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diff --git a/matita/help/C/sec_tactics.xml b/matita/help/C/sec_tactics.xml
index 130c08e56..ff8d099c0 100644
--- a/matita/help/C/sec_tactics.xml
+++ b/matita/help/C/sec_tactics.xml
@@ -86,6 +86,61 @@
       </variablelist>
     </para>
   </sect1>
+  <sect1 id="tac_applyS">
+    <title>applyS</title>
+    <titleabbrev>applyS</titleabbrev>
+    <para><userinput>applyS t auto_params</userinput></para>
+    <para>
+      <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">applyS</emphasis> &sterm; &autoparams;</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).
+             The <command>auto_params</command> parameters are passed
+             directly to <command>auto paramodulation</command>.
+            </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>
@@ -123,13 +178,13 @@
   <sect1 id="tac_auto">
     <title>auto</title>
     <titleabbrev>auto</titleabbrev>
-    <para><userinput>auto depth=d width=w paramodulation full</userinput></para>
+    <para><userinput>auto params</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>
+            <para><emphasis role="bold">auto</emphasis> &autoparams;</para>
           </listitem>
         </varlistentry>
         <varlistentry>
@@ -137,10 +192,10 @@
           <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 <command>d</command> and <command>w</command>.
+             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>
+             a sequent is ...&TODO;</para>
           </listitem>
         </varlistentry>
         <varlistentry>
@@ -450,16 +505,16 @@
       </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>
@@ -483,30 +538,35 @@
       </variablelist>
     </para>
   </sect1>
-  <sect1 id="tac_discriminate">
-    <title>discriminate</title>
-    <titleabbrev>discriminate</titleabbrev>
-    <para><userinput>discriminate p</userinput></para>
+  <sect1 id="tac_destruct">
+    <title>destruct</title>
+    <titleabbrev>destruct</titleabbrev>
+    <para><userinput>destruct p</userinput></para>
     <para>
       <variablelist>
         <varlistentry role="tactic.synopsis">
           <term>Synopsis:</term>
           <listitem>
-            <para><emphasis role="bold">discriminate</emphasis> &sterm;</para>
+            <para><emphasis role="bold">destruct</emphasis> &sterm;</para>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>Pre-conditions:</term>
           <listitem>
-            <para><command>p</command> must have type <command>K t<subscript>1</subscript> ... t<subscript>n</subscript> = K' t'<subscript>1</subscript> ... t'<subscript>m</subscript></command> where <command>K</command> and <command>K'</command> must be different constructors of the same inductive type and each argument list can be empty if
-its constructor takes no arguments.</para>
+            <para><command>p</command> must have type <command>E<subscript>1</subscript> = E<subscript>2</subscript></command> where the two sides of the equality are possibly applied constructors of an inductive type.</para>
           </listitem>
         </varlistentry>
         <varlistentry>
           <term>Action:</term>
           <listitem>
-            <para>It closes the current sequent by proving the absurdity of
-             <command>p</command>.</para>
+            <para>The tactic recursively compare the two sides of the equality
+             looking for different constructors in corresponding position.
+             If two of them are found, the tactic closes the current sequent
+             by proving the absurdity of <command>p</command>. Otherwise
+             it adds a new hypothesis for each leaf of the formula that
+             states the equality of the subformulae in the corresponding
+             positions on the two sides of the equality.
+            </para>
           </listitem>
         </varlistentry>
         <varlistentry>
@@ -897,43 +957,6 @@ its constructor takes no arguments.</para>
       </variablelist>
     </para>
   </sect1>
-  <sect1 id="tac_injection">
-    <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>
-            <para><command>p</command> must have type <command>K t<subscript>1</subscript> ... t<subscript>n</subscript> = K t'<subscript>1</subscript> ... t'<subscript>n</subscript></command> where both argument lists are empty if
-<command>K</command> takes no arguments.</para>
-          </listitem>
-        </varlistentry>
-        <varlistentry>
-          <term>Action:</term>
-          <listitem>
-            <para>It derives new hypotheses by injectivity of
-             <command>K</command>.</para>
-          </listitem>
-        </varlistentry>
-        <varlistentry>
-          <term>New sequents to prove:</term>
-          <listitem>
-            <para>The new sequent to prove is equal to the current sequent
-             with the additional hypotheses
-             <command>t<subscript>1</subscript>=t'<subscript>1</subscript></command> ... <command>t<subscript>n</subscript>=t'<subscript>n</subscript></command>.</para>
-          </listitem>
-        </varlistentry>
-      </variablelist>
-    </para>
-  </sect1>
   <sect1 id="tac_intro">
     <title>intro</title>
     <titleabbrev>intro</titleabbrev>
@@ -1232,39 +1255,6 @@ its constructor takes no arguments.</para>
       </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>
@@ -1558,6 +1548,46 @@ its constructor takes no arguments.</para>
       </variablelist>
     </para>
   </sect1>
+  
+  <sect1 id="tac_subst">
+    <title>subst</title>
+    <titleabbrev>subst</titleabbrev>
+    <para><userinput>subst</userinput></para>
+    <para>
+      <variablelist>
+        <varlistentry role="tactic.synopsis">
+          <term>Synopsis:</term>
+          <listitem>
+            <para><emphasis role="bold">subst</emphasis></para>
+          </listitem>
+        </varlistentry>
+        <varlistentry>
+          <term>Pre-conditions:</term>
+          <listitem><para>
+	    None.
+	  </para></listitem>
+        </varlistentry>
+        <varlistentry>
+          <term>Action:</term>
+          <listitem><para>
+	    For each premise of the form 
+	    <command>H: x = t</command> or <command>H: t = x</command>
+	    where <command>x</command> is a local variable and 
+	    <command>t</command> does not depend on <command>x</command>,
+	    the tactic rewrites <command>H</command> wherever 
+	    <command>x</command> appears clearing <command>H</command> and
+	    <command>x</command> afterwards.
+	  </para></listitem>
+        </varlistentry>
+        <varlistentry>
+          <term>New sequents to prove:</term>
+          <listitem><para>
+	    The one opened by the applied tactics.
+          </para></listitem>
+        </varlistentry>
+      </variablelist>
+    </para>
+  </sect1>
   <sect1 id="tac_symmetry">
     <title>symmetry</title>
     <titleabbrev>symmetry</titleabbrev>