X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fhelp%2FC%2Fsec_tactics.xml;h=bc5095fae94061d264bf51662680b1da622db51f;hb=a094832a413d3d11cd4031b01a5119452384a7ac;hp=90c7f49757699601a1620d5608d7c22f43b8a03e;hpb=3beaf3083a6677e1ea8228e618f385bef67b7f15;p=helm.git

diff --git a/matita/help/C/sec_tactics.xml b/matita/help/C/sec_tactics.xml
index 90c7f4975..bc5095fae 100644
--- 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>
@@ -130,11 +161,17 @@
     </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>
       <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">clear</emphasis> &id;</para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
@@ -159,11 +196,17 @@
     </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 +231,17 @@
     </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 +269,17 @@
     </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 +307,17 @@
     </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 +342,17 @@
     </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>
@@ -312,38 +379,68 @@
     </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 ???</userinput></para>
+    <para><userinput>
+     decompose (T<subscript>1</subscript> ... T<subscript>n</subscript>) H hips
+    </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; &intros-spec;
+	    </para>
+          </listitem>
+        </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
-            <para>TODO.</para>
+            <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>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>Action:</term>
           <listitem>
-            <para>TODO.</para>
+            <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.
+	    </para>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>New sequents to prove:</term>
           <listitem>
-            <para>TODO.</para>
+            <para>
+	     The ones generated by all the <command>elim</command> tactics run.
+	    </para>
           </listitem>
         </varlistentry>
       </variablelist>
     </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>
@@ -366,11 +463,17 @@
     </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>
@@ -395,11 +498,17 @@ 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>
@@ -432,11 +541,17 @@ 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>
@@ -459,11 +574,17 @@ 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>
@@ -487,11 +608,17 @@ 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>
@@ -518,11 +645,17 @@ 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>
@@ -545,11 +678,17 @@ 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>
@@ -577,11 +716,17 @@ 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>
@@ -607,38 +752,67 @@ 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>
@@ -670,11 +844,17 @@ 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>
@@ -697,11 +877,17 @@ 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>
@@ -728,11 +914,17 @@ 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>
@@ -761,11 +953,17 @@ 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>
@@ -798,11 +996,17 @@ 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>
@@ -833,38 +1037,73 @@ 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 ???</userinput></para>
+    <para><userinput>
+     lapply 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">depth=</emphasis>&nat;] &sterm; [<emphasis role="bold">to</emphasis> &sterm; [&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>
+	     It 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
+	     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.
+	    </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>
@@ -891,11 +1130,17 @@ 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>
@@ -919,11 +1164,17 @@ 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>
@@ -947,11 +1198,17 @@ 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>
@@ -974,11 +1231,17 @@ 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>
@@ -1002,11 +1265,17 @@ 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>
@@ -1031,11 +1300,17 @@ 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>
@@ -1063,11 +1338,17 @@ 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>
@@ -1098,11 +1379,17 @@ 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>
@@ -1129,11 +1416,17 @@ 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>
@@ -1160,11 +1453,17 @@ 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>
@@ -1188,11 +1487,17 @@ 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>
@@ -1219,12 +1524,18 @@ 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>
@@ -1248,11 +1559,17 @@ 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>
@@ -1277,11 +1594,17 @@ 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>
@@ -1309,11 +1632,17 @@ 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>