- "linear" flag added to lapply (automatic clearing)

[helm.git] / matita / help / C / sec_tactics.xml

diff --git a/matita/help/C/sec_tactics.xml b/matita/help/C/sec_tactics.xml
index fc3681074429c8f29b7d90b975937df1628332ec..130c08e56749cf2f08e9eb607fc3999e19781f83 100644 (file)
--- a/matita/help/C/sec_tactics.xml
+++ b/matita/help/C/sec_tactics.xml
@@ -1,14 +1,27 @@
 
 <!-- ============ Tactics ====================== -->
 <chapter id="sec_tactics">
- <title>Tactics</title>
+  <title>Tactics</title>
+
+  <sect1 id="tactics_quickref">
+    <title>Quick reference card</title>
+    <para>
+      &tacticref;
+    </para>
+  </sect1>
 
   <sect1 id="tac_absurd">
-    <title><emphasis role="bold">absurd</emphasis> &sterm;</title>
+    <title>absurd</title>
     <titleabbrev>absurd</titleabbrev>
     <para><userinput>absurd P</userinput></para>
      <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">absurd</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -33,11 +46,17 @@
      </para>
   </sect1>
   <sect1 id="tac_apply">
-    <title><emphasis role="bold">apply</emphasis> &sterm;</title>
+    <title>apply</title>
     <titleabbrev>apply</titleabbrev>
     <para><userinput>apply t</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">apply</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -68,11 +87,17 @@
     </para>
   </sect1>
   <sect1 id="tac_assumption">
-    <title><emphasis role="bold">assumption</emphasis></title>
+    <title>assumption</title>
     <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>
@@ -96,11 +121,17 @@
     </para>
   </sect1>
   <sect1 id="tac_auto">
-    <title><emphasis role="bold">auto</emphasis> [<emphasis role="bold">depth=</emphasis>&nat;] [<emphasis role="bold">width=</emphasis>&nat;] [<emphasis role="bold">paramodulation</emphasis>] [<emphasis role="bold">full</emphasis>]</title>
+    <title>auto</title>
     <titleabbrev>auto</titleabbrev>
     <para><userinput>auto depth=d width=w paramodulation full</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">auto</emphasis> [<emphasis role="bold">depth=</emphasis>&nat;] [<emphasis role="bold">width=</emphasis>&nat;] [<emphasis role="bold">paramodulation</emphasis>] [<emphasis role="bold">full</emphasis>]</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -130,23 +161,42 @@
     </para>
   </sect1>
   <sect1 id="tac_clear">
-    <title><emphasis role="bold">clear</emphasis> &id;</title>
+    <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; [&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>
@@ -159,11 +209,17 @@
     </para>
   </sect1>
   <sect1 id="tac_clearbody">
-    <title><emphasis role="bold">clearbody</emphasis> &id;</title>
+    <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>
@@ -188,11 +244,17 @@
     </para>
   </sect1>
   <sect1 id="tac_change">
-    <title><emphasis role="bold">change</emphasis> &pattern; <emphasis role="bold">with</emphasis> &sterm;</title>
+    <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>
@@ -220,11 +282,17 @@
     </para>
   </sect1>
   <sect1 id="tac_constructor">
-    <title><emphasis role="bold">constructor</emphasis> &nat;</title>
+    <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>
@@ -252,11 +320,17 @@
     </para>
   </sect1>
   <sect1 id="tac_contradiction">
-    <title><emphasis role="bold">contradiction</emphasis></title>
+    <title>contradiction</title>
     <titleabbrev>contradiction</titleabbrev>
     <para><userinput>contradiction </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">contradiction</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -281,11 +355,17 @@
     </para>
   </sect1>
   <sect1 id="tac_cut">
-    <title><emphasis role="bold">cut</emphasis> &sterm; [<emphasis role="bold">as</emphasis> &id;]</title>
+    <title>cut</title>
     <titleabbrev>cut</titleabbrev>
     <para><userinput>cut P as H</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">cut</emphasis> &sterm; [<emphasis role="bold">as</emphasis> &id;]</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -312,13 +392,27 @@
     </para>
   </sect1>
   <sect1 id="tac_decompose">
-    <title><emphasis role="bold">decompose</emphasis> &id; [&id;]… &intros-spec;</title>
+    <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>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <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>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -335,9 +429,13 @@
           <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>
@@ -353,11 +451,17 @@
     </para>
   </sect1>
   <sect1 id="tac_demodulation">
-    <title><emphasis role="bold">demodulation</emphasis> &pattern;</title>
+    <title>demodulation</title>
     <titleabbrev>demodulation</titleabbrev>
     <para><userinput>demodulation patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">demodulation</emphasis> &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -380,11 +484,17 @@
     </para>
   </sect1>
   <sect1 id="tac_discriminate">
-    <title><emphasis role="bold">discriminate</emphasis> &sterm;</title>
+    <title>discriminate</title>
     <titleabbrev>discriminate</titleabbrev>
     <para><userinput>discriminate p</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">discriminate</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -409,11 +519,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_elim">
-    <title><emphasis role="bold">elim</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] &intros-spec;</title>
+    <title>elim</title>
     <titleabbrev>elim</titleabbrev>
     <para><userinput>elim t using th hyps</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">elim</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] &intros-spec;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -446,11 +562,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_elimType">
-    <title><emphasis role="bold">elimType</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] &intros-spec;</title>
+    <title>elimType</title>
     <titleabbrev>elimType</titleabbrev>
     <para><userinput>elimType T using th hyps</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">elimType</emphasis> &sterm; [<emphasis role="bold">using</emphasis> &sterm;] &intros-spec;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -473,11 +595,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_exact">
-    <title><emphasis role="bold">exact</emphasis> &sterm;</title>
+    <title>exact</title>
     <titleabbrev>exact</titleabbrev>
     <para><userinput>exact p</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">exact</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -501,11 +629,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_exists">
-    <title><emphasis role="bold">exists</emphasis></title>
+    <title>exists</title>
     <titleabbrev>exists</titleabbrev>
     <para><userinput>exists </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">exists</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -532,11 +666,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_fail">
-    <title><emphasis role="bold">fail</emphasis></title>
+    <title>fail</title>
     <titleabbrev>fail</titleabbrev>
     <para><userinput>fail</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">fail</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -559,11 +699,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_fold">
-    <title><emphasis role="bold">fold</emphasis> &reduction-kind; &sterm; &pattern;</title>
+    <title>fold</title>
     <titleabbrev>fold</titleabbrev>
     <para><userinput>fold red t patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">fold</emphasis> &reduction-kind; &sterm; &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -591,11 +737,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_fourier">
-    <title><emphasis role="bold">fourier</emphasis></title>
+    <title>fourier</title>
     <titleabbrev>fourier</titleabbrev>
     <para><userinput>fourier </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">fourier</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -621,38 +773,67 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_fwd">
-    <title><emphasis role="bold">fwd</emphasis> &id; [<emphasis role="bold">(</emphasis>[&id;]…<emphasis role="bold">)</emphasis>]</title>
+    <title>fwd</title>
     <titleabbrev>fwd</titleabbrev>
-    <para><userinput>fwd ...TODO</userinput></para>
+    <para><userinput>fwd H as H<subscript>0</subscript> ... H<subscript>n</subscript></userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">fwd</emphasis> &id; [<emphasis role="bold">as</emphasis> &id; [&id;]…]</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+              The type of <command>H</command> must be the premise of a
+               forward simplification theorem.
+           </para>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>Action:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+            This tactic is under development.
+             It simplifies the current context by removing
+            <command>H</command> using the following methods:
+            forward application (by <command>lapply</command>) of a suitable
+            simplification theorem, chosen automatically, of which the type
+            of <command>H</command> is a premise, 
+            decomposition (by <command>decompose</command>),
+            rewriting (by <command>rewrite</command>).
+            <command>H<subscript>0</subscript> ... H<subscript>n</subscript></command>
+            are passed to the tactics <command>fwd</command> invokes, as
+             names for the premise they introduce.
+           </para>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>New sequents to prove:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+            The ones opened by the tactics <command>fwd</command> invokes.
+           </para>
           </listitem>
         </varlistentry>
       </variablelist>
     </para>
   </sect1>
   <sect1 id="tac_generalize">
-    <title><emphasis role="bold">generalize</emphasis> &pattern; [<emphasis role="bold">as</emphasis> &id;]</title>
+    <title>generalize</title>
     <titleabbrev>generalize</titleabbrev>
     <para><userinput>generalize patt as H</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">generalize</emphasis> &pattern; [<emphasis role="bold">as</emphasis> &id;]</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -684,11 +865,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_id">
-    <title><emphasis role="bold">id</emphasis></title>
+    <title>id</title>
     <titleabbrev>id</titleabbrev>
     <para><userinput>id </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">id</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -711,11 +898,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_injection">
-    <title><emphasis role="bold">injection</emphasis> &sterm;</title>
-    <titleabbrev><emphasis role="bold">injection</emphasis></titleabbrev>
+    <title>injection</title>
+    <titleabbrev>injection</titleabbrev>
     <para><userinput>injection p</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">injection</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -742,11 +935,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_intro">
-    <title><emphasis role="bold">intro</emphasis> [&id;]</title>
+    <title>intro</title>
     <titleabbrev>intro</titleabbrev>
     <para><userinput>intro H</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">intro</emphasis> [&id;]</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -775,11 +974,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_intros">
-    <title><emphasis role="bold">intros</emphasis> &intros-spec;</title>
+    <title>intros</title>
     <titleabbrev>intros</titleabbrev>
     <para><userinput>intros hyps</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">intros</emphasis> &intros-spec;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -812,11 +1017,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_inversion">
-    <title><emphasis role="bold">inversion</emphasis> &sterm;</title>
+    <title>inversion</title>
     <titleabbrev>inversion</titleabbrev>
     <para><userinput>inversion t</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">inversion</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -847,41 +1058,87 @@ its constructor takes no arguments.</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> &sterm; [&sterm;]…] [<emphasis role="bold">using</emphasis> &id;]</title>
+    <title>lapply</title>
     <titleabbrev>lapply</titleabbrev>
     <para><userinput>
-     lapply depth=d t 
-     to t<subscript>1</subscript>, ..., t<subscript>n</subscript> using H
+     lapply linear depth=d t 
+     to t<subscript>1</subscript>, ..., t<subscript>n</subscript> as H
     </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <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>Pre-conditions:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+            <command>t</command> must have at least <command>d</command>
+            independent premises and <command>n</command> must not be
+            greater than <command>d</command>.
+           </para>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>Action:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+            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 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
+            <command>t</command>.
+            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>
         <varlistentry>
           <term>New sequents to prove:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+            The ones opened by the tactics <command>lapply</command> invokes.
+           </para>
           </listitem>
         </varlistentry>
       </variablelist>
     </para>
   </sect1>
   <sect1 id="tac_left">
-    <title><emphasis role="bold">left</emphasis></title>
+    <title>left</title>
     <titleabbrev>left</titleabbrev>
     <para><userinput>left </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">left</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -908,11 +1165,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_letin">
-    <title><emphasis role="bold">letin</emphasis> &id; <emphasis role="bold">≝</emphasis> &sterm;</title>
+    <title>letin</title>
     <titleabbrev>letin</titleabbrev>
     <para><userinput>letin x ≝ t</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">letin</emphasis> &id; <emphasis role="bold">≝</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -936,11 +1199,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_normalize">
-    <title><emphasis role="bold">normalize</emphasis> &pattern;</title>
+    <title>normalize</title>
     <titleabbrev>normalize</titleabbrev>
     <para><userinput>normalize patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">normalize</emphasis> &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -964,11 +1233,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_paramodulation">
-    <title><emphasis role="bold">paramodulation</emphasis> &pattern;</title>
+    <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>
@@ -991,11 +1266,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_reduce">
-    <title><emphasis role="bold">reduce</emphasis> &pattern;</title>
+    <title>reduce</title>
     <titleabbrev>reduce</titleabbrev>
     <para><userinput>reduce patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">reduce</emphasis> &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1019,11 +1300,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_reflexivity">
-    <title><emphasis role="bold">reflexivity</emphasis></title>
+    <title>reflexivity</title>
     <titleabbrev>reflexivity</titleabbrev>
     <para><userinput>reflexivity </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">reflexivity</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1048,11 +1335,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_replace">
-    <title><emphasis role="bold">replace</emphasis> &pattern; <emphasis role="bold">with</emphasis> &sterm;</title>
+    <title>replace</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">replace</emphasis> &pattern; <emphasis role="bold">with</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1080,11 +1373,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_rewrite">
-    <title><emphasis role="bold">rewrite</emphasis> [<emphasis role="bold">&lt;</emphasis>|<emphasis role="bold">&gt;</emphasis>] &sterm; &pattern;</title>
+    <title>rewrite</title>
     <titleabbrev>rewrite</titleabbrev>
     <para><userinput>rewrite dir p patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">rewrite</emphasis> [<emphasis role="bold">&lt;</emphasis>|<emphasis role="bold">&gt;</emphasis>] &sterm; &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1115,11 +1414,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_right">
-    <title><emphasis role="bold">right</emphasis></title>
+    <title>right</title>
     <titleabbrev>right</titleabbrev>
     <para><userinput>right </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">right</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1146,11 +1451,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_ring">
-    <title><emphasis role="bold">ring</emphasis></title>
+    <title>ring</title>
     <titleabbrev>ring</titleabbrev>
     <para><userinput>ring </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">ring</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1177,11 +1488,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_simplify">
-    <title><emphasis role="bold">simplify</emphasis> &pattern;</title>
+    <title>simplify</title>
     <titleabbrev>simplify</titleabbrev>
     <para><userinput>simplify patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">simplify</emphasis> &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1205,11 +1522,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_split">
-    <title><emphasis role="bold">split</emphasis></title>
+    <title>split</title>
     <titleabbrev>split</titleabbrev>
     <para><userinput>split </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">split</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1236,12 +1559,18 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_symmetry">
-    <title><emphasis role="bold">symmetry</emphasis></title>
+    <title>symmetry</title>
     <titleabbrev>symmetry</titleabbrev>
     <para>The tactic <command>symmetry</command> </para>
     <para><userinput>symmetry </userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">symmetry</emphasis></para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1265,11 +1594,17 @@ its constructor takes no arguments.</para>
     </para>
   </sect1>
   <sect1 id="tac_transitivity">
-    <title><emphasis role="bold">transitivity</emphasis> &sterm;</title>
+    <title>transitivity</title>
     <titleabbrev>transitivity</titleabbrev>
     <para><userinput>transitivity t</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">transitivity</emphasis> &sterm;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1294,11 +1629,17 @@ the current sequent to prove.</para>
     </para>
   </sect1>
   <sect1 id="tac_unfold">
-    <title><emphasis role="bold">unfold</emphasis> [&sterm;] &pattern;</title>
+    <title>unfold</title>
     <titleabbrev>unfold</titleabbrev>
     <para><userinput>unfold t patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">unfold</emphasis> [&sterm;] &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -1326,11 +1667,17 @@ the current sequent to prove.</para>
     </para>
   </sect1>
   <sect1 id="tac_whd">
-    <title><emphasis role="bold">whd</emphasis> &pattern;</title>
+    <title>whd</title>
     <titleabbrev>whd</titleabbrev>
     <para><userinput>whd patt</userinput></para>
     <para>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">whd</emphasis> &pattern;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>