+ <titleabbrev>assumption</titleabbrev>
+ <para><userinput>assumption </userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">assumption</emphasis></para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>There must exist an hypothesis whose type can be unified with
+ the conclusion of the current sequent.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>It closes the current sequent exploiting an hypothesis.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>None</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_auto">
+ <title>auto</title>
+ <titleabbrev>auto</titleabbrev>
+ <para><userinput>auto params</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">auto</emphasis> &autoparams;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>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 <command>params</command>.
+ Moreover, only lemmas whose type signature is a subset of the
+ signature of the current sequent are considered. The signature of
+ a sequent is ...&TODO;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>It closes the current sequent by repeated application of
+ rewriting steps (unless <command>paramodulation</command> is
+ omitted), hypothesis and lemmas in the library.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>None</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_cases">
+ <title>cases</title>
+ <titleabbrev>cases</titleabbrev>
+ <para><userinput>
+ cases t hyps
+ </userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para>
+ <emphasis role="bold">cases</emphasis>
+ &term; [<emphasis role="bold">(</emphasis>[&id;]…<emphasis role="bold">)</emphasis>]
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>
+ <command>t</command> must inhabit an inductive type
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>
+ It proceed by cases on <command>t</command>. The new generated
+ hypothesis in each branch are named according to
+ <command>hyps</command>.
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>One new sequent for each constructor of the type of
+ <command>t</command>. Each sequent has a new hypothesis for
+ each argument of the constructor.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_clear">
+ <title>clear</title>
+ <titleabbrev>clear</titleabbrev>
+ <para><userinput>
+ clear H<subscript>1</subscript> ... H<subscript>m</subscript>
+ </userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para>
+ <emphasis role="bold">clear</emphasis>
+ &id; [&id;…]
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>
+ <command>
+ H<subscript>1</subscript> ... H<subscript>m</subscript>
+ </command> must be hypotheses of the
+ current sequent to prove.
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>
+ It hides the hypotheses
+ <command>
+ H<subscript>1</subscript> ... H<subscript>m</subscript>
+ </command> from the current sequent.
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>None</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_clearbody">
+ <title>clearbody</title>
+ <titleabbrev>clearbody</titleabbrev>
+ <para><userinput>clearbody H</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">clearbody</emphasis> &id;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para><command>H</command> must be an hypothesis of the
+ current sequent to prove.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>It hides the definiens of a definition in the current
+ sequent context. Thus the definition becomes an hypothesis.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>None.</para>
+ </listitem>
+ </varlistentry>
+ </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>
+ <para><userinput>change patt with t</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">change</emphasis> &pattern; <emphasis role="bold">with</emphasis> &sterm;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>Each subterm matched by the pattern must be convertible
+ with the term <command>t</command> disambiguated in the context
+ of the matched subterm.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>It replaces the subterms of the current sequent matched by
+ <command>patt</command> with the new term <command>t</command>.
+ For each subterm matched by the pattern, <command>t</command> is
+ disambiguated in the context of the subterm.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>None.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_constructor">
+ <title>constructor</title>
+ <titleabbrev>constructor</titleabbrev>
+ <para><userinput>constructor n</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">constructor</emphasis> &nat;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para>The conclusion of the current sequent must be
+ an inductive type or the application of an inductive type with
+ at least <command>n</command> constructors.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para>It applies the <command>n</command>-th constructor of the
+ inductive type of the conclusion of the current sequent.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>It opens a new sequent for each premise of the constructor
+ that can not be inferred by unification. For more details,
+ see the <command>apply</command> tactic.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
+ <sect1 id="tac_contradiction">