</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>
<sect1 id="tac_clear">
<title>clear</title>
<titleabbrev>clear</titleabbrev>
- <para><userinput>clear H</userinput></para>
+ <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;</para>
+ <para>
+ <emphasis role="bold">clear</emphasis>
+ &id; [&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>
+ <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 hypothesis <command>H</command> from the
- current sequent.</para>
+ <para>
+ It hides the hypotheses
+ <command>
+ H<subscript>1</subscript> ... H<subscript>m</subscript>
+ </command> from the current sequent.
+ </para>
</listitem>
</varlistentry>
<varlistentry>
<title>decompose</title>
<titleabbrev>decompose</titleabbrev>
<para><userinput>
- decompose (T<subscript>1</subscript> ... T<subscript>n</subscript>) H hips
+ decompose (T<subscript>1</subscript> ... T<subscript>n</subscript>)
+ H 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; &intros-spec;
+ [<emphasis role="bold">(</emphasis>
+ &id;…
+ <emphasis role="bold">)</emphasis>]
+ [&id;]
+ [<emphasis role="bold">as</emphasis> &id;…]
</para>
</listitem>
</varlistentry>
<term>Action:</term>
<listitem>
<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.
+ 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
+ <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>
</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>
<varlistentry role="tactic.synopsis">
<term>Synopsis:</term>
<listitem>
- <para><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;]</para>
+ <para>
+ <emphasis role="bold">lapply</emphasis>
+ [<emphasis role="bold">linear</emphasis>]
+ [<emphasis role="bold">depth=</emphasis>&nat;]
+ &sterm;
+ [<emphasis role="bold">to</emphasis>
+ &sterm;
+ [<emphasis role="bold">,</emphasis>&sterm;…]
+ ]
+ [<emphasis role="bold">as</emphasis> &id;]
+ </para>
</listitem>
</varlistentry>
<varlistentry>
<term>Action:</term>
<listitem>
<para>
- It invokes <command>letin H ≝ (t ? ... ?)</command>
+ Invokes <command>letin H ≝ (t ? ... ?)</command>
with enough <command>?</command>'s to reach the
<command>d</command>-th independent premise of
<command>t</command>
(<command>d</command> is maximum if unspecified).
- Then it istantiates (by <command>apply</command>) with
+ Then istantiates (by <command>apply</command>) with
t<subscript>1</subscript>, ..., t<subscript>n</subscript>
the <command>?</command>'s corresponding to the first
<command>n</command> independent premises of
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>