</para>
</sect1>
<sect1 id="tac_change">
- <title><emphasis role="bold">change</emphasis> <pattern> <emphasis role="bold">with</emphasis> &sterm;</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_decompose">
- <title><emphasis role="bold">decompose</emphasis> &id; [&id;]… [<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_elim">
- <title><emphasis role="bold">elim</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] [<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><emphasis role="bold">elimType</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] [<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_fold">
- <title><emphasis role="bold">fold</emphasis> <reduction_kind> &sterm; <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_fwd">
- <title><emphasis role="bold">fwd</emphasis> &id; [<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><emphasis role="bold">generalize</emphasis> <pattern> [<emphasis role="bold">as</emphasis> &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_intros">
- <title><emphasis role="bold">intros</emphasis> <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_lapply">
- <title><emphasis role="bold">lapply</emphasis> [<emphasis role="bold">depth=</emphasis>&nat;] &sterm; [<emphasis role="bold">to</emphasis> <term list>] [<emphasis role="bold">using</emphasis> &id;]</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_normalize">
- <title><emphasis role="bold">normalize</emphasis> <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><emphasis role="bold">paramodulation</emphasis> <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><emphasis role="bold">reduce</emphasis> <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_replace">
- <title><emphasis role="bold">replace</emphasis> <pattern> <emphasis role="bold">with</emphasis> &sterm;</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><emphasis role="bold">rewrite</emphasis> [<emphasis role="bold"><</emphasis>|<emphasis role="bold">></emphasis>] &sterm; <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_simplify">
- <title><emphasis role="bold">simplify</emphasis> <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_unfold">
- <title><emphasis role="bold">unfold</emphasis> [&sterm;] <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><emphasis role="bold">whd</emphasis> <pattern></title>
+ <title><emphasis role="bold">whd</emphasis> &pattern;</title>
<titleabbrev>whd</titleabbrev>
<para><userinput>whd patt</userinput></para>
<para>