X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fstyle%2Fproofs.xsl;h=1d619260a2dbe6bd22fa5c64d5e14f57b4666081;hb=a38dce333847f6a1eaed563f7a2260e1cfc1ff2e;hp=96d1ee7de532142ee3ce9ac18f7e4c6644950351;hpb=0e9cfa8af4ac6569e350dac51b8f8482d124f71a;p=helm.git

diff --git a/helm/style/proofs.xsl b/helm/style/proofs.xsl
index 96d1ee7de..1d619260a 100644
--- a/helm/style/proofs.xsl
+++ b/helm/style/proofs.xsl
@@ -72,13 +72,17 @@
    <m:apply helm:xref="{@id}">
     <m:csymbol>proof</m:csymbol>
     <xsl:apply-templates mode="proof_transform" select="."/>
+    <!-- <xsl:apply-templates mode="try_inductive" select="."/> -->
     <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
    </m:apply>
   </xsl:when>
   <xsl:otherwise>
    <xsl:choose>
     <xsl:when test="name()='APPLY'">
-     <xsl:apply-templates select="." mode="letin"/>
+     <!-- This is the case of an applicative expression wich is not
+          a proof but could contains proofs...
+          MODE LETIN OR MODE PURE ??? Big question -->
+     <xsl:apply-templates select="." mode="pure"/>
     </xsl:when>
     <xsl:otherwise>
      <xsl:apply-templates select="." mode="pure"/>
@@ -88,43 +92,380 @@
  </xsl:choose>
 </xsl:template>
 
+<!-- si presuppone che il tipo induttivo non sia mutuamente 
+     induttivo. Bisognerebbe andare a vedere l'utlimo parametro
+     del presunto "principio di induzione", tirare fuori il tipo induttivo
+     e vedere se il suo nome coincide con il prefisso di _ind. 
+     Ad esempio nat_double_ind e' definito dall'utente. L'ultimo
+     parametro di nat_double_ind e' di tipo nat, e nat e' diverso
+     da nat_double. Per ora, verifico solo l'esistenza di nat_double,
+     ma questo, benche' non porti ad errore, non copre tutti i
+     casi per quelli mutuamente induttivi -->
+
+<xsl:template mode="try_inductive" match="APPLY">
+   <xsl:variable name="id" select="@id"/>
+   <xsl:choose>
+    <xsl:when test="CONST[1]">
+     <xsl:variable name="uri" select="CONST[1]/@uri"/>
+     <xsl:choose>
+      <xsl:when test="contains($uri,'_ind.con')">
+       <xsl:variable name="ind_uri" 
+         select="concat(substring-before($uri,'_ind.con'),'.ind')"/>
+       <xsl:variable name="InductiveTypeUrl"><xsl:call-template name="URLofURI4getter"><xsl:with-param name="uri" select="$ind_uri"/></xsl:call-template></xsl:variable>
+       <xsl:variable name="inductive_def" 
+     select="document($InductiveTypeUrl)/InductiveDefinition"/>
+       <!-- check if the corresponding inductive definition actually
+            exists -->
+       <xsl:choose>
+        <xsl:when test="$inductive_def">
+         <xsl:variable name="ind_name">
+          <xsl:call-template name="get_name">
+           <xsl:with-param name="uri" select="$uri"/>
+          </xsl:call-template>
+         </xsl:variable>
+         <xsl:variable name="no_params">
+          <xsl:call-template name="get_no_params">
+           <xsl:with-param name="first_uri" select="$CICURI"/>
+           <xsl:with-param name="second_uri" select="$uri"/>
+          </xsl:call-template>
+         </xsl:variable>
+         <xsl:apply-templates mode="inductive" select=".">
+          <xsl:with-param name="inductive_def_uri" 
+           select="$ind_uri"/>
+          <xsl:with-param name="inductive_def" 
+           select="$inductive_def"/>
+          <xsl:with-param name="section_params" select="$no_params"/>
+          <xsl:with-param name="inductive_def_index" select="1"/>
+          <xsl:with-param name="inductive_def_name" select="$ind_name"/>
+         </xsl:apply-templates>
+        </xsl:when>
+        <xsl:otherwise>
+         <xsl:apply-templates mode="letin" select="."/>
+        </xsl:otherwise>
+       </xsl:choose>
+      </xsl:when>
+      <xsl:otherwise>
+       <xsl:apply-templates mode="letin" select="."/>
+      </xsl:otherwise>
+     </xsl:choose>
+    </xsl:when>
+    <xsl:otherwise>
+     <xsl:apply-templates mode="letin" select="."/>
+    </xsl:otherwise>
+   </xsl:choose>
+</xsl:template>
+
+<xsl:template mode="eq_transitive" match="*">
+ <!-- <m:ci>eccomi-1: <xsl:value-of select="name()"/></m:ci> -->
+ <xsl:choose>
+  <xsl:when test="name()='APPLY'">
+   <!-- <m:ci>eccomi-2: <xsl:value-of select="CONST[1]/@uri"/></m:ci> -->
+   <xsl:variable name="id" select="@id"/>
+   <xsl:choose>
+    <!-- ricordarsi di trattare il parametro -->
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/CSetoids/CSetoid_basics/eq_transitive_unfolded.con'] and count(child::*) = 7">
+     <!-- <m:ci>eccomi-3</m:ci> -->
+     <xsl:apply-templates mode="eq_transitive" select="*[6]"/>
+     <xsl:apply-templates mode="noannot" select="*[4]"/>
+     <xsl:apply-templates mode="eq_transitive" select="*[7]"/>
+    </xsl:when>
+    <xsl:otherwise>
+     <xsl:call-template name="generate_side_proof">
+      <xsl:with-param name="proof" select="."/>
+      <xsl:with-param name="show_statement" select="0"/>
+     </xsl:call-template> 
+    </xsl:otherwise>
+   </xsl:choose>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:call-template name="generate_side_proof">
+    <xsl:with-param name="proof" select="."/>
+    <xsl:with-param name="show_statement" select="0"/>
+   </xsl:call-template>
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template mode="diseq" match="*">
+  <xsl:param name="rel" select="'eq'"/>
+  <xsl:choose>
+  <xsl:when test="name()='APPLY'">
+      <xsl:variable name="id" select="@id"/>
+   <xsl:choose>
+    <!-- ricordarsi di trattare il parametro -->
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_transitive.con'] and count(child::*) = 7">
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+    </xsl:when> 
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_wdl.con'] and count(child::*) = 7">
+       <m:eq/>
+       <!-- <m:ci><xsl:value-of select="'eq'"/></m:ci> -->
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="*[7]"/>
+        <xsl:with-param name="show_statement" select="0"/>
+       </xsl:call-template>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+    </xsl:when> 
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_less_trans.con'] and count(child::*) = 7">
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+    </xsl:when>
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/less_leEq_trans.con'] and count(child::*) = 7">
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+    </xsl:when>  
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_wdr.con'] and count(child::*) = 7">
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'eq'"/>
+       </xsl:apply-templates>
+    </xsl:when>  
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/COrdField_axioms/less_transitive_unfolded.con'] and count(child::*) = 7">
+      <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+     </xsl:when> 
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/COrdField_axioms/less_wdr.con'] and count(child::*) = 7">
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'eq'"/>
+       </xsl:apply-templates>
+     </xsl:when>
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/COrdField_axioms/less_wdl.con'] and count(child::*) = 7">
+       <m:eq/>
+       <!-- <m:ci><xsl:value-of select="'eq'"/></m:ci> -->
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="*[7]"/>
+        <xsl:with-param name="show_statement" select="0"/>
+       </xsl:call-template>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+    </xsl:when> 
+    <!-- 
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/CSetoids/CSetoid_basics/eq_transitive_unfolded.con'] and count(child::*) = 7">
+     <xsl:apply-templates mode="diseq" select="*[6]"/>
+     <m:eq/>
+     <xsl:apply-templates mode="noannot" select="*[4]"/>
+     <m:eq/>
+     <xsl:apply-templates mode="diseq" select="*[7]"/>
+    </xsl:when> 
+    -->
+    <xsl:otherwise>
+     <xsl:element name="{concat('m:',$rel)}"/>
+     <!-- <m:ci><xsl:value-of select="$rel"/></m:ci> -->  
+     <xsl:call-template name="generate_side_proof">
+      <xsl:with-param name="proof" select="."/>
+      <xsl:with-param name="show_statement" select="0"/>
+     </xsl:call-template> 
+    </xsl:otherwise>
+   </xsl:choose>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:element name="{concat('m:',$rel)}"/> 
+   <!-- <m:ci><xsl:value-of select="$rel"/></m:ci> --> 
+   <xsl:call-template name="generate_side_proof">
+    <xsl:with-param name="proof" select="."/>
+    <xsl:with-param name="show_statement" select="0"/>
+   </xsl:call-template>
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
 <xsl:template mode="proof_transform" match="*">
+ <xsl:choose>
+  <xsl:when test="name()='APPLY'">
    <xsl:variable name="id" select="@id"/>
    <xsl:choose>
-    <!-- NATIND 3 parametri -->
-    <xsl:when test="name()='APPLY' and CONST[
- attribute::uri='cic:/Coq/Init/Datatypes/nat_ind.con'] and count(child::*) = 4">
+    <!-- Algebra equality (eq_transitive_unfolded) -->
+    <!-- It requires a special mode "eq_transitive"-->
+    <!-- togliere il parametro -->
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/CSetoids/CSetoid_basics/eq_transitive_unfolded.con'] and count(child::*) = 7">
      <m:apply>
-      <m:csymbol>nat_ind</m:csymbol>
-      <xsl:apply-templates mode="noannot" select="*[3]"/>
-      <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <m:csymbol>eq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="eq_transitive" select="*[6]"/>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="eq_transitive" select="*[7]"/>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
      </m:apply>
     </xsl:when>
-    <!-- NATIND 4 parametri -->
-    <xsl:when test="name()='APPLY' and CONST[
- attribute::uri='cic:/Coq/Init/Datatypes/nat_ind.con'] and count(child::*) = 5">
+    <!-- Algebra disequalities -->
+    <!-- It requires a special mode "diseq"-->
+    <!-- togliere il parametro -->
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_transitive.con'] and count(child::*) = 7">
      <m:apply>
-      <m:csymbol>nat_ind</m:csymbol>
-      <xsl:apply-templates mode="noannot" select="*[3]"/>
-      <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+     </m:apply>
+    </xsl:when> 
+     <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_wdl.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+       <m:eq/>
+       <!-- <m:ci><xsl:value-of select="'eq'"/></m:ci> -->
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="*[7]"/>
+        <xsl:with-param name="show_statement" select="0"/>
+       </xsl:call-template>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+     </m:apply>
+    </xsl:when>
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_less_trans.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+     </m:apply>
+    </xsl:when> 
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/less_leEq_trans.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+     </m:apply>
+    </xsl:when>  
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/Basic_Properties_of_leEq/leEq_wdr.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'leq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'eq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+     </m:apply>
+    </xsl:when>  
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/COrdField_axioms/less_transitive_unfolded.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+     </m:apply>
+    </xsl:when>  
+    <!-- togliere il parametro -->
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/COrdField_axioms/less_wdr.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+       <xsl:apply-templates mode="diseq" select="*[7]">
+        <xsl:with-param name="rel" select="'eq'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
      </m:apply>
     </xsl:when>
+    <!-- togliere il parametro -->
+    <xsl:when test="CONST[attribute::uri='cic:/Algebra/COrdFields/COrdField_axioms/less_wdl.con'] and count(child::*) = 7">
+     <m:apply>
+       <m:csymbol>diseq_chain</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
+       <m:eq/>
+       <!-- <m:ci><xsl:value-of select="'eq'"/></m:ci> -->
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="*[7]"/>
+        <xsl:with-param name="show_statement" select="0"/>
+       </xsl:call-template>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+       <xsl:apply-templates mode="diseq" select="*[6]">
+        <xsl:with-param name="rel" select="'lt'"/>
+       </xsl:apply-templates>
+       <xsl:apply-templates mode="noannot" select="*[4]"/>
+     </m:apply>
+    </xsl:when> 
     <!-- EQUALITY -->
-    <xsl:when test="name()= 'APPLY' and CONST[
+    <xsl:when test="CONST[
  attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
+ attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
  attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
+ attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
  attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) = 7">
       <m:apply>
        <m:csymbol>rw_step</m:csymbol>
        <xsl:apply-templates mode="noannot" select="*[5]"/>
        <xsl:apply-templates mode="pure" select="*[3]"/>
        <xsl:apply-templates mode="pure" select="*[6]"/>
-       <xsl:apply-templates mode="pure" select="*[7]"/>
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="*[7]"/>
+       </xsl:call-template>
+       <!-- <xsl:apply-templates mode="proof_transform" select="*[7]"/> -->
       </m:apply>
     </xsl:when>
     <!-- EQUALITY with extra-parameters -->
-    <xsl:when test="name()= 'APPLY' and CONST[
+    <xsl:when test="CONST[
+ attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
+ attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
  attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
+ attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
  attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) > 7">
       <xsl:variable name="no_extraproofs" select="count(*[position()>7 and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>      
       <xsl:choose>
@@ -136,7 +477,10 @@
           <xsl:apply-templates mode="noannot" select="*[5]"/>
           <xsl:apply-templates mode="pure" select="*[3]"/>
           <xsl:apply-templates mode="pure" select="*[6]"/>
-          <xsl:apply-templates mode="pure" select="*[7]"/>
+          <xsl:call-template name="generate_side_proof">
+           <xsl:with-param name="proof" select="*[7]"/>
+           </xsl:call-template>
+          <!-- <xsl:apply-templates mode="pure" select="*[7]"/> -->
          </m:apply>
          <xsl:apply-templates mode="noannot" select="*[position()>7]"/>
         </m:apply>
@@ -170,7 +514,10 @@
              </m:ci>
              <xsl:apply-templates mode="pure" select="*[3]"/>
              <xsl:apply-templates mode="pure" select="*[6]"/>
-             <xsl:apply-templates mode="pure" select="*[7]"/>
+             <xsl:call-template name="generate_side_proof">
+              <xsl:with-param name="proof" select="*[7]"/>
+             </xsl:call-template>
+             <!-- <xsl:apply-templates mode="pure" select="*[7]"/> -->
             </m:apply>
             <xsl:apply-templates mode="flat" select="*[8]">
              <xsl:with-param name="n">
@@ -193,8 +540,11 @@
              <m:csymbol>rw_step</m:csymbol>
              <xsl:apply-templates mode="pure" select="*[5]"/>
              <xsl:apply-templates mode="pure" select="*[3]"/>
-             <xsl:apply-templates mode="pure" select="*[6]"/>
-             <xsl:apply-templates mode="pure" select="*[7]"/>
+             <xsl:apply-templates mode="pure" select="*[6]"/>             
+             <xsl:call-template name="generate_side_proof">
+              <xsl:with-param name="proof" select="*[7]"/>
+             </xsl:call-template>
+             <!-- <xsl:apply-templates mode="pure" select="*[7]"/> -->
             </m:apply>
             <xsl:apply-templates mode="flat" select="*[8]">
              <xsl:with-param name="n">
@@ -208,9 +558,19 @@
        </xsl:otherwise>
       </xsl:choose>
     </xsl:when>
+    <!-- False_ind -->
+    <xsl:when test="CONST[
+     attribute::uri='cic:/Coq/Init/Logic/False_ind.con'] and 
+     count(child::*) = 3">
+     <m:apply helm:xref="{@id}">
+       <m:csymbol>false_ind</m:csymbol>
+       <m:ci>cic:/Coq/Init/Logic/False_ind.con</m:ci>
+       <xsl:apply-templates mode="noannot" select="*[3]"/>
+     </m:apply>
+    </xsl:when>
     <!-- gestire meglio il caso di and_ind quando la prova 
          non e' della forma \x.\y.M -->
-    <xsl:when test="name()= 'APPLY' and CONST[
+    <xsl:when test="CONST[
  attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con'] 
  and count(child::*) = 6 
  and name(*[5])='LAMBDA' 
@@ -225,20 +585,59 @@
        <xsl:apply-templates mode="proof_transform" select="*[5]/target/LAMBDA/target/*"/> 
       </m:apply>
     </xsl:when>
-    <xsl:when test="name()= 'APPLY' and CONST[
+    <xsl:when test="CONST[
  attribute::uri='cic:/Coq/Init/Logic/Disjunction/or_ind.con'] 
  and count(child::*) = 7">
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>or_ind</m:csymbol>
-      <xsl:apply-templates mode="noannot" select="*[7]"/>
-      <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
-      <xsl:apply-templates mode="pure" select="*[5]"/>
-      <xsl:apply-templates mode="pure" select="*[6]"/>
-     </m:apply>
+      <xsl:choose>
+       <xsl:when test="name(*[5])='LAMBDA' 
+                 and name(*[6])='LAMBDA'">
+        <xsl:variable name="definition_url" 
+            select="'cic:/Coq/Init/Logic/Disjunction/or.ind'"/>
+        <m:apply helm:xref="{@id}">
+         <m:csymbol>full_or_ind</m:csymbol>
+         <xsl:apply-templates mode="noannot" select="*[7]"/>
+         <xsl:apply-templates mode="pure" 
+              select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*[1]"/>
+         <m:apply>
+          <m:csymbol>left_case</m:csymbol>
+          <m:bvar>
+           <m:ci>
+            <xsl:value-of select="*[5]/target/@binder"/>
+           </m:ci>
+           <m:type>
+            <xsl:apply-templates mode="pure" select="*[5]/source/*[1]"/>
+           </m:type>
+          </m:bvar>
+          <xsl:apply-templates mode="noannot" select="*[5]/target/*[1]"/>
+         </m:apply>
+         <m:apply>
+          <m:csymbol>right_case</m:csymbol>
+          <m:bvar>
+           <m:ci>
+            <xsl:apply-templates mode="pure" select="*[6]/target/@binder"/>
+           </m:ci>
+           <m:type>
+            <xsl:apply-templates mode="pure" select="*[6]/source/*[1]"/>
+           </m:type>
+          </m:bvar>
+          <xsl:apply-templates mode="noannot" select="*[6]/target/*[1]"/>
+         </m:apply>
+        </m:apply>
+       </xsl:when>
+       <xsl:otherwise>
+        <m:apply helm:xref="{@id}">
+         <m:csymbol>or_ind</m:csymbol>
+         <xsl:apply-templates mode="noannot" select="*[7]"/>
+         <xsl:apply-templates mode="pure" 
+              select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*[1]"/>
+         <xsl:apply-templates mode="pure" select="*[5]"/>
+         <xsl:apply-templates mode="pure" select="*[6]"/>
+        </m:apply>
+       </xsl:otherwise>
+      </xsl:choose>
     </xsl:when>
     <!-- ex_ind, exT_ind -->
-      <xsl:when test="name()= 'APPLY' 
- and (CONST[attribute::uri='cic:/Coq/Init/Logic_Type/exT_ind.con'] or
+      <xsl:when test="(CONST[attribute::uri='cic:/Coq/Init/Logic_Type/exT_ind.con'] or
       CONST[attribute::uri='cic:/Coq/Init/Logic/First_order_quantifiers/ex_ind.con'])  
  and count(child::*) = 6 
  and name(*[5])='LAMBDA' 
@@ -253,19 +652,111 @@
        <xsl:apply-templates mode="proof_transform" select="*[5]/target/LAMBDA/target/*"/>
       </m:apply>
     </xsl:when>
+    <xsl:when test="name(*[1])='CONST'">
+     <xsl:apply-templates mode="try_inductive" select="."/>
+    </xsl:when>
+    <!-- patch temporanea per la gestione di redex -->
+    <xsl:when test="name(*[1])='LAMBDA' and count(child::*)=2
+         and *[2]/@sort='Prop'">
+     <m:apply helm:xref="{@id}">
+      <m:csymbol>letin</m:csymbol>
+      <m:apply>
+       <m:csymbol>let</m:csymbol>
+       <m:ci>
+        <xsl:call-template name="insert_subscript">
+         <xsl:with-param name="node_value">
+          <xsl:value-of select="*[1]/target/@binder"/>
+         </xsl:with-param>
+        </xsl:call-template>
+       </m:ci>
+       <xsl:apply-templates mode="noannot" select="*[2]"/>
+      </m:apply>
+      <xsl:apply-templates mode="proof_transform" select="*[1]/target/*[1]"/>
+     </m:apply>
+    </xsl:when>
     <xsl:otherwise>
-      <xsl:choose>
-       <xsl:when test="name()='APPLY'">
-        <xsl:apply-templates select="." mode="letin"/>
-       </xsl:when>
-       <xsl:otherwise>
-        <xsl:apply-templates select="." mode="pure"/>
-       </xsl:otherwise>
-      </xsl:choose>
+     <xsl:apply-templates select="." mode="letin"/>
     </xsl:otherwise>
    </xsl:choose>
+  </xsl:when>
+  <xsl:when test="name()='LAMBDA'">
+   <xsl:choose>
+     <xsl:when test="(name(target/*[1])='APPLY'  and
+      name(target/*[1]/*[1])='CONST' and
+      (target/*[1]/*[1]/@uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
+       target/*[1]/*[1]/@uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
+       target/*[1]/*[1]/@uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con')
+      and count(target/*[1]/*) = 8 
+      and name(target/*[1]/*[8])='REL'
+      and target/@binder = target/*[1]/*[8]/@binder )"> 
+      <m:apply>
+       <m:csymbol>rw_step</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="target/*[1]/*[5]"/>
+       <xsl:apply-templates mode="pure" select="target/*[1]/*[3]"/>
+       <xsl:apply-templates mode="pure" select="target/*[1]/*[6]"/>
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="target/*[1]/*[7]"/>
+       </xsl:call-template>
+       <!-- <xsl:apply-templates mode="proof_transform" select="target/*[1]/*[7]"/> -->
+      </m:apply>
+     </xsl:when>
+     <xsl:otherwise>
+      <xsl:apply-templates mode="pure" select="."/>
+     </xsl:otherwise>
+    </xsl:choose>
+   </xsl:when>
+  <xsl:otherwise>
+   <xsl:apply-templates select="." mode="pure"/>
+  </xsl:otherwise>
+ </xsl:choose>
 </xsl:template>
 
+<xsl:template name="is_simple">
+ <xsl:param name="proof" select="/.."/>
+ <xsl:value-of select="(count($proof/*)=0) or ((name($proof)='APPLY') and (count($proof/*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]) = 0))"/>
+</xsl:template>
+
+<xsl:template name="generate_side_proof">
+ <xsl:param name="proof" select="/.."/>
+ <xsl:param name="show_statement" select="1"/>
+<!-- 
+ <xsl:variable name="is_simple">
+  <xsl:call-template name="is_simple">
+   <xsl:with-param name="proof" select="$proof"/>
+  </xsl:call-template>
+ </xsl:variable> -->
+<xsl:variable name="is_simple" select="(count($proof/*)=0) or ((name($proof)='APPLY') and (count($proof/*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]) = 0))"/>
+ <xsl:choose>
+  <xsl:when test="$is_simple">
+   <xsl:choose>
+    <xsl:when test="name($proof)='APPLY'">
+     <xsl:apply-templates select="$proof" mode="letin"/>
+    </xsl:when>
+    <xsl:otherwise>
+     <xsl:apply-templates select="$proof" mode="pure"/>
+    </xsl:otherwise>
+   </xsl:choose>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:variable name="id" select="@id"/>
+   <m:apply helm:xref="{@id}">
+    <xsl:choose>
+     <xsl:when test="$show_statement = 1">
+      <m:csymbol>proof</m:csymbol>
+     </xsl:when>
+     <xsl:otherwise>
+      <m:csymbol>side_proof</m:csymbol>
+     </xsl:otherwise>
+    </xsl:choose>
+    <xsl:apply-templates mode="proof_transform" select="$proof"/>
+    <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$proof/@id]/*"/>
+   </m:apply>
+   <!-- <xsl:apply-templates select="$proof" mode="noannot"/> -->
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:variable name="no_subproofs" select="count(*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
 
 <xsl:template match="APPLY" mode="letin">
    <xsl:variable name="no_subproofs" select="count(*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
@@ -298,7 +789,17 @@
      </m:apply>
     </xsl:when>
     <xsl:otherwise>
-     <xsl:apply-templates mode="pure" select="."/>
+     <xsl:choose>
+     <xsl:when test="@sort='Prop'">
+      <m:apply>
+       <m:csymbol>app</m:csymbol>
+       <xsl:apply-templates mode="erase" select="*[1]"/>
+      </m:apply>
+     </xsl:when>
+     <xsl:otherwise>
+      <xsl:apply-templates mode="pure" select="."/>
+     </xsl:otherwise>
+     </xsl:choose>
     </xsl:otherwise>
    </xsl:choose>
 </xsl:template>
@@ -315,13 +816,34 @@
       </xsl:for-each>
 </xsl:template>
 
+<xsl:template match="*" mode="erase">
+  <xsl:choose>
+   <xsl:when test="@sort='Prop' or $naturalLanguage='no'">
+    <xsl:apply-templates mode="pure" select="."/>
+   </xsl:when>
+   <xsl:otherwise>
+    <m:ci>.</m:ci>
+   </xsl:otherwise>
+   </xsl:choose>
+ <xsl:apply-templates mode="erase" select="following-sibling::*[1]"/>
+</xsl:template>
+
 <xsl:template match="*" mode="previous">
  <xsl:choose>
-  <xsl:when test="$naturalLanguage='yes' and(@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX'))">
+  <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
    <m:ci>previous</m:ci>
   </xsl:when>
   <xsl:otherwise>
-   <xsl:apply-templates select="." mode="pure"/>
+   <!-- forse bisognerebbe trattare solo l'elemento di testa -->
+   <xsl:choose>
+   <xsl:when test="@sort='Prop' or $naturalLanguage='no'">
+    <xsl:apply-templates mode="pure" select="."/>
+   </xsl:when>
+   <xsl:otherwise>
+    <m:ci>.</m:ci>
+   </xsl:otherwise>
+   </xsl:choose>
+   <!-- <xsl:apply-templates select="." mode="pure"/> -->
   </xsl:otherwise>
  </xsl:choose>
  <xsl:apply-templates mode="previous" select="following-sibling::*[1]"/>
@@ -331,8 +853,6 @@
  <xsl:param name="n" select="1"/>
  <xsl:variable name="id" select="@id"/>
  <xsl:choose>
-  <!-- <xsl:when test="key('typeid',@id)"> -->
-  <!-- <xsl:when test="$InnerTypes/InnerTypes/TYPE[@of=$id]"> -->
   <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
    <m:ci>
     <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',$n)"/></xsl:with-param></xsl:call-template>
@@ -342,7 +862,15 @@
    </xsl:apply-templates>
   </xsl:when>
   <xsl:otherwise>
-   <xsl:apply-templates mode="pure" select="."/>
+   <xsl:choose>
+    <xsl:when test="name()='REL' or @sort='Prop' or $naturalLanguage='no'">
+     <xsl:apply-templates mode="pure" select="."/>
+    </xsl:when>
+    <xsl:otherwise>
+     <m:ci>.</m:ci>
+    </xsl:otherwise>
+   </xsl:choose>
+   <!-- <xsl:apply-templates mode="pure" select="."/> -->
    <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
     <xsl:with-param name="n" select="$n"/>
    </xsl:apply-templates>
@@ -350,6 +878,23 @@
  </xsl:choose>
 </xsl:template>
 
+<!-- Auxiliary functions -->
+<!-- OMDOC: now we have name_of_uri generalized on the extension that -->
+<!-- can replace the next template                                    -->
+<xsl:template name="get_name">
+ <xsl:param name="uri" select="''"/>
+ <xsl:variable name="sub_after" select="substring-after($uri,'/')"/>
+ <xsl:choose>
+  <xsl:when test="contains($sub_after,'/')">
+   <xsl:call-template name="get_name">
+    <xsl:with-param name="uri" select="$sub_after"/>
+   </xsl:call-template>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:value-of select="substring-before($sub_after,'_ind.con')"/>
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
 
 <!-- <xsl:template match="APPLY[CONST[
  attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con']]" mode="appflat">
@@ -375,9 +920,3 @@
 
 
 </xsl:stylesheet>
-
-
-
-
-
-