<title>Tactics</title>
<sect1 id="tac_absurd">
- <title>absurd <term></title>
+ <title><emphasis role="bold">absurd</emphasis> &sterm;</title>
<titleabbrev>absurd</titleabbrev>
<para><userinput>absurd P</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_apply">
- <title>apply <term></title>
+ <title><emphasis role="bold">apply</emphasis> &sterm;</title>
<titleabbrev>apply</titleabbrev>
<para><userinput>apply t</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_assumption">
- <title>assumption</title>
+ <title><emphasis role="bold">assumption</emphasis></title>
<titleabbrev>assumption</titleabbrev>
<para><userinput>assumption </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_auto">
- <title>auto [depth=<int>] [width=<int>] [paramodulation] [full]</title>
+ <title><emphasis role="bold">auto</emphasis> [<emphasis role="bold">depth=</emphasis>&nat;] [<emphasis role="bold">width=</emphasis>&nat;] [<emphasis role="bold">paramodulation</emphasis>] [<emphasis role="bold">full</emphasis>]</title>
<titleabbrev>auto</titleabbrev>
<para><userinput>auto depth=d width=w paramodulation full</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_clear">
- <title>clear <id></title>
+ <title><emphasis role="bold">clear</emphasis> &id;</title>
<titleabbrev>clear</titleabbrev>
<para><userinput>clear H</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_clearbody">
- <title>clearbody <id></title>
+ <title><emphasis role="bold">clearbody</emphasis> &id;</title>
<titleabbrev>clearbody</titleabbrev>
<para><userinput>clearbody H</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_change">
- <title>change <pattern> with <term></title>
+ <title><emphasis role="bold">change</emphasis> &pattern; <emphasis role="bold">with</emphasis> &sterm;</title>
<titleabbrev>change</titleabbrev>
<para><userinput>change patt with t</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_constructor">
- <title>constructor <int></title>
+ <title><emphasis role="bold">constructor</emphasis> &nat;</title>
<titleabbrev>constructor</titleabbrev>
<para><userinput>constructor n</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_contradiction">
- <title>contradiction</title>
+ <title><emphasis role="bold">contradiction</emphasis></title>
<titleabbrev>contradiction</titleabbrev>
<para><userinput>contradiction </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_cut">
- <title>cut <term> [as <id>]</title>
+ <title><emphasis role="bold">cut</emphasis> &sterm; [<emphasis role="bold">as</emphasis> &id;]</title>
<titleabbrev>cut</titleabbrev>
<para><userinput>cut P as H</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_decompose">
- <title>decompose [<ident list>] <ident> [<intros_spec>]</title>
+ <title><emphasis role="bold">decompose</emphasis> &id; [&id;]… &intros-spec;</title>
<titleabbrev>decompose</titleabbrev>
- <para><userinput>decompose ???</userinput></para>
+ <para><userinput>
+ decompose (T<subscript>1</subscript> ... T<subscript>n</subscript>) H hips
+ </userinput></para>
<para>
<variablelist>
<varlistentry>
<term>Pre-conditions:</term>
<listitem>
- <para>TODO.</para>
+ <para>
+ <command>H</command> must inhabit one inductive type among
+ <command>
+ T<subscript>1</subscript> ... T<subscript>n</subscript>
+ </command>
+ and the types of a predefined list.
+ </para>
</listitem>
</varlistentry>
<varlistentry>
<term>Action:</term>
<listitem>
- <para>TODO.</para>
+ <para>
+ Runs <command>elim H hyps</command>, clears H and tries to run
+ itself recursively on each new identifier introduced by
+ <command>elim</command> in the opened sequents.
+ </para>
</listitem>
</varlistentry>
<varlistentry>
<term>New sequents to prove:</term>
<listitem>
- <para>TODO.</para>
+ <para>
+ The ones generated by all the <command>elim</command> tactics run.
+ </para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_demodulation">
+ <title><emphasis role="bold">demodulation</emphasis> &pattern;</title>
+ <titleabbrev>demodulation</titleabbrev>
+ <para><userinput>demodulation patt</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>None.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>&TODO;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>None.</para>
</listitem>
</varlistentry>
</variablelist>
</para>
</sect1>
<sect1 id="tac_discriminate">
- <title>discriminate <term></title>
+ <title><emphasis role="bold">discriminate</emphasis> &sterm;</title>
<titleabbrev>discriminate</titleabbrev>
<para><userinput>discriminate p</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_elim">
- <title>elim <term> [using <term>] [<intros_spec>]</title>
+ <title><emphasis role="bold">elim</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] &intros-spec;</title>
<titleabbrev>elim</titleabbrev>
<para><userinput>elim t using th hyps</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_elimType">
- <title>elimType <term> [using <term>] [<intros_spec>]</title>
+ <title><emphasis role="bold">elimType</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] &intros-spec;</title>
<titleabbrev>elimType</titleabbrev>
<para><userinput>elimType T using th hyps</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_exact">
- <title>exact <term></title>
+ <title><emphasis role="bold">exact</emphasis> &sterm;</title>
<titleabbrev>exact</titleabbrev>
<para><userinput>exact p</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_exists">
- <title>exists</title>
+ <title><emphasis role="bold">exists</emphasis></title>
<titleabbrev>exists</titleabbrev>
<para><userinput>exists </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_fail">
- <title>fail </title>
- <titleabbrev>failt</titleabbrev>
+ <title><emphasis role="bold">fail</emphasis></title>
+ <titleabbrev>fail</titleabbrev>
<para><userinput>fail</userinput></para>
<para>
<variablelist>
</para>
</sect1>
<sect1 id="tac_fold">
- <title>fold <reduction_kind> <term> <pattern></title>
+ <title><emphasis role="bold">fold</emphasis> &reduction-kind; &sterm; &pattern;</title>
<titleabbrev>fold</titleabbrev>
<para><userinput>fold red t patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_fourier">
- <title>fourier</title>
+ <title><emphasis role="bold">fourier</emphasis></title>
<titleabbrev>fourier</titleabbrev>
<para><userinput>fourier </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_fwd">
- <title>fwd <ident> [<ident list>]</title>
+ <title><emphasis role="bold">fwd</emphasis> &id; [<emphasis role="bold">(</emphasis>[&id;]…<emphasis role="bold">)</emphasis>]</title>
<titleabbrev>fwd</titleabbrev>
<para><userinput>fwd ...TODO</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_generalize">
- <title>generalize <pattern> [as <id>]</title>
+ <title><emphasis role="bold">generalize</emphasis> &pattern; [<emphasis role="bold">as</emphasis> &id;]</title>
<titleabbrev>generalize</titleabbrev>
<para><userinput>generalize patt as H</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_id">
- <title>id</title>
+ <title><emphasis role="bold">id</emphasis></title>
<titleabbrev>id</titleabbrev>
<para><userinput>id </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_injection">
- <title>injection <term></title>
- <titleabbrev>injection</titleabbrev>
+ <title><emphasis role="bold">injection</emphasis> &sterm;</title>
+ <titleabbrev><emphasis role="bold">injection</emphasis></titleabbrev>
<para><userinput>injection p</userinput></para>
<para>
<variablelist>
</para>
</sect1>
<sect1 id="tac_intro">
- <title>intro [<ident>]</title>
+ <title><emphasis role="bold">intro</emphasis> [&id;]</title>
<titleabbrev>intro</titleabbrev>
<para><userinput>intro H</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_intros">
- <title>intros <intros_spec></title>
+ <title><emphasis role="bold">intros</emphasis> &intros-spec;</title>
<titleabbrev>intros</titleabbrev>
<para><userinput>intros hyps</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_inversion">
- <title>inversion <term></title>
+ <title><emphasis role="bold">inversion</emphasis> &sterm;</title>
<titleabbrev>inversion</titleabbrev>
<para><userinput>inversion t</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_lapply">
- <title>lapply [depth=<int>] <term> [to <term list] [using <ident>]</title>
+ <title><emphasis role="bold">lapply</emphasis> [<emphasis role="bold">depth=</emphasis>&nat;] &sterm; [<emphasis role="bold">to</emphasis> &sterm; [&sterm;]…] [<emphasis role="bold">as</emphasis> &id;]</title>
<titleabbrev>lapply</titleabbrev>
- <para><userinput>lapply ???</userinput></para>
+ <para><userinput>
+ lapply depth=d t
+ to t<subscript>1</subscript>, ..., t<subscript>n</subscript> as H
+ </userinput></para>
<para>
<variablelist>
<varlistentry>
</para>
</sect1>
<sect1 id="tac_left">
- <title>left</title>
+ <title><emphasis role="bold">left</emphasis></title>
<titleabbrev>left</titleabbrev>
<para><userinput>left </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_letin">
- <title>letin <ident> ≝ <term></title>
+ <title><emphasis role="bold">letin</emphasis> &id; <emphasis role="bold">≝</emphasis> &sterm;</title>
<titleabbrev>letin</titleabbrev>
<para><userinput>letin x ≝ t</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_normalize">
- <title>normalize <pattern></title>
+ <title><emphasis role="bold">normalize</emphasis> &pattern;</title>
<titleabbrev>normalize</titleabbrev>
<para><userinput>normalize patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_paramodulation">
- <title>paramodulation <pattern></title>
+ <title><emphasis role="bold">paramodulation</emphasis> &pattern;</title>
<titleabbrev>paramodulation</titleabbrev>
<para><userinput>paramodulation patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_reduce">
- <title>reduce <pattern></title>
+ <title><emphasis role="bold">reduce</emphasis> &pattern;</title>
<titleabbrev>reduce</titleabbrev>
<para><userinput>reduce patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_reflexivity">
- <title>reflexivity</title>
+ <title><emphasis role="bold">reflexivity</emphasis></title>
<titleabbrev>reflexivity</titleabbrev>
<para><userinput>reflexivity </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_replace">
- <title>replace <pattern> with <term></title>
+ <title><emphasis role="bold">replace</emphasis> &pattern; <emphasis role="bold">with</emphasis> &sterm;</title>
<titleabbrev>change</titleabbrev>
<para><userinput>change patt with t</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_rewrite">
- <title>rewrite {<|>} <term> <pattern></title>
+ <title><emphasis role="bold">rewrite</emphasis> [<emphasis role="bold"><</emphasis>|<emphasis role="bold">></emphasis>] &sterm; &pattern;</title>
<titleabbrev>rewrite</titleabbrev>
<para><userinput>rewrite dir p patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_right">
- <title>right</title>
+ <title><emphasis role="bold">right</emphasis></title>
<titleabbrev>right</titleabbrev>
<para><userinput>right </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_ring">
- <title>ring</title>
+ <title><emphasis role="bold">ring</emphasis></title>
<titleabbrev>ring</titleabbrev>
<para><userinput>ring </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_simplify">
- <title>simplify <pattern></title>
+ <title><emphasis role="bold">simplify</emphasis> &pattern;</title>
<titleabbrev>simplify</titleabbrev>
<para><userinput>simplify patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_split">
- <title>split</title>
+ <title><emphasis role="bold">split</emphasis></title>
<titleabbrev>split</titleabbrev>
<para><userinput>split </userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_symmetry">
- <title>symmetry</title>
+ <title><emphasis role="bold">symmetry</emphasis></title>
<titleabbrev>symmetry</titleabbrev>
<para>The tactic <command>symmetry</command> </para>
<para><userinput>symmetry </userinput></para>
</para>
</sect1>
<sect1 id="tac_transitivity">
- <title>transitivity <term></title>
+ <title><emphasis role="bold">transitivity</emphasis> &sterm;</title>
<titleabbrev>transitivity</titleabbrev>
<para><userinput>transitivity t</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_unfold">
- <title>unfold [<term>] <pattern></title>
+ <title><emphasis role="bold">unfold</emphasis> [&sterm;] &pattern;</title>
<titleabbrev>unfold</titleabbrev>
<para><userinput>unfold t patt</userinput></para>
<para>
</para>
</sect1>
<sect1 id="tac_whd">
- <title>whd <pattern></title>
+ <title><emphasis role="bold">whd</emphasis> &pattern;</title>
<titleabbrev>whd</titleabbrev>
<para><userinput>whd patt</userinput></para>
<para>