"><a href="axiom_definition_declaration.html#record">record</a></span></dt></dl></dd><dt><span class="sect1"><a href="proofs.html">Proofs</a></span></dt><dd><dl><dt><span class="sect2"><a href="proofs.html#theorem">theorem</a></span></dt><dt><span class="sect2"><a href="proofs.html#corollary">corollary</a></span></dt><dt><span class="sect2"><a href="proofs.html#lemma">lemma</a></span></dt><dt><span class="sect2"><a href="proofs.html#fact">fact</a></span></dt><dt><span class="sect2"><a href="proofs.html#example">example</a></span></dt></dl></dd><dt><span class="sect1"><a href="tacticargs.html">Tactic arguments</a></span></dt><dd><dl><dt><span class="sect2"><a href="tacticargs.html#pattern">pattern</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#reduction-kind">reduction-kind</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#auto-params">auto-params</a></span></dt><dt><span class="sect2"><a href="tacticargs.html#justification">justification</a></span></dt></dl></dd></dl></div><p>To describe syntax in this manual we use the following conventions:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Non terminal symbols are emphasized and have a link to their
- definition. E.g.: <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></li><li class="listitem"><p>Terminal symbols are in bold. E.g.:
- <span class="bold"><strong>theorem</strong></span></p></li><li class="listitem"><p>Optional sequences of elements are put in square brackets.
- E.g.: [<span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</p></li><li class="listitem"><p>Alternatives are put in square brakets and they are
- separated by vertical bars. E.g.: [<span class="bold"><strong><</strong></span>|<span class="bold"><strong>></strong></span>]</p></li><li class="listitem"><p>Repetitions of a sequence of elements are given by putting the
- sequence in square brackets, that are followed by three dots. The empty
- sequence is a valid repetition.
- E.g.: [<span class="bold"><strong>and</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…</p></li><li class="listitem"><p>Characters belonging to a set of characters are given
- by listing the set elements in square brackets. Hyphens are used to
- specify ranges of characters in the set.
- E.g.: [<span class="bold"><strong>a</strong></span>-<span class="bold"><strong>zA</strong></span>-<span class="bold"><strong>Z0</strong></span>-<span class="bold"><strong>9_-</strong></span>]</p></li></ol></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="terms_and_co"></a>Terms & co.</h2></div></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="lexical"></a>Lexical conventions</h3></div></div></div><div class="table"><a id="idm389"></a><p class="title"><strong>Table 4.1. qstring</strong></p><div class="table-contents"><table class="table" summary="qstring" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.qstring"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.qstring">qstring</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>"</strong></span><span class="emphasis"><em>〈〈any sequence of characters excluded "〉〉</em></span><span class="bold"><strong>"</strong></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm402"></a><p class="title"><strong>Table 4.2. id</strong></p><div class="table-contents"><table class="table" summary="id" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.id"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em>〈〈any sequence of letters, underscores or valid <a class="ulink" href="http://www.w3.org/TR/2004/REC-xml-20040204/#NT-Digit" target="_top">XML digits</a> prefixed by a latin letter ([a-zA-Z]) and post-fixed by a possible empty sequence of decorators ([?'`])〉〉</em></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm414"></a><p class="title"><strong>Table 4.3. nat</strong></p><div class="table-contents"><table class="table" summary="nat" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.nat"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em>〈〈any sequence of valid <a class="ulink" href="http://www.w3.org/TR/2004/REC-xml-20040204/#NT-Digit" target="_top">XML digits</a>〉〉</em></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm426"></a><p class="title"><strong>Table 4.4. char</strong></p><div class="table-contents"><table class="table" summary="char" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.char"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.char">char</a></em></span></td><td style="">::=</td><td style="">[<span class="bold"><strong>a</strong></span>-<span class="bold"><strong>zA</strong></span>-<span class="bold"><strong>Z0</strong></span>-<span class="bold"><strong>9_-</strong></span>]</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm440"></a><p class="title"><strong>Table 4.5. uri-step</strong></p><div class="table-contents"><table class="table" summary="uri-step" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.uri-step"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri-step">uri-step</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.char">char</a></em></span>[<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.char">char</a></em></span>]…</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm454"></a><p class="title"><strong>Table 4.6. uri</strong></p><div class="table-contents"><table class="table" summary="uri" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.uri"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span></td><td style="">::=</td><td style="">[<span class="bold"><strong>cic:/</strong></span>|<span class="bold"><strong>theory:/</strong></span>]<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri-step">uri-step</a></em></span>[<span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri-step">uri-step</a></em></span>]…<span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…[<span class="bold"><strong>#xpointer(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span><span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>[<span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>]…<span class="bold"><strong>)</strong></span>]</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm487"></a><p class="title"><strong>Table 4.7. csymbol</strong></p><div class="table-contents"><table class="table" summary="csymbol" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.csymbol"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>'</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm500"></a><p class="title"><strong>Table 4.8. symbol</strong></p><div class="table-contents"><table class="table" summary="symbol" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.symbol"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.symbol">symbol</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>〈〈None of the above〉〉</strong></span></td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="terms"></a>Terms</h3></div></div></div><p>
- </p><div class="table"><a id="tbl_terms"></a><p class="title"><strong>Table 4.9. Terms</strong></p><div class="table-contents"><table class="table" summary="Terms" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.term"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td><td style="">simple or delimited term</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">application</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>λ</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span><span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">λ-abstraction</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Π</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span><span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">dependent product meant to define a datatype</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>∀</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span><span class="bold"><strong>.</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">dependent product meant to define a proposition</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>→</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">non-dependent product (logical implication or function space)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>let</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>|(<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>)] <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">local definition</td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>let</strong></span>
- [<span class="bold"><strong>co</strong></span>]<span class="bold"><strong>rec</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.rec_def">rec_def</a></em></span>
- </td><td style="">(co)recursive definitions</td></tr><tr><td style=""> </td><td style=""> </td><td style="">
- [<span class="bold"><strong>and</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.rec_def">rec_def</a></em></span>]…
- </td><td style=""> </td></tr><tr><td style=""> </td><td style=""> </td><td style="">
- <span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- </td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style="">…</td><td style="">user provided notation</td></tr><tr><td style=""><a id="grammar.rec_def"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.rec_def">rec_def</a></em></span></td><td style="">::=</td><td style="">
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>|<span class="bold"><strong>_</strong></span>|<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]… <span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span>]…
- </td><td style=""> </td></tr><tr><td style=""> </td><td style=""> </td><td style="">
- [<span class="bold"><strong>on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]
- [<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]
- <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]
- </td><td style=""> </td></tr></tbody></table></div></div><p><br class="table-break" />
-
- </p><div class="table"><a id="idm665"></a><p class="title"><strong>Table 4.10. Simple terms</strong></p><div class="table-contents"><table class="table" summary="Simple terms" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.sterm"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>\subst[</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>≔</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- [<span class="bold"><strong>;</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>≔</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…
- <span class="bold"><strong>]</strong></span>]
- </td><td style="">identifier with optional explicit named substitution</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span></td><td style="">a qualified reference</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Prop</strong></span></td><td style="">the impredicative sort of propositions</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Set</strong></span></td><td style="">the impredicate sort of datatypes</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>CProp</strong></span></td><td style="">one fixed predicative sort of constructive propositions</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>Type</strong></span></td><td style="">one predicative sort of datatypes</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>?</strong></span></td><td style="">implicit argument</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>?n</strong></span>
- [<span class="bold"><strong>[</strong></span>
- [<span class="bold"><strong>_</strong></span>|<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]…
- <span class="bold"><strong>]</strong></span>]</td><td style="">metavariable</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>match</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- [ <span class="bold"><strong>in</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> ]
- [ <span class="bold"><strong>return</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> ]
- <span class="bold"><strong>with</strong></span>
- </td><td style="">case analysis</td></tr><tr><td style=""> </td><td style=""> </td><td style="">
- <span class="bold"><strong>[</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_branch">match_branch</a></em></span>[<span class="bold"><strong>|</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_branch">match_branch</a></em></span>]…
- <span class="bold"><strong>]</strong></span>
- </td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>:</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span></td><td style="">cast</td></tr><tr><td style=""> </td><td style="">|</td><td style="">…</td><td style="">user provided notation at precedence 90</td></tr></tbody></table></div></div><p><br class="table-break" />
-
- </p><div class="table"><a id="idm792"></a><p class="title"><strong>Table 4.11. Arguments</strong></p><div class="table-contents"><table class="table" summary="Arguments" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.args"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args">args</a></em></span></td><td style="">::=</td><td style="">
- <span class="bold"><strong>_</strong></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]
- </td><td style="">ignored argument</td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>(</strong></span><span class="bold"><strong>_</strong></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]<span class="bold"><strong>)</strong></span>
- </td><td style="">ignored argument</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]</td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>]<span class="bold"><strong>)</strong></span></td><td style=""> </td></tr><tr><td style=""><a id="grammar.args2"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.args2">args2</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span><span class="bold"><strong>)</strong></span></td><td style=""> </td></tr></tbody></table></div></div><p><br class="table-break" />
-
- </p><div class="table"><a id="idm870"></a><p class="title"><strong>Table 4.12. Pattern matching</strong></p><div class="table-contents"><table class="table" summary="Pattern matching" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.match_branch"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_branch">match_branch</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_pattern">match_pattern</a></em></span> <span class="bold"><strong>⇒</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style=""> </td></tr><tr><td style=""><a id="grammar.match_pattern"></a><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.match_pattern">match_pattern</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">0-ary constructor</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…<span class="bold"><strong>)</strong></span></td><td style="">n-ary constructor (binds the n arguments)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]…</td><td style="">n-ary constructor (binds the n arguments)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>_</strong></span></td><td style="">any remaining constructor (ignoring its arguments)</td></tr></tbody></table></div></div><p><br class="table-break" />
- </p></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="authoring.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="axiom_definition_declaration.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Authoring </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Definitions and declarations</td></tr></table></div></body></html>
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+++ /dev/null
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Chapter 5. Extending the syntax</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="prev" href="tacticargs.html" title="Tactic arguments" /><link rel="next" href="ch05s02.html" title="interpretation" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 5. Extending the syntax</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tacticargs.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="ch05s02.html">Next</a></td></tr></table><hr /></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a id="sec_usernotation"></a>Chapter 5. Extending the syntax</h1></div></div></div><div class="toc"><p><strong>Table of Contents</strong></p><dl class="toc"><dt><span class="sect1"><a href="sec_usernotation.html#idm1489">notation</a></span></dt><dt><span class="sect1"><a href="ch05s02.html">interpretation</a></span></dt></dl></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="idm1489"></a>notation</h2></div></div></div><p><strong class="userinput"><code>notation usage "presentation" associativity with precedence p for content</code></strong></p><p><a id="notation"></a>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>notation</strong></span>
- [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.usage">usage</a></em></span>] <span class="bold"><strong>"</strong></span><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_lhs">notation_lhs</a></em></span><span class="bold"><strong>"</strong></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.associativity">associativity</a></em></span>] <span class="bold"><strong>with</strong></span> <span class="bold"><strong>precedence</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>
- <span class="bold"><strong>for</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_rhs">notation_rhs</a></em></span>
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>Declares a mapping between the presentation
- AST <span class="command"><strong>presentation</strong></span> and the content AST
- <span class="command"><strong>content</strong></span>. The declared presentation AST fragment
- <span class="command"><strong>presentation</strong></span> is at precedence level
- <span class="command"><strong>p</strong></span>. The precedence level is used to determine where
- parentheses must be inserted. In particular, the content AST fragment
- <span class="command"><strong>content</strong></span> is actually a pattern, since it contains
- placeholders (variables) for sub-ASTs. Every placeholder for a term
- is given an expected precedence level. Parentheses must be inserted
- around sub-ASTs having a precedence level strictly smaller than the
- expected one.</p><p>If <span class="command"><strong>presentation</strong></span> describes a binary
- infix operator and if no precedence level is explicitly given for the
- operator arguments, an <span class="command"><strong>associativity</strong></span> declaration
- can be given to automatically choose the right level for the operands.
- Otherwise, no <span class="command"><strong>associativity</strong></span> can be given.</p><p>If <span class="command"><strong>direction</strong></span> is
- omitted, the mapping is bi-directional and is used both during
- parsing and pretty-printing of terms. If <span class="command"><strong>direction</strong></span>
- is <span class="command"><strong>></strong></span>, the mapping is used only during parsing;
- if it is <span class="command"><strong><</strong></span>, it is used only during
- pretty-printing. Thus it is possible to use simple notations to type
- for writing the term, and nicer ones for rendering it.</p></dd><dt><span class="term">Notation arguments:</span></dt><dd><div class="table"><a id="idm1537"></a><p class="title"><strong>Table 5.1. usage</strong></p><div class="table-contents"><table class="table" summary="usage" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.usage"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.usage">usage</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong><</strong></span></td><td style="">Only for pretty-printing</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>></strong></span></td><td style="">Only for parsing</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1555"></a><p class="title"><strong>Table 5.2. associativity</strong></p><div class="table-contents"><table class="table" summary="associativity" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.associativity"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.associativity">associativity</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>left</strong></span> <span class="bold"><strong>associative</strong></span></td><td style="">Left associative</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>right</strong></span> <span class="bold"><strong>associative</strong></span></td><td style="">Right associative</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>non</strong></span> <span class="bold"><strong>associative</strong></span></td><td style="">Non associative (default)</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1582"></a><p class="title"><strong>Table 5.3. notation_rhs</strong></p><div class="table-contents"><table class="table" summary="notation_rhs" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.notation_rhs"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_rhs">notation_rhs</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_ast">unparsed_ast</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_meta">unparsed_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1604"></a><p class="title"><strong>Table 5.4. unparsed_ast</strong></p><div class="table-contents"><table class="table" summary="unparsed_ast" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.unparsed_ast"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_ast">unparsed_ast</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>@{</strong></span><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.enriched_term">enriched_term</a></em></span><span class="bold"><strong>}</strong></span></td><td style="">A content level AST (a term which is parsed, but not disambiguated).</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>@</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="command"><strong>@id</strong></span> is just an abbreviation for <span class="command"><strong>@{id}</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>@</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span></td><td style=""><span class="command"><strong>@'symbol</strong></span> is just an abbreviation for <span class="command"><strong>@{'symbol}</strong></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1639"></a><p class="title"><strong>Table 5.5. enriched_term</strong></p><div class="table-contents"><table class="table" summary="enriched_term" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.enriched_term"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.enriched_term">enriched_term</a></em></span></td><td style="">::=</td><td style="">〈〈A term that may contain occurrences of <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_meta">unparsed_meta</a></em></span>, even as variable names in binders, and occurrences of <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.csymbol">csymbol</a></em></span>〉〉</td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1655"></a><p class="title"><strong>Table 5.6. unparsed_meta</strong></p><div class="table-contents"><table class="table" summary="unparsed_meta" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.unparsed_meta"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_meta">unparsed_meta</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>${</strong></span><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span><span class="bold"><strong>}</strong></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>$</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="command"><strong>$id</strong></span> is just an abbreviation for <span class="command"><strong>${id}</strong></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>$</strong></span><span class="bold"><strong>_</strong></span></td><td style=""><span class="command"><strong>$_</strong></span> is just an abbreviation for <span class="command"><strong>${_}</strong></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1690"></a><p class="title"><strong>Table 5.7. level2_meta</strong></p><div class="table-contents"><table class="table" summary="level2_meta" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.level2_meta"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.unparsed_ast">unparsed_ast</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>term</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>number</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>ident</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fresh</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>anonymous</strong></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fold</strong></span> [<span class="bold"><strong>left</strong></span>|<span class="bold"><strong>right</strong></span>] <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="bold"><strong>rec</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>default</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>if</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="bold"><strong>then</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span> <span class="bold"><strong>else</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.level2_meta">level2_meta</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fail</strong></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1806"></a><p class="title"><strong>Table 5.8. notation_lhs</strong></p><div class="table-contents"><table class="table" summary="notation_lhs" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.notation_lhs"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.notation_lhs">notation_lhs</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]…</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1820"></a><p class="title"><strong>Table 5.9. layout</strong></p><div class="table-contents"><table class="table" summary="layout" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.layout"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\sub</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Subscript</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\sup</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Superscript</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\below</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\above</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\over</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\atop</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style=""> </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\frac</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Fraction</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>\infrule</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Inference rule (premises, conclusion, rule name)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>\sqrt</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Square root</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>\root</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> <span class="bold"><strong>\of</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Generalized root</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>hbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Horizontal box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>vbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Vertical box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>hvbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Horizontal and vertical box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>hovbox</strong></span> <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Horizontal or vertical box</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>break</strong></span></td><td style="">Breakable space</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>]… <span class="bold"><strong>)</strong></span></td><td style="">Group</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for a term with no explicit precedence</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>term</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for a term with explicit expected precedence</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>number</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for a natural number</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>ident</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></td><td style="">Placeholder for an identifier</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span></td><td style="">Literal</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>opt</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span></td><td style="">Optional layout (it can be omitted for parsing)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>list0</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>
- [<span class="bold"><strong>sep</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span>]</td><td style="">List of layouts separated by <span class="command"><strong>sep</strong></span> (default:
- any blank)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>list1</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>
- [<span class="bold"><strong>sep</strong></span> <span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span>]</td><td style="">Non empty list of layouts separated by <span class="command"><strong>sep</strong></span>
- (default: any blank)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>mstyle</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> value (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>)
- </td><td style="">Style attributes like color #ff0000</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>mpadded</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> value (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>)
- </td><td style="">padding attributes like width -150%</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>maction</strong></span> (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>)
- [ (<span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.layout">layout</a></em></span>) … ]
- </td><td style="">Alternative notations (output only)</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm2094"></a><p class="title"><strong>Table 5.10. literal</strong></p><div class="table-contents"><table class="table" summary="literal" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.literal"></a><span class="emphasis"><em><a class="link" href="sec_usernotation.html#grammar.literal">literal</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.symbol">symbol</a></em></span></td><td style="">Unicode symbol</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></td><td style="">Natural number (a constant)</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>'</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span><span class="bold"><strong>'</strong></span></td><td style="">New keyword for the lexer</td></tr></tbody></table></div></div><br class="table-break" /></dd></dl></div><p>
- </p></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tacticargs.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="ch05s02.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Tactic arguments </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> interpretation</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we have</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_existselim.html" title="let such that" /><link rel="next" href="tac_weproceedbyinduction.html" title="we proceed by induction on" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we have</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_existselim.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weproceedbyinduction.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_andelim"></a>we have</h2></div></div></div><p><strong class="userinput"><code>justification we have A (H1) and B (H2)</code></strong>
- </p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>we have</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- <span class="bold"><strong>( </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> ) and </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- <span class="bold"><strong> ( </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- None.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It applies the left multiplicative introduction rule for the conjunction on the formula <span class="command"><strong>A ∧ B</strong></span> (in Natural Deduction this corresponds to the elimination rule for the conjunction).
- </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent with <span class="command"><strong>A ∧ B</strong></span> as the conclusion is opened and then immediately closed using the given justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and two new hypotheses <span class="command"><strong>H1 : A</strong></span> and <span class="command"><strong>H2 : B</strong></span> are added to the context.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_existselim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weproceedbyinduction.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">let such that </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proceed by induction on</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>apply</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="next" href="tac_auto.html" title="auto" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">apply</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_tactics.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_auto.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_apply"></a>apply</h2></div></div></div><p><strong class="userinput"><code>@t</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>@</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must have type
- <span class="command"><strong>T<sub>1</sub> → … →
- T<sub>n</sub> → G</strong></span>
- where <span class="command"><strong>G</strong></span> can be unified with the conclusion
- of the current sequent.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent by applying <span class="command"><strong>t</strong></span> to <span class="command"><strong>n</strong></span> implicit arguments (that become new sequents).</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each premise
- <span class="command"><strong>T<sub>i</sub></strong></span> that is not
- instantiated by unification. <span class="command"><strong>T<sub>i</sub></strong></span> is
- the conclusion of the <span class="command"><strong>i</strong></span>-th new sequent to
- prove.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_tactics.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_auto.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 7. Tactics </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> auto</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>applyS</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_rewrite.html" title="rewrite" /><link rel="next" href="tac_assumption.html" title="assumption" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">applyS</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_rewrite.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_assumption.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_applyS"></a>applyS</h2></div></div></div><p><strong class="userinput"><code>applyS t auto_params</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>applyS</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must have type
- <span class="command"><strong>T<sub>1</sub> → ... →
- T<sub>n</sub> → G</strong></span>.</p></dd><dt><span class="term">Action:</span></dt><dd><p><span class="command"><strong>applyS</strong></span> is useful when
- <span class="command"><strong>apply</strong></span> fails because the current goal
- and the conclusion of the applied theorems are extensionally
- equivalent up to instantiation of metavariables, but cannot
- be unified. E.g. the goal is <span class="command"><strong>P(n*O+m)</strong></span> and
- the theorem to be applied proves <span class="command"><strong>∀m.P(m+O)</strong></span>.
- </p><p>
- It tries to automatically rewrite the current goal using
- <a class="link" href="tac_auto.html" title="auto">auto paramodulation</a>
- to make it unifiable with <span class="command"><strong>G</strong></span>.
- Then it closes the current sequent by applying
- <span class="command"><strong>t</strong></span> to <span class="command"><strong>n</strong></span>
- implicit arguments (that become new sequents).
- The <span class="command"><strong>auto_params</strong></span> parameters are passed
- directly to <span class="command"><strong>auto paramodulation</strong></span>.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each premise
- <span class="command"><strong>T<sub>i</sub></strong></span> that is not
- instantiated by unification. <span class="command"><strong>T<sub>i</sub></strong></span> is
- the conclusion of the <span class="command"><strong>i</strong></span>-th new sequent to
- prove.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_rewrite.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_assumption.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">rewrite </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> assumption</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>assume</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="next" href="tac_suppose.html" title="suppose" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">assume</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="sec_declarative_tactics.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_suppose.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_assume"></a>assume</h2></div></div></div><p><strong class="userinput"><code>assume x : T</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>assume</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> : </strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>
- The conclusion of the sequent to prove must be a universal quantification.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It applies the right introduction rule for the universal quantifier, closing the current sequent (in Natural Deduction this corresponds to the introduction rule for the quantifier).
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
- It opens a new sequent to prove the quantified subformula adding <span class="command"><strong>x : T</strong></span> to the hypotheses.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="sec_declarative_tactics.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_suppose.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Chapter 8. Declarative Tactics </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> suppose</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>assumption</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_applyS.html" title="applyS" /><link rel="next" href="tac_cases.html" title="cases" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">assumption</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_applyS.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_cases.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_assumption"></a>assumption</h2></div></div></div><p><strong class="userinput"><code>assumption </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>assumption</strong></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>There must exist an hypothesis whose type can be unified with
- the conclusion of the current sequent.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent exploiting an hypothesis.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_applyS.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_cases.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">applyS </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> cases</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>auto</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_apply.html" title="apply" /><link rel="next" href="tac_intro.html" title="intro" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">auto</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_apply.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_intro.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_auto"></a>auto</h2></div></div></div><p><strong class="userinput"><code>/params/</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>/</strong></span><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span><span class="bold"><strong>/</strong></span>. </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None, but the tactic may fail finding a proof if every
- proof is in the search space that is pruned away. Pruning is
- controlled by the optional <span class="command"><strong>params</strong></span>.
- Moreover, only lemmas whose type signature is a subset of the
- signature of the current sequent are considered. The signature of
- a sequent is essentially the set of constats appearing in it.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent by repeated application of
- rewriting steps (unless <span class="command"><strong>paramodulation</strong></span> is
- omitted), hypothesis and lemmas in the library.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_apply.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_intro.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">apply </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> intro</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>done</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_rewrite_step.html" title="=" /><link rel="next" href="sec_commands.html" title="Chapter 9. Other commands" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">done</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_rewrite_step.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="sec_commands.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_bydone"></a>done</h2></div></div></div><p><strong class="userinput"><code>justification done</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>done</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The user is proving a sequent which was opened with the tactic <span class="bold"><strong>we need to prove</strong></span>, or the user is proving a sequent which was opened with the tactic <span class="bold"><strong>we proceed by induction/cases on</strong></span>, or the user is proving a chain of equalities that was started with either the tactic <span class="bold"><strong>conclude</strong></span> or <span class="bold"><strong>obtain</strong></span>.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent with the given justification.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_rewrite_step.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_commands.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">= </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 9. Other commands</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>by induction hypothesis we know</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_case.html" title="case" /><link rel="next" href="tac_conclude.html" title="conclude" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">by induction hypothesis we know</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_case.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_conclude.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_byinduction"></a>by induction hypothesis we know</h2></div></div></div><p><strong class="userinput"><code>by induction hypothesis we know P (id)</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>by induction hypothesis we know</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The user must have started proving a case for a proof by induction/case-analysis.</p></dd><dt><span class="term">Action:</span></dt><dd><p> It introduces the inductive hypothesis. </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_case.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_conclude.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">case </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> conclude</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proved</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_weneedtoprove.html" title="we need to prove" /><link rel="next" href="tac_existselim.html" title="let such that" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proved</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_weneedtoprove.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_existselim.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_bytermweproved"></a>we proved</h2></div></div></div><p><strong class="userinput"><code>justification we proved T [(id)]</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>we proved</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>)</strong></span>]
- </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- None.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- If <span class="command"><strong>id</strong></span> is supplied, a logical cut on <span class="command"><strong>T</strong></span> is made. Otherwise, if <span class="command"><strong>T</strong></span> is identical to the current conclusion, it allows the user to start a chain of reductions on the conclusion with the tactic <span class="bold"><strong>that is equivalent to</strong></span>.
- </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>
- If <span class="command"><strong>id</strong></span> is supplied, a new sequent with <span class="command"><strong>T</strong></span> as the conclusion is opened and then immediately closed using the supplied justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and a new hypotesis <span class="command"><strong>T</strong></span> is added to the context, with name <span class="command"><strong>id</strong></span>.
- If <span class="command"><strong>id</strong></span> is not supplied, no new sequents are opened.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_weneedtoprove.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_existselim.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we need to prove </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> let such that</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>case</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_weproceedbycases.html" title="we proceed by cases on" /><link rel="next" href="tac_byinduction.html" title="by induction hypothesis we know" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">case</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_weproceedbycases.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_byinduction.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_case"></a>case</h2></div></div></div><p><strong class="userinput"><code>case id (id1:T1) … (idn:Tn)</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>case</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>] … [<span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>)</strong></span>]</p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The user must have started a proof by induction/cases that has not been concluded yet, <span class="command"><strong>id</strong></span> must be a constructor for the inductive type of the term under induction/case-analysis, and the case must not have already been proved.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It starts the proof for the case <span class="command"><strong>id</strong></span>, where <span class="command"><strong>id1:T1</strong></span>,…,<span class="command"><strong>idn:Tn</strong></span> are the arguments of the constructor, each declared with its type.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>The sequent for the case <span class="command"><strong>id</strong></span>.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_weproceedbycases.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_byinduction.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we proceed by cases on </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> by induction hypothesis we know</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>cases</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_assumption.html" title="assumption" /><link rel="next" href="tac_change.html" title="change" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">cases</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_assumption.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_change.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_cases"></a>cases</h2></div></div></div><p><strong class="userinput"><code>
- cases t pattern
- </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>cases</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
- </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>
- <span class="command"><strong>t</strong></span> must inhabit an inductive type
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It proceed by cases on <span class="command"><strong>t</strong></span>. The new generated
- hypothesis in each branch are named according to
- <span class="command"><strong>hyps</strong></span>.
- The elimintation predicate is restricted by
- <span class="command"><strong>pattern</strong></span>. In particular, if some hypothesis
- is listed in <span class="command"><strong>pattern</strong></span>, the hypothesis is
- generalized and cleared before proceeding by cases on
- <span class="command"><strong>t</strong></span>. Currently, we only support patterns of the
- form <span class="command"><strong>H<sub>1</sub> … H<sub>n</sub> ⊢ %</strong></span>. This limitation will be lifted in the future.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>One new sequent for each constructor of the type of
- <span class="command"><strong>t</strong></span>. Each sequent has a new hypothesis for
- each argument of the constructor.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_assumption.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_change.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">assumption </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> change</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>change</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_cases.html" title="cases" /><link rel="next" href="tac_cut.html" title="cut" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">change</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_cases.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_cut.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_change"></a>change</h2></div></div></div><p><strong class="userinput"><code>change patt with t</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>change</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> <span class="bold"><strong>with</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>Each subterm matched by the pattern must be convertible
- with the term <span class="command"><strong>t</strong></span> disambiguated in the context
- of the matched subterm.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It replaces the subterms of the current sequent matched by
- <span class="command"><strong>patt</strong></span> with the new term <span class="command"><strong>t</strong></span>.
- For each subterm matched by the pattern, <span class="command"><strong>t</strong></span> is
- disambiguated in the context of the subterm.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_cases.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_cut.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">cases </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> cut</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>clear</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="macro_intro.html" title="macro_input" /><link rel="next" href="tac_constructor.html" title="constructor" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">clear</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="macro_intro.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_constructor.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_clear"></a>clear</h2></div></div></div><p><strong class="userinput"><code>-H</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>-</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>
- <span class="command"><strong>H</strong></span> must be an hypothesis of the
- current sequent to prove.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It hides the hypothesis <span class="command"><strong>H</strong></span>
- from the current sequent.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="macro_intro.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_constructor.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">macro_input </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> constructor</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>conclude</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_byinduction.html" title="by induction hypothesis we know" /><link rel="next" href="tac_obtain.html" title="obtain" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">conclude</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_byinduction.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_obtain.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_conclude"></a>conclude</h2></div></div></div><p><strong class="userinput"><code>conclude t1 </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>conclude</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- The current conclusion must be an equality <span class="command"><strong>t1 = tk</strong></span>
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It starts an equality chain on the conclusion. It allows the user to apply the tactic <span class="bold"><strong>=</strong></span> to continue the chain.</p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_byinduction.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_obtain.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">by induction hypothesis we know </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> obtain</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>constructor</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_clear.html" title="clear" /><link rel="next" href="tac_decompose.html" title="decompose" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">constructor</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_clear.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_decompose.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_constructor"></a>constructor</h2></div></div></div><p><strong class="userinput"><code>%n {args}</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>%</strong></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] [<span class="bol">{</span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>…<span class="bol">}</span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The conclusion of the current sequent must be
- an inductive type or the application of an inductive type with
- at least <span class="command"><strong>n</strong></span> constructors.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the <span class="command"><strong>n</strong></span>-th constructor of the
- inductive type of the conclusion of the current sequent to
- the arguments <span class="command"><strong>args</strong></span>.
- If <span class="command"><strong>n</strong></span> is omitted, it defaults to 1.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each premise of the constructor
- that can not be inferred by unification. For more details,
- see the <span class="command"><strong>apply</strong></span> tactic.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_clear.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_decompose.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">clear </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> decompose</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>cut</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_change.html" title="change" /><link rel="next" href="tac_destruct.html" title="destruct" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">cut</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_change.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_destruct.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_cut"></a>cut</h2></div></div></div><p><strong class="userinput"><code>cut P</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>cut</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>P</strong></span> must be a type.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens two new sequents. The first one has conclusion
- <span class="command"><strong>P → G</strong></span> where <span class="command"><strong>G</strong></span> is the
- old conclusion.
- The second sequent has conclusion <span class="command"><strong>P</strong></span> and
- hypotheses the hypotheses of the current sequent to prove.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_change.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_destruct.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">change </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> destruct</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>decompose</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_constructor.html" title="constructor" /><link rel="next" href="tac_rewrite.html" title="rewrite" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">decompose</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_constructor.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_rewrite.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_decompose"></a>decompose</h2></div></div></div><p><strong class="userinput"><code>
- * as H
- </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>*</strong></span>
- [<span class="bold"><strong>as</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>]
- </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The current conclusion must be of the form
- <span class="command"><strong>T → G</strong></span> where <span class="command"><strong>I</strong></span> is
- an inductive type applied to its arguments, if any.</p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It introduces a new hypothesis <span class="command"><strong>H</strong></span> of type
- <span class="command"><strong>T</strong></span>. Then it proceeds by cases over
- <span class="command"><strong>H</strong></span>. Finally, if the name <span class="command"><strong>H</strong></span>
- is not specified, it clears the new hypothesis from all contexts.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
- The ones generated by case analysis.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_constructor.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_rewrite.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">constructor </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> rewrite</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>destruct</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_cut.html" title="cut" /><link rel="next" href="tac_elim.html" title="elim" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">destruct</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_cut.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_elim.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_destruct"></a>destruct</h2></div></div></div><p><strong class="userinput"><code>destruct (H<sub>0</sub> ... H<sub>n</sub>) skip (K<sub>0</sub> ... K<sub>m</sub>)</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>destruct</strong></span>
- [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>] [<span class="bold"><strong>skip</strong></span> <span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>…<span class="bold"><strong>)</strong></span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>Each hypothesis <span class="command"><strong>H<sub>i</sub></strong></span> must be either a Leibniz or a John Major equality where the two sides of the equality are possibly applied constructors of an inductive type.</p></dd><dt><span class="term">Action:</span></dt><dd><p>The tactic recursively compare the two sides of each equality
- looking for different constructors in corresponding position.
- If two of them are found, the tactic closes the current sequent
- by proving the absurdity of <span class="command"><strong>p</strong></span>. Otherwise
- it adds a new hypothesis for each leaf of the formula that
- states the equality of the subformulae in the corresponding
- positions on the two sides of the equality. If the newly
- added hypothesis is an equality between a variable and a term,
- the variable is substituted for the term everywhere in the
- sequent, except for the hypotheses <span class="command"><strong>K<sub>j</sub></strong></span>, and it is then cleared from the list of hypotheses.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_cut.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_elim.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">cut </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> elim</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>elim</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_destruct.html" title="destruct" /><link rel="next" href="tac_generalize.html" title="generalize" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">elim</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_destruct.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_generalize.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_elim"></a>elim</h2></div></div></div><p><strong class="userinput"><code>elim t pattern</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>elim</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>t</strong></span> must inhabit an inductive type.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It proceeds by cases on the values of <span class="command"><strong>t</strong></span>,
- according to the most appropriate elimination principle for
- the current goal.
- The induction predicate is restricted by
- <span class="command"><strong>pattern</strong></span>. In particular, if some hypothesis
- is listed in <span class="command"><strong>pattern</strong></span>, the hypothesis is
- generalized and cleared before eliminating <span class="command"><strong>t</strong></span>
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each case.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_destruct.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_generalize.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">destruct </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> generalize</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>let such that</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_bytermweproved.html" title="we proved" /><link rel="next" href="tac_andelim.html" title="we have" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">let such that</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_bytermweproved.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_andelim.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_existselim"></a>let such that</h2></div></div></div><p><strong class="userinput"><code>justification let x:T such that P (H)</code></strong>
- </p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span> <span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>such that</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- <span class="bold"><strong>(</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>)</strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- None.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It applies the left introduction rule of the existential quantifier on the formula <span class="command"><strong>∃ x. P(x)</strong></span> (in Natural Deduction this corresponds to the elimination rule for the quantifier).
- </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent with <span class="command"><strong>∃ x. P(x)</strong></span> as the conclusion is opened and then immediately closed using the given justification. A new sequent with the conclusion of the sequent on which this tactic was applied is opened, and two new hypotheses <span class="command"><strong>x : T</strong></span> and <span class="command"><strong>H : P</strong></span> are added to the context.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_bytermweproved.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_andelim.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we proved </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we have</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>generalize</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_elim.html" title="elim" /><link rel="next" href="tac_inversion.html" title="inversion" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">generalize</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_elim.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_inversion.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_generalize"></a>generalize</h2></div></div></div><p><strong class="userinput"><code>generalize patt</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>generalize</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>All the terms matched by <span class="command"><strong>patt</strong></span> must be
- convertible and close in the context of the current sequent.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It closes the current sequent by applying a stronger
- lemma that is proved using the new generated sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent where the current sequent conclusion
- <span class="command"><strong>G</strong></span> is generalized to
- <span class="command"><strong>∀x.G{x/t}</strong></span> where <span class="command"><strong>{x/t}</strong></span>
- is a notation for the replacement with <span class="command"><strong>x</strong></span> of all
- the occurrences of the term <span class="command"><strong>t</strong></span> matched by
- <span class="command"><strong>patt</strong></span>. If <span class="command"><strong>patt</strong></span> matches no
- subterm then <span class="command"><strong>t</strong></span> is defined as the
- <span class="command"><strong>wanted</strong></span> part of the pattern.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_elim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_inversion.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">elim </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> inversion</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>intro</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_auto.html" title="auto" /><link rel="next" href="tac_intro_clear.html" title="intro_clear" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">intro</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_auto.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_intro_clear.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_intro"></a>intro</h2></div></div></div><p><strong class="userinput"><code>#H</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>#</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The conclusion of the sequent to prove must be an implication
- or a universal quantification.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the right introduction rule for implication,
- closing the current sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent to prove adding to the hypothesis
- the antecedent of the implication and setting the conclusion
- to the consequent of the implicaiton. The name of the new
- hypothesis is <span class="command"><strong>H</strong></span>.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_auto.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_intro_clear.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">auto </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> intro_clear</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>intro_clear</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_intro.html" title="intro" /><link rel="next" href="macro_intro.html" title="macro_input" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">intro_clear</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_intro.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="macro_intro.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_intro_clear"></a>intro_clear</h2></div></div></div><p><strong class="userinput"><code>#_</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>#_</strong></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The conclusion of the sequent to prove must be an implication.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the ``a fortiori'' rule for implication,
- closing the current sequent.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent whose conclusion is the conclusion
- of the implication of the original sequent.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_intro.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="macro_intro.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">intro </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> macro_input</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>inversion</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_generalize.html" title="generalize" /><link rel="next" href="tac_lapply.html" title="lapply" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">inversion</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_generalize.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_lapply.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_inversion"></a>inversion</h2></div></div></div><p><strong class="userinput"><code>inversion t</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>inversion</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>The type of the term <span class="command"><strong>t</strong></span> must be an inductive
- type or the application of an inductive type.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It proceeds by cases on <span class="command"><strong>t</strong></span> paying attention
- to the constraints imposed by the actual "right arguments"
- of the inductive type.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent to prove for each case in the
- definition of the type of <span class="command"><strong>t</strong></span>. With respect to
- a simple elimination, each new sequent has additional hypotheses
- that states the equalities of the "right parameters"
- of the inductive type with terms originally present in the
- sequent to prove. It uses either Leibniz or John Major equality
- for the new hypotheses, according to the included files.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_generalize.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_lapply.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">generalize </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> lapply</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>lapply</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_inversion.html" title="inversion" /><link rel="next" href="tac_letin.html" title="letin" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">lapply</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_inversion.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_letin.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_lapply"></a>lapply</h2></div></div></div><p><strong class="userinput"><code>
- lapply t
- </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>lapply</strong></span>
- <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>
- </p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It generalizes the conclusion of the current goal
- adding as a premise the type of <span class="command"><strong>t</strong></span>,
- closing the current goal.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
- The new sequent has conclusion <span class="command"><strong>T → G</strong></span> where
- <span class="command"><strong>T</strong></span> is the type of <span class="command"><strong>t</strong></span>
- and <span class="command"><strong>G</strong></span> the old conclusion.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_inversion.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_letin.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">inversion </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> letin</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>letin</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_suppose.html" title="suppose" /><link rel="next" href="tac_thatisequivalentto.html" title="that is equivalent to" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">letin</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_suppose.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_thatisequivalentto.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_let"></a>letin</h2></div></div></div><p><strong class="userinput"><code>let x := T </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>let</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong> = </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>None</p></dd><dt><span class="term">Action:</span></dt><dd><p>It adds a new local definition <span class="command"><strong>x := T</strong></span> to the context of the sequent to prove.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_suppose.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_thatisequivalentto.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">suppose </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> that is equivalent to</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>letin</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_lapply.html" title="lapply" /><link rel="next" href="tac_normalize.html" title="normalize" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">letin</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_lapply.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_normalize.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_letin"></a>letin</h2></div></div></div><p><strong class="userinput"><code>letin x ≝ t</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>letin</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="bold"><strong>≝</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It adds to the context of the current sequent to prove a new
- definition <span class="command"><strong>x ≝ t</strong></span>.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_lapply.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_normalize.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">lapply </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> normalize</td></tr></table></div></body></html>
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>normalize</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_letin.html" title="letin" /><link rel="next" href="tac_whd.html" title="whd" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">normalize</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_letin.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_whd.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_normalize"></a>normalize</h2></div></div></div><p><strong class="userinput"><code>normalize patt nodelta</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>normalize</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span>
- [<span class="bold"><strong>nodelta</strong></span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It replaces all the terms matched by <span class="command"><strong>patt</strong></span>
- with their βδιζ-normal form. If <span class="command"><strong>nodelta</strong></span> is
- specified, δ-expansions are not performed.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_letin.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_whd.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">letin </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> whd</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>obtain</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_conclude.html" title="conclude" /><link rel="next" href="tac_rewrite_step.html" title="=" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">obtain</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_conclude.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_rewrite_step.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_obtain"></a>obtain</h2></div></div></div><p><strong class="userinput"><code>obtain H t1 </code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>obtain</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- None.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It starts an equality chain <span class="command"><strong>t1 = ?</strong></span>, which, when concluded, will be added to hypoteses of the current sequent. It allows the user to apply the tactic <span class="bold"><strong>=</strong></span> to continue the chain.</p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>A new sequent for <span class="command"><strong>t1 = ?</strong></span> is opened, a new sequent for <span class="command"><strong>?</strong></span> is opened, and a new sequent with the conclusion of the sequent on which this tactic was applied is opened, with <span class="command"><strong>H: t1 = ?</strong></span> added to its hypotheses. This hypotesis will be changed when the equality chain is concluded with <span class="command"><strong>H: t1 = tk</strong></span>, where <span class="command"><strong>tk</strong></span> is the last term of the equality chain. The goal for <span class="command"><strong>?</strong></span> can be safely ignored, as it will be automatically closed when the equality chain is concluded.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_conclude.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_rewrite_step.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">conclude </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> =</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>rewrite</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_decompose.html" title="decompose" /><link rel="next" href="tac_applyS.html" title="applyS" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">rewrite</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_decompose.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_applyS.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_rewrite"></a>rewrite</h2></div></div></div><p><strong class="userinput"><code>> p patt</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>[<span class="bold"><strong><</strong></span>|<span class="bold"><strong>></strong></span>] <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p><span class="command"><strong>p</strong></span> must be the proof of an equality,
- possibly under some hypotheses.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It looks in every term matched by <span class="command"><strong>patt</strong></span>
- for all the occurrences of the
- left hand side of the equality that <span class="command"><strong>p</strong></span> proves
- (resp. the right hand side if <span class="command"><strong><</strong></span> is used).
- Every occurence found is replaced with
- the opposite side of the equality.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each hypothesis of the
- equality proved by <span class="command"><strong>p</strong></span> that is not closed
- by unification.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_decompose.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_applyS.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">decompose </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> applyS</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>=</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_obtain.html" title="obtain" /><link rel="next" href="tac_bydone.html" title="done" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">=</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_obtain.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_bydone.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_rewrite_step"></a>=</h2></div></div></div><p><strong class="userinput"><code>= t2 justification</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>=</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> [<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span> | <span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>using once</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> | <span class="bold"><strong>proof</strong></span>] [<span class="bold"><strong>done</strong></span>]
- </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- The user must have started an equality chain with <span class="bold"><strong>conclude</strong></span> or <span class="bold"><strong>obtain</strong></span> that has not been concluded yet.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It applies the transitivity of <span class="command"><strong>=</strong></span> on the left-hand-side of the current conclusion, <span class="command"><strong>t2</strong></span>, and the right-hand-side of the current conclusion, using the given justification. If <span class="bold"><strong>done</strong></span> is supplied, this represents the last step in the equality chain.
- </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>
- A new sequent for <span class="command"><strong>lhs = t2</strong></span> is opened and then immediately closed using the given justification. A new sequent with the conclusion <span class="command"><strong>t2 = rhs</strong></span> is opened.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_obtain.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_bydone.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">obtain </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> done</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>suppose</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_assume.html" title="assume" /><link rel="next" href="tac_let.html" title="letin" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">suppose</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_assume.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_let.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_suppose"></a>suppose</h2></div></div></div><p><strong class="userinput"><code>suppose A (H)</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>suppose</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> (</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>) </strong></span></p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- The conclusion of the sequent to prove must be an implication.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- It applies the right introduction rule for the implication, closing the current sequent (in Natural Deduction this corresponds to the introduction rule for the implication).
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>
- It opens a new sequent to prove the consequent of the implication adding the antecedent <span class="command"><strong>A</strong></span> to the hypotheses. The name of the new hypothesis is <span class="command"><strong>H</strong></span>.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_assume.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_let.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">assume </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> letin</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>that is equivalent to</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_let.html" title="letin" /><link rel="next" href="tac_thesisbecomes.html" title="the thesis becomes" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">that is equivalent to</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_let.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_thesisbecomes.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_thatisequivalentto"></a>that is equivalent to</h2></div></div></div><p><strong class="userinput"><code>that is equivalent to t</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p>
- <span class="bold"><strong>that is equivalent to</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>
- The user must have applied one of the following tactics immediately before applying this tactic: <span class="bold"><strong>assume</strong></span>, <span class="bold"><strong>suppose</strong></span>, <span class="bold"><strong>we need to prove</strong></span>, <span class="bold"><strong>by just we proved</strong></span>,<span class="bold"><strong>the thesis becomes</strong></span>, <span class="bold"><strong>that is equivalent to</strong></span>.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>
- If the tactic that was applied before this introduced a new hypothesis in the context, this tactic works on this hypothesis; otherwise, it works on the conclusion. Either way, if the term <span class="command"><strong>t</strong></span> is beta-equivalent to the term <span class="command"><strong>t1</strong></span> on which this tactic is working (i.e. they can be reduced to a common term), <span class="command"><strong>t1</strong></span> is changed with <span class="command"><strong>t</strong></span>.
-
- If the tactic that was applied before this tactic was <span class="bold"><strong>that is equivalent to</strong></span>, and that tactic was working on a term <span class="command"><strong>t1</strong></span>, this tactic keeps working on <span class="command"><strong>t1</strong></span>.
- </p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>
- If this tactic is working on the conclusion, a new sequent with the same hypotheses and the conclusion changed to <span class="command"><strong>t</strong></span> is opened. If this tactic is working on the last introduced hypotesis, a new sequent with the same conclusion is opened. The hypotheses of this sequent are the same, except for the one on which the tactic is working on, which is changed with <span class="command"><strong>t</strong></span>.
- </p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_let.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_thesisbecomes.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">letin </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> the thesis becomes</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>the thesis becomes</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_thatisequivalentto.html" title="that is equivalent to" /><link rel="next" href="tac_weneedtoprove.html" title="we need to prove" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">the thesis becomes</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_thatisequivalentto.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weneedtoprove.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_thesisbecomes"></a>the thesis becomes</h2></div></div></div><p><strong class="userinput"><code>the thesis becomes P</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>the thesis becomes</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The provided term <span class="command"><strong>P</strong></span> must be identical to the current conclusion.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It allows the user to start a chain of reductions on the conclusion with the tactic <span class="bold"><strong>that is equivalent to</strong></span>, after stating the current conclusion.</p></dd><dt><span class="term">New sequent to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_thatisequivalentto.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weneedtoprove.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">that is equivalent to </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we need to prove</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we need to prove</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_thesisbecomes.html" title="the thesis becomes" /><link rel="next" href="tac_bytermweproved.html" title="we proved" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we need to prove</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_thesisbecomes.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_bytermweproved.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weneedtoprove"></a>we need to prove</h2></div></div></div><p><strong class="userinput"><code>we need to prove T [(H)]</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we need to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span>
- [<span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>
- <span class="bold"><strong>)</strong></span>]
- </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>If <span class="command"><strong>id</strong></span> is provided, it applies a logical cut on <span class="command"><strong>T</strong></span>. Otherwise, it allows the user to start a chain of reductions on the conclusion with the tactic <span class="bold"><strong>that is equivalent to</strong></span>.
- </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>If <span class="command"><strong>id</strong></span> is supplied, a new sequent with <span class="command"><strong>T</strong></span> as the conclusion is opened, and a new sequent with the conclusion of the sequent on which this tactic was applied is opened, with <span class="command"><strong>H:T</strong></span> added to the hypotheses.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_thesisbecomes.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_bytermweproved.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">the thesis becomes </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proved</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proceed by cases on</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_weproceedbyinduction.html" title="we proceed by induction on" /><link rel="next" href="tac_case.html" title="case" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proceed by cases on</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_weproceedbyinduction.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_case.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weproceedbycases"></a>we proceed by cases on</h2></div></div></div><p><strong class="userinput"><code>we proceed by cases on t to prove P</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we proceed by cases on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong>to prove</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The type of <span class="command"><strong>t</strong></span> must be an inductive type and <span class="command"><strong>P</strong></span> must be identical to the current conclusion.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p> It proceeds by case-analysis on <span class="command"><strong>t</strong></span> </p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens one new sequent for each constructor of the
- type of <span class="command"><strong>t</strong></span>, each with the conclusion <span class="command"><strong>P</strong></span> instantiated for the constructor.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_weproceedbyinduction.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_case.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we proceed by induction on </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> case</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>we proceed by induction on</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /><link rel="prev" href="tac_andelim.html" title="we have" /><link rel="next" href="tac_weproceedbycases.html" title="we proceed by cases on" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">we proceed by induction on</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_andelim.html">Prev</a> </td><th width="60%" align="center">Chapter 8. Declarative Tactics</th><td width="20%" align="right"> <a accesskey="n" href="tac_weproceedbycases.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_weproceedbyinduction"></a>we proceed by induction on</h2></div></div></div><p><strong class="userinput"><code>we proceed by induction on t to prove P</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>we proceed by induction on</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> <span class="bold"><strong> to prove </strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span> </p></dd><dt><span class="term">Pre-condition:</span></dt><dd><p>The type of <span class="command"><strong>t</strong></span> must be an inductive type and <span class="command"><strong>P</strong></span> must be identical to the current conclusion.
- </p></dd><dt><span class="term">Action:</span></dt><dd><p>It applies the induction principle on <span class="command"><strong>t</strong></span> to prove <span class="command"><strong>P</strong></span>.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>It opens a new sequent for each constructor of the type of <span class="command"><strong>t</strong></span>, each with the conclusion <span class="command"><strong>P</strong></span> instantiated for the constructor. For the inductive constructors (i.e. if the inductive type is <span class="command"><strong>T</strong></span>, constructors with an argument of type <span class="command"><strong>T</strong></span>), the conclusion is a logical implication, where the antecedent is the inductive hypothesis for the constructor, and the consequent is <span class="command"><strong>P</strong></span>.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_andelim.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_declarative_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="tac_weproceedbycases.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">we have </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> we proceed by cases on</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>whd</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tactics.html" title="Chapter 7. Tactics" /><link rel="prev" href="tac_normalize.html" title="normalize" /><link rel="next" href="sec_declarative_tactics.html" title="Chapter 8. Declarative Tactics" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">whd</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tac_normalize.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Tactics</th><td width="20%" align="right"> <a accesskey="n" href="sec_declarative_tactics.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tac_whd"></a>whd</h2></div></div></div><p><strong class="userinput"><code>whd patt nodelta</code></strong></p><p>
- </p><div class="variablelist"><dl class="variablelist"><dt><span class="term">Synopsis:</span></dt><dd><p><span class="bold"><strong>whd</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span> [<span class="bold"><strong>nodelta</strong></span>]</p></dd><dt><span class="term">Pre-conditions:</span></dt><dd><p>None.</p></dd><dt><span class="term">Action:</span></dt><dd><p>It replaces all the terms matched by <span class="command"><strong>patt</strong></span>
- with their βδιζ-weak-head normal form. If <span class="command"><strong>nodelta</strong></span> is specified, δ-expansions are not performed.</p></dd><dt><span class="term">New sequents to prove:</span></dt><dd><p>None.</p></dd></dl></div><p>
- </p></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="tac_normalize.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tactics.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_declarative_tactics.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">normalize </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 8. Declarative Tactics</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Tacticals</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_tacticals.html" title="Chapter 6. Tacticals" /><link rel="prev" href="proofstatus.html" title="The proof status" /><link rel="next" href="sec_tactics.html" title="Chapter 7. Tactics" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Tacticals</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="proofstatus.html">Prev</a> </td><th width="60%" align="center">Chapter 6. Tacticals</th><td width="20%" align="right"> <a accesskey="n" href="sec_tactics.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tacticals"></a>Tacticals</h2></div></div></div><div class="table"><a id="idm2266"></a><p class="title"><strong>Table 6.1. proof script</strong></p><div class="table-contents"><table class="table" summary="proof script" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.proofscript"></a><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofscript">proof-script</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofstep">proof-step</a></em></span> [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofstep">proof-step</a></em></span>]…</td><td class="auto-generated" style=""> </td></tr></tbody></table></div></div><br class="table-break" /><p>Every proof step can be immediately executed.</p><div class="table"><a id="idm2281"></a><p class="title"><strong>Table 6.2. proof steps</strong></p><div class="table-contents"><table class="table" summary="proof steps" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.proofstep"></a><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.proofstep">proof-step</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style="">The tactical is applied to each
- <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>.
- Each new sequent becomes a selected sequent.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>.</strong></span></td><td style="">The first
- <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a> becomes
- the only one selected. All the remaining previously selected sequents
- are proposed to the user one at a time when the next
- "<span class="bold"><strong>.</strong></span>" is used.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>;</strong></span></td><td style="">Nothing changes. Use this proof step as a separator in
- concrete syntax.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>[</strong></span></td><td style="">Every <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>
- becomes a <a class="link" href="proofstatus.html#siblingsequents">sibling sequent</a>
- that constitute a branch in the proof.
- Moreover, the first sequent is also selected.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>|</strong></span></td><td style="">Stop working on the current branch of the innermost branching
- proof.
- The sibling branches become the <a class="link" href="proofstatus.html#siblingsequents">sibling
- sequents</a> and the first one is also selected.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>[<span class="bold"><strong>,</strong></span><span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>]…<span class="bold"><strong>:</strong></span></td><td style="">The <a class="link" href="proofstatus.html#siblingsequents">sibling sequents</a>
- specified by the user become the next
- <a class="link" href="proofstatus.html#selectedsequents">selected sequents</a>.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>*:</strong></span></td><td style="">Every sibling branch not considered yet in the innermost
- branching proof becomes a
- <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>skip</strong></span></td><td style="">Accept the automatically provided instantiation (not shown
- to the user) for the currently selected
- <a class="link" href="proofstatus.html#solvedsequents">automatically closed sibling sequent</a>.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>]</strong></span></td><td style="">Stop analyzing branches for the innermost branching proof.
- Every sequent opened during the branching proof and not closed yet
- becomes a <a class="link" href="proofstatus.html#selectedsequents">selected sequent</a>.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>focus</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span> [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>]…</td><td style="">
- Selects the sequents specified by the user. The selected sequents
- must be completely closed (no new sequents left open) before doing an
- "<span class="bold"><strong>unfocus</strong></span> that restores
- the current set of sibling branches.
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>unfocus</strong></span></td><td style="">
- Used to match the innermost
- "<span class="bold"><strong>focus</strong></span>" tactical
- when all the sequents selected by it have been closed.
- Until "<span class="bold"><strong>unfocus</strong></span>" is
- performed, it is not possible to progress in the rest of the
- proof.
- </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm2377"></a><p class="title"><strong>Table 6.3. tactics and LCF tacticals</strong></p><div class="table-contents"><table class="table" summary="tactics and LCF tacticals" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.LCFtactical"></a><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em><a class="link" href="sec_tactics.html#grammar.tactic">tactic</a></em></span></td><td style="">Applies the specified tactic.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span> <span class="bold"><strong>;</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style="">Applies the first tactical first and the second tactical
- to each sequent opened by the first one.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>
- <span class="bold"><strong>[</strong></span>
- [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]
- [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]…
- <span class="bold"><strong>]</strong></span>
- </td><td style="">Applies the first tactical first and each tactical in the
- list of tacticals to the corresponding sequent opened by the
- first one. The number of tacticals provided in the list must be
- equal to the number of sequents opened by the first tactical.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>do</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>
- <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>
- </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>repeat</strong></span>
- <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>
- </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>first [</strong></span>
- [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]
- [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]…
- <span class="bold"><strong>]</strong></span>
- </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>try</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span></td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style="">
- <span class="bold"><strong>solve [</strong></span>
- [<span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]
- [<span class="bold"><strong>|</strong></span> <span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span>]…
- <span class="bold"><strong>]</strong></span>
- </td><td style=""><span class="emphasis"><em>TODO</em></span></td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>(</strong></span><span class="emphasis"><em><a class="link" href="tacticals.html#grammar.LCFtactical">LCF-tactical</a></em></span><span class="bold"><strong>)</strong></span></td><td style="">Used for grouping during parsing.</td></tr></tbody></table></div></div><br class="table-break" /></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="proofstatus.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_tacticals.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_tactics.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">The proof status </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 7. Tactics</td></tr></table></div></body></html>
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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Tactic arguments</title><link rel="stylesheet" type="text/css" href="docbook.css" /><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot" /><link rel="home" href="index.html" title="Matita V0.99.5 User Manual (rev. 0.99.5 )" /><link rel="up" href="sec_terms.html" title="Chapter 4. Syntax" /><link rel="prev" href="proofs.html" title="Proofs" /><link rel="next" href="sec_usernotation.html" title="Chapter 5. Extending the syntax" /></head><body><a xmlns="" href="../../../"><div class="matita_logo"><img src="figures/matita.png" alt="Tiny Matita logo" /><span>Matita Home</span></div></a><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Tactic arguments</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="proofs.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Syntax</th><td width="20%" align="right"> <a accesskey="n" href="sec_usernotation.html">Next</a></td></tr></table><hr /></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="tacticargs"></a>Tactic arguments</h2></div></div></div><p>This section documents the syntax of some recurring arguments for
- tactics.</p><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="pattern"></a>pattern</h3></div></div></div><div class="table"><a id="idm1235"></a><p class="title"><strong>Table 4.13. pattern</strong></p><div class="table-contents"><table class="table" summary="pattern" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.pattern"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.pattern">pattern</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>in</strong></span>
- [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]…
- [<span class="bold"><strong>⊢</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]<span class="bold"><strong>;</strong></span></td><td style="">simple pattern</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>in</strong></span> <span class="bold"><strong>match</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
- [<span class="bold"><strong>in</strong></span>
- [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>[<span class="bold"><strong>:</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]…
- [<span class="bold"><strong>⊢</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>]]<span class="bold"><strong>;</strong></span></td><td style="">full pattern</td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1275"></a><p class="title"><strong>Table 4.14. path</strong></p><div class="table-contents"><table class="table" summary="path" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.path"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span></td><td style="">::=</td><td style=""><span class="emphasis"><em>〈〈any <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span> without occurrences of <span class="bold"><strong>Set</strong></span>, <span class="bold"><strong>Prop</strong></span>, <span class="bold"><strong>CProp</strong></span>, <span class="bold"><strong>Type</strong></span>, <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.id">id</a></em></span>, <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.uri">uri</a></em></span> and user provided notation; however, <span class="bold"><strong>%</strong></span> is now an additional production for <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>〉〉</em></span></td></tr></tbody></table></div></div><br class="table-break" /><p>A <span class="emphasis"><em>path</em></span> locates zero or more subterms of a given term by mimicking the term structure up to:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Occurrences of the subterms to locate that are
- represented by <span class="bold"><strong>%</strong></span>.</p></li><li class="listitem"><p>Subterms without any occurrence of subterms to locate
- that can be represented by <span class="bold"><strong>?</strong></span>.
- </p></li></ol></div><p>Warning: the format for a path for a <span class="bold"><strong>match</strong></span> … <span class="bold"><strong>with</strong></span>
- expression is restricted to: <span class="bold"><strong>match</strong></span> <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
- <span class="bold"><strong>with</strong></span>
- <span class="bold"><strong>[</strong></span>
- <span class="bold"><strong>_</strong></span>
- <span class="bold"><strong>⇒</strong></span>
- <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
- <span class="bold"><strong>|</strong></span> …
- <span class="bold"><strong>|</strong></span>
- <span class="bold"><strong>_</strong></span>
- <span class="bold"><strong>⇒</strong></span>
- <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>
- <span class="bold"><strong>]</strong></span>
- Its semantics is the following: the n-th
- "<span class="bold"><strong>_</strong></span>
- <span class="bold"><strong>⇒</strong></span>
- <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span>" branch is matched against the n-th constructor of the
- inductive data type. The head λ-abstractions of <span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.path">path</a></em></span> are matched
- against the corresponding constructor arguments.
- </p><p>For instance, the path
- <strong class="userinput"><code>∀_,_:?.(? ? % ?)→(? ? ? %)</code></strong>
- locates at once the subterms
- <strong class="userinput"><code>x+y</code></strong> and <strong class="userinput"><code>x*y</code></strong> in the
- term <strong class="userinput"><code>∀x,y:nat.x+y=1→0=x*y</code></strong>
- (where the notation <strong class="userinput"><code>A=B</code></strong> hides the term
- <strong class="userinput"><code>(eq T A B)</code></strong> for some type <strong class="userinput"><code>T</code></strong>).
- </p><p>A <span class="emphasis"><em>simple pattern</em></span> extends paths to locate
- subterms in a whole sequent. In particular, the pattern
- <strong class="userinput"><code>{ H: p K: q ⊢ r }</code></strong> locates at once all the subterms
- located by the pattern <strong class="userinput"><code>r</code></strong> in the conclusion of the
- sequent and by the patterns <strong class="userinput"><code>p</code></strong> and
- <strong class="userinput"><code>q</code></strong> in the hypotheses <strong class="userinput"><code>H</code></strong>
- and <strong class="userinput"><code>K</code></strong> of the sequent.
- </p><p>If no list of hypotheses is provided in a simple pattern, no subterm
- is selected in the hypothesis. If the <strong class="userinput"><code>⊢ p</code></strong>
- part of the pattern is not provided, no subterm will be matched in the
- conclusion if at least one hypothesis is provided; otherwise the whole
- conclusion is selected.
- </p><p>Finally, a <span class="emphasis"><em>full pattern</em></span> is interpreted in three
- steps. In the first step the <strong class="userinput"><code>match T in</code></strong>
- part is ignored and a set <span class="emphasis"><em>S</em></span> of subterms is
- located as for the case of
- simple patterns. In the second step the term <strong class="userinput"><code>T</code></strong>
- is parsed and interpreted in the context of each subterm
- <span class="emphasis"><em>s ∈ S</em></span>. In the last term for each
- <span class="emphasis"><em>s ∈ S</em></span> the interpreted term <strong class="userinput"><code>T</code></strong>
- computed in the previous step is looked for. The final set of subterms
- located by the full pattern is the set of occurrences of
- the interpreted <strong class="userinput"><code>T</code></strong> in the subterms <span class="emphasis"><em>s</em></span>.
- </p><p>A full pattern can always be replaced by a simple pattern,
- often at the cost of increased verbosity or decreased readability.</p><p>Example: the pattern
- <strong class="userinput"><code>{ match x+y in ⊢ ∀_,_:?.(? ? % ?) }</code></strong>
- locates only the first occurrence of <strong class="userinput"><code>x+y</code></strong>
- in the sequent <strong class="userinput"><code>x,y: nat ⊢ ∀z,w:nat. (x+y) * (z+w) =
- z * (x+y) + w * (x+y)</code></strong>. The corresponding simple pattern
- is <strong class="userinput"><code>{ ⊢ ∀_,_:?.(? ? (? % ?) ?) }</code></strong>.
- </p><p>Every tactic that acts on subterms of the selected sequents have
- a pattern argument for uniformity. To automatically generate a simple
- pattern:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Select in the current goal the subterms to pass to the
- tactic by using the mouse. In order to perform a multiple selection of
- subterms, hold the Ctrl key while selecting every subterm after the
- first one.</p></li><li class="listitem"><p>From the contextual menu select "Copy".</p></li><li class="listitem"><p>From the "Edit" or the contextual menu select
- "Paste as pattern"</p></li></ol></div></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="reduction-kind"></a>reduction-kind</h3></div></div></div><p>Reduction kinds are normalization functions that transform a term
- to a convertible but simpler one. Each reduction kind can be used both
- as a tactic argument and as a stand-alone tactic.</p><div class="table"><a id="idm1378"></a><p class="title"><strong>Table 4.15. reduction-kind</strong></p><div class="table-contents"><table class="table" summary="reduction-kind" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.reduction-kind"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.reduction-kind">reduction-kind</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>normalize</strong></span> [<span class="bold"><strong>nodelta</strong></span>]</td><td style="">Computes the βδιζ-normal form. If <strong class="userinput"><code>nodelta</code></strong>
- is specified, δ-expansions are not performed.</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>whd</strong></span> [<span class="bold"><strong>nodelta</strong></span>]</td><td style="">Computes the βδιζ-weak-head normal form. If <strong class="userinput"><code>nodelta</code></strong>
- is specified, δ-expansions are not performed.</td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="auto-params"></a>auto-params</h3></div></div></div><div class="table"><a id="idm1402"></a><p class="title"><strong>Table 4.16. auto-params</strong></p><div class="table-contents"><table class="table" summary="auto-params" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.autoparams"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></td><td style="">::=</td><td style="">[<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span>] [<span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.simpleautoparam">simple_auto_param</a></em></span>]…
- [<span class="bold"><strong>by</strong></span>
- [<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.sterm">sterm</a></em></span>… | <span class="bold"><strong>_</strong></span>]]
- </td><td style="">The natural number, which defaults to 1, gives a bound to
- the depth of the search tree. The terms listed is the only
- knowledge base used by automation together with all indexed factual
- and equational theorems in the included library. If the list of terms
- is empty, only equational theorems and facts in the library are
- used. If the list is omitted, it defaults to all indexed theorems
- in the library. Finally, if the list is <span class="command"><strong>_</strong></span>,
- the automation command becomes a macro that is expanded in a new
- automation command where <span class="command"><strong>_</strong></span> is replaced with the
- list of theorems required to prove the sequent.
- </td></tr></tbody></table></div></div><br class="table-break" /><div class="table"><a id="idm1423"></a><p class="title"><strong>Table 4.17. simple-auto-param</strong></p><div class="table-contents"><table class="table" summary="simple-auto-param" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.simpleautoparam"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.simpleautoparam">simple_auto_param</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>width=<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></strong></span></td><td style="">The maximal width of the search tree</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>size=<span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.nat">nat</a></em></span></strong></span></td><td style="">The maximal number of nodes in the proof</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>demod</strong></span></td><td style="">Simplifies the current sequent using the current set of
- equations known to automation
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>paramod</strong></span></td><td style="">Try to close the goal performing unit-equality paramodulation
- </td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="bold"><strong>fast_paramod</strong></span></td><td style="">A bounded version of <span class="command"><strong>paramod</strong></span> that is granted to terminate quickly
- </td></tr></tbody></table></div></div><br class="table-break" /></div><div class="sect2"><div class="titlepage"><div><div><h3 class="title"><a id="justification"></a>justification</h3></div></div></div><div class="table"><a id="idm1466"></a><p class="title"><strong>Table 4.18. justification</strong></p><div class="table-contents"><table class="table" summary="justification" style="border-collapse: collapse;border-top: 1px solid ; border-bottom: 1px solid ; "><colgroup><col /><col /><col /><col /></colgroup><tbody><tr><td style=""><a id="grammar.justification"></a><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.justification">justification</a></em></span></td><td style="">::=</td><td style=""><span class="bold"><strong>using</strong></span> <span class="emphasis"><em><a class="link" href="sec_terms.html#grammar.term">term</a></em></span></td><td style="">Proof term manually provided</td></tr><tr><td style=""> </td><td style="">|</td><td style=""><span class="emphasis"><em><a class="link" href="tacticargs.html#grammar.autoparams">auto_params</a></em></span></td><td style="">Call automation</td></tr></tbody></table></div></div><br class="table-break" /></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="proofs.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="sec_terms.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="sec_usernotation.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Proofs </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 5. Extending the syntax</td></tr></table></div></body></html>
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