</variablelist>
</para>
</sect1>
+ <sect1 id="tac_compose">
+ <title>compose</title>
+ <titleabbrev>compose</titleabbrev>
+ <para><userinput>compose n t1 with t2 hyps</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">compose</emphasis> [&nat;] &sterm; [<emphasis role="bold">with</emphasis> &sterm;] [&intros-spec;]</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para></para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>Composes t1 with t2 in every possible way
+ <command>n</command> times introducing generated terms
+ as if <command>intros hyps</command> was issued.</para>
+ <para>If <command>t1:∀x:A.B[x]</command> and
+ <command>t2:∀x,y:A.B[x]→B[y]→C[x,y]</command> it generates:
+ <itemizedlist>
+ <listitem>
+ <para><command>λx,y:A.t2 x y (t1 x) : ∀x,y:A.B[y]→C[x,y]</command></para>
+ </listitem>
+ <listitem>
+ <para><command>λx,y:A.λH:B[x].t2 x y H (t1 y) : ∀x,y:A.B[x]→C[x,y]
+ </command></para>
+ </listitem>
+ </itemizedlist>
+ </para>
+ <para>If <command>t2</command> is omitted it composes
+ <command>t1</command>
+ with every hypothesis that can be introduced.
+ <command>n</command> iterates the process.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>The same, but with more hypothesis eventually introduced
+ by the &intros-spec;.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
<sect1 id="tac_change">
<title>change</title>
<titleabbrev>change</titleabbrev>
<title>decompose</title>
<titleabbrev>decompose</titleabbrev>
<para><userinput>
- decompose (T<subscript>1</subscript> ... T<subscript>n</subscript>)
- H as H<subscript>1</subscript> ... H<subscript>m</subscript>
+ decompose as H<subscript>1</subscript> ... H<subscript>m</subscript>
</userinput></para>
<para>
<variablelist>
<listitem>
<para>
<emphasis role="bold">decompose</emphasis>
- [<emphasis role="bold">(</emphasis>
- &id;…
- <emphasis role="bold">)</emphasis>]
- [&id;]
[<emphasis role="bold">as</emphasis> &id;…]
</para>
</listitem>
<varlistentry>
<term>Pre-conditions:</term>
<listitem>
- <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>
+ <para>None.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Action:</term>
<listitem>
<para>
- Runs <command>
- elim H H<subscript>1</subscript> ... H<subscript>m</subscript>
- </command>, clears <command>H</command> and tries to run itself
- recursively on each new identifier introduced by
+ For each each premise <command>H</command> of type
+ <command>T</command> in the current context where
+ <command>T</command> is a non-recursive inductive type without
+ right parameters and of sort Prop or CProp, the tactic runs
+ <command>
+ elim H as H<subscript>1</subscript> ... H<subscript>m</subscript>
+ </command>, clears <command>H</command> and runs itself
+ recursively on each new premise introduced by
<command>elim</command> in the opened sequents.
- If <command>H</command> is not provided tries this operation on
- each premise in the current context.
</para>
</listitem>
</varlistentry>