</variablelist>
</para>
</sect1>
+ <sect1 id="tac_applyS">
+ <title>applyS</title>
+ <titleabbrev>applyS</titleabbrev>
+ <para><userinput>applyS t</userinput></para>
+ <para>
+ <variablelist>
+ <varlistentry role="tactic.synopsis">
+ <term>Synopsis:</term>
+ <listitem>
+ <para><emphasis role="bold">applyS</emphasis> &sterm;</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Pre-conditions:</term>
+ <listitem>
+ <para><command>t</command> must have type
+ <command>T<subscript>1</subscript> → ... →
+ T<subscript>n</subscript> → G</command>.</para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>Action:</term>
+ <listitem>
+ <para><command>applyS</command> is useful when
+ <command>apply</command> 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 <command>P(n*O+m)</command> and
+ the theorem to be applied proves <command>∀m.P(m+O)</command>.
+ </para>
+ <para>
+ It tries to automatically rewrite the current goal using
+ <link linkend="tac_auto">auto paramodulation</link>
+ to make it unifiable with <command>G</command>.
+ Then it closes the current sequent by applying
+ <command>t</command> to <command>n</command>
+ implicit arguments (that become new sequents).
+ </para>
+ </listitem>
+ </varlistentry>
+ <varlistentry>
+ <term>New sequents to prove:</term>
+ <listitem>
+ <para>It opens a new sequent for each premise
+ <command>T<subscript>i</subscript></command> that is not
+ instantiated by unification. <command>T<subscript>i</subscript></command> is
+ the conclusion of the <command>i</command>-th new sequent to
+ prove.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </para>
+ </sect1>
<sect1 id="tac_assumption">
<title>assumption</title>
<titleabbrev>assumption</titleabbrev>
</variablelist>
</para>
</sect1>
- <sect1 id="tac_demodulation">
- <title>demodulation</title>
- <titleabbrev>demodulation</titleabbrev>
- <para><userinput>demodulation patt</userinput></para>
+ <sect1 id="tac_demodulate">
+ <title>demodulate</title>
+ <titleabbrev>demodulate</titleabbrev>
+ <para><userinput>demodulate</userinput></para>
<para>
<variablelist>
<varlistentry role="tactic.synopsis">
<term>Synopsis:</term>
<listitem>
- <para><emphasis role="bold">demodulation</emphasis> &pattern;</para>
+ <para><emphasis role="bold">demodulate</emphasis></para>
</listitem>
</varlistentry>
<varlistentry>
<title>lapply</title>
<titleabbrev>lapply</titleabbrev>
<para><userinput>
- lapply depth=d t
+ lapply linear depth=d t
to t<subscript>1</subscript>, ..., t<subscript>n</subscript> as H
</userinput></para>
<para>
<listitem>
<para>
<emphasis role="bold">lapply</emphasis>
+ [<emphasis role="bold">linear</emphasis>]
[<emphasis role="bold">depth=</emphasis>&nat;]
&sterm;
[<emphasis role="bold">to</emphasis>
Usually the other <command>?</command>'s preceding the
<command>n</command>-th independent premise of
<command>t</command> are istantiated as a consequence.
+ If the <command>linear</command> flag is specified and if
+ <command>t, t<subscript>1</subscript>, ..., t<subscript>n</subscript></command>
+ are (applications of) premises in the current context, they are
+ <command>clear</command>ed.
</para>
</listitem>
</varlistentry>
</variablelist>
</para>
</sect1>
- <sect1 id="tac_paramodulation">
- <title>paramodulation</title>
- <titleabbrev>paramodulation</titleabbrev>
- <para><userinput>paramodulation patt</userinput></para>
- <para>
- <variablelist>
- <varlistentry role="tactic.synopsis">
- <term>Synopsis:</term>
- <listitem>
- <para><emphasis role="bold">paramodulation</emphasis> &pattern;</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>Pre-conditions:</term>
- <listitem>
- <para>TODO.</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>Action:</term>
- <listitem>
- <para>TODO.</para>
- </listitem>
- </varlistentry>
- <varlistentry>
- <term>New sequents to prove:</term>
- <listitem>
- <para>TODO.</para>
- </listitem>
- </varlistentry>
- </variablelist>
- </para>
- </sect1>
<sect1 id="tac_reduce">
<title>reduce</title>
<titleabbrev>reduce</titleabbrev>