X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fstyle%2Fproofs.xsl;h=f61cbe6d90d1ea9fece3bf22847b6a25ab8a357f;hb=89262281b6e83bd2321150f81f1a0583645eb0c8;hp=760511fd2b193d513c98b05b56f9754d628ce261;hpb=c539f832ce69f7488e79e80d78c2c5003674dc50;p=helm.git

diff --git a/helm/style/proofs.xsl b/helm/style/proofs.xsl
index 760511fd2..f61cbe6d9 100644
--- a/helm/style/proofs.xsl
+++ b/helm/style/proofs.xsl
@@ -26,7 +26,7 @@
 
 <!--******************************************************************--> 
 <!-- Basic Logic                                                      -->
-<!-- First draft: April 3 2000                                        -->
+<!-- (completely) Revisited: february 2001, Andrea Asperti            -->
 <!-- HELM Group: Asperti, Padovani, Sacerdoti, Schena                 -->
 <!--******************************************************************-->
 
@@ -34,25 +34,67 @@
                               xmlns:m="http://www.w3.org/1998/Math/MathML"
                               xmlns:helm="http://www.cs.unibo.it/helm">
 
-
 <!-- ************************* LOGIC *********************************-->
 
 <!-- Proof objects -->
 
 <!-- <xsl:key name="typeid" use="@of" match="TYPE"/> -->
+<xsl:key name="typeid" use="@of" match="TYPE"/>
 
 <!-- ALL this elements does not have inner type -->
-<xsl:template match="LETIN|PROD|REL|SORT|VAR|META|CONST|MUTIND|MUTCONSTRUCT" mode="noannot">
-<xsl:apply-templates select="." mode="pure"/>
+<xsl:template match="PROD|SORT|MUTIND" mode="noannot">
+ <xsl:apply-templates select="." mode="pure"/>
 </xsl:template>
 
+<!-- Atomic elements that have an inner type iff the expected type -->
+<!-- is different from the synthesized type.                       -->
+<xsl:template match="REL|VAR|META|CONST|MUTCONSTRUCT" mode="noannot">
+ <xsl:variable name="id" select="@id"/>
+ <xsl:variable name="innertype_available">
+  <xsl:for-each select="$InnerTypes">
+   <xsl:if test="key('typeid',$id)/*">
+    <xsl:text>yes</xsl:text>
+   </xsl:if>
+  </xsl:for-each>
+ </xsl:variable>
+ <xsl:choose>
+  <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and $innertype_available='yes'">
+   <m:apply helm:xref="{@id}">
+    <m:csymbol>proof</m:csymbol>
+    <xsl:apply-templates mode="proof_transform" select="."/>
+    <!-- <xsl:apply-templates mode="try_inductive" select="."/> -->
+    <xsl:for-each select="$InnerTypes">
+     <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+    </xsl:for-each>
+   </m:apply>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:apply-templates select="." mode="pure"/>
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<!-- ALL ELEMENTS WITH A TYPE ARE TRANSLATED AS A PROOF-ELEMENT -->
+
 <!-- LAMBDA has inner type only if it is not nested inside another lambda -->
 <xsl:template match="LAMBDA" mode="noannot">
  <xsl:variable name="id" select="@id"/>
+ <xsl:variable name="innertype_available">
+  <xsl:for-each select="$InnerTypes">
+   <xsl:if test="key('typeid',$id)/*">
+    <xsl:text>yes</xsl:text>
+   </xsl:if>
+  </xsl:for-each>
+ </xsl:variable>
  <xsl:choose>
-  <xsl:when test="//InnerTypes and @sort='Prop' and name(../..) != 'LAMBDA'">
-  <!-- <xsl:when test="@sort='Prop' and //InnerTypes/TYPE[@of=$id]"> -->
-   <xsl:call-template name="has_inner_type"/>
+  <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and $innertype_available='yes'">
+   <m:apply helm:xref="{@id}">
+    <m:csymbol>proof</m:csymbol>
+    <xsl:apply-templates mode="proof_transform" select="."/>
+    <xsl:for-each select="$InnerTypes">
+     <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+    </xsl:for-each>
+   </m:apply>
   </xsl:when>
   <xsl:otherwise>
    <xsl:apply-templates select="." mode="pure"/>
@@ -60,240 +102,898 @@
  </xsl:choose>
 </xsl:template>
 
-<!-- ALL this elements have inner type -->
-<xsl:template match="CAST|APPLY|MUTCASE|FIX|COFIX" mode="noannot">
+<!-- ALL these elements have inner type -->
+<xsl:template match="LETIN|CAST|APPLY|MUTCASE|FIX|COFIX" mode="noannot">
+ <xsl:variable name="id" select="@id"/>
  <xsl:choose>
-  <!-- <xsl:when test="//InnerTypes and key('typeid',@id)"> -->
-  <!-- <xsl:when test="//InnerTypes/TYPE[@of=$id]"> -->
-  <xsl:when test="//InnerTypes and @sort='Prop'">
-   <xsl:call-template name="has_inner_type"/>
+  <xsl:when test="$naturalLanguage='yes' and @sort='Prop'">
+   <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:for-each select="$InnerTypes">
+     <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+    </xsl:for-each>
+   </m:apply>
   </xsl:when>
   <xsl:otherwise>
-   <xsl:apply-templates select="." mode="pure"/>
+   <xsl:choose>
+    <xsl:when test="name()='APPLY'">
+     <!-- 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"/>
+    </xsl:otherwise>
+   </xsl:choose>
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<!-- si presuppone che il tipo induttivo non sia mutuamente 
+     induttivo. Bisognerebbe andare a vedere l'ultimo 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 name="has_inner_type">
+<xsl:template mode="proof_transform" match="*">
+ <xsl:choose>
+  <xsl:when test="name()='APPLY'">
    <xsl:variable name="id" select="@id"/>
    <xsl:choose>
-    <xsl:when test="name()= 'APPLY' and CONST[
+    <!-- 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>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>
+    <!-- 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>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="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 helm:xref="{@id}">
-      <m:csymbol>thread</m:csymbol>
-      <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
       <m:apply>
        <m:csymbol>rw_step</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
        <xsl:apply-templates mode="pure" select="*[3]"/>
        <xsl:apply-templates mode="pure" select="*[6]"/>
-       <xsl:apply-templates mode="pure" select="*[7]"/>
+       <xsl:call-template name="generate_side_proof">
+        <xsl:with-param name="proof" select="*[7]"/>
+       </xsl:call-template>
+       <!-- <xsl:apply-templates mode="proof_transform" select="*[7]"/> -->
       </m:apply>
-      <xsl:apply-templates mode="thread" select="*[5]"/>
+    </xsl:when>
+    <!-- EQUALITY with extra-parameters -->
+    <xsl:when test="CONST[
+ attribute::uri='cic:/Coq/Init/Logic/Equality/eq_ind.con' or
+ attribute::uri='cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con' or
+ attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
+ attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind_r.con' or
+ attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) > 7">
+      <xsl:variable name="no_extraproofs" select="count(*[position()>7 and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>      
+      <xsl:choose>
+       <xsl:when test="$no_extraproofs=0"> 
+        <m:apply>
+         <m:csymbol>rewrite_and_apply</m:csymbol>
+         <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: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>
+       </xsl:when>
+       <xsl:otherwise>
+        <xsl:choose>
+         <xsl:when test="*[5]/@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" select="'h1'"/>
+             </xsl:call-template>
+            </m:ci>
+            <xsl:apply-templates mode="noannot" select="*[5]"/>
+           </m:apply>
+           <xsl:call-template name="gen_let">
+            <xsl:with-param name="init_pos" select="1"/>
+            <xsl:with-param name="from" select="7"/>
+           </xsl:call-template>
+           <m:apply>
+            <m:csymbol>rewrite_and_apply</m:csymbol>
+            <m:apply>
+             <m:csymbol>rw_step</m:csymbol>
+             <m:ci>
+              <xsl:call-template name="insert_subscript">
+               <xsl:with-param name="node_value" select="'h1'"/>
+              </xsl:call-template>
+             </m:ci>
+             <xsl:apply-templates mode="pure" select="*[3]"/>
+             <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">
+              <xsl:value-of select="2"/>
+             </xsl:with-param>
+            </xsl:apply-templates>
+           </m:apply>
+          </m:apply>
+         </xsl:when>
+         <xsl:otherwise>
+          <m:apply helm:xref="{@id}">
+           <m:csymbol>letin</m:csymbol>
+           <xsl:call-template name="gen_let">
+            <xsl:with-param name="init_pos" select="0"/>
+            <xsl:with-param name="form" select="7"/>
+           </xsl:call-template>
+           <m:apply>
+            <m:csymbol>rewrite_and_apply</m:csymbol>
+            <m:apply>
+             <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: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">
+              <xsl:value-of select="1"/>
+             </xsl:with-param>
+            </xsl:apply-templates>
+           </m:apply>
+          </m:apply>
+         </xsl:otherwise>
+        </xsl:choose>
+       </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' 
  and name(*[5]/target/*[1])='LAMBDA'"> 
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>and_ind</m:csymbol>
-      <xsl:apply-templates mode="noannot" select="*[6]"/>
-      <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
-      <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
-      <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/LAMBDA/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
-      <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
-      <xsl:apply-templates mode="noannot" select="*[5]/target/LAMBDA/target/*"/>
-     </m:apply>
+      <m:apply helm:xref="{@id}">
+       <m:csymbol>and_ind</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[6]"/>
+       <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
+       <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
+       <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/LAMBDA/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
+       <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
+       <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/TYPE[@of=$id]/*"/>
-      <xsl:apply-templates mode="pure" select="*[5]"/>
-      <xsl:apply-templates mode="pure" select="*[6]"/>
-     </m:apply>
+      <xsl:choose>
+       <xsl:when test="name(*[5])='LAMBDA' 
+                 and name(*[6])='LAMBDA'">
+        <xsl:variable name="definition_url" 
+            select="'cic:/Coq/Init/Logic/Disjunction/or.ind'"/>
+        <m:apply helm:xref="{@id}">
+         <m:csymbol>full_or_ind</m:csymbol>
+         <xsl:apply-templates mode="noannot" select="*[7]"/>
+         <xsl:for-each select="$InnerTypes">
+          <xsl:apply-templates mode="pure" select="key('typeid',$id)/*[1]"/>
+         </xsl:for-each>
+         <m:apply>
+          <m:csymbol>left_case</m:csymbol>
+          <m:bvar>
+           <m:ci>
+            <xsl:value-of select="*[5]/target/@binder"/>
+           </m:ci>
+           <m:type>
+            <xsl:apply-templates mode="pure" select="*[5]/source/*[1]"/>
+           </m:type>
+          </m:bvar>
+          <xsl:apply-templates mode="noannot" select="*[5]/target/*[1]"/>
+         </m:apply>
+         <m:apply>
+          <m:csymbol>right_case</m:csymbol>
+          <m:bvar>
+           <m:ci>
+            <xsl:apply-templates mode="pure" select="*[6]/target/@binder"/>
+           </m:ci>
+           <m:type>
+            <xsl:apply-templates mode="pure" select="*[6]/source/*[1]"/>
+           </m:type>
+          </m:bvar>
+          <xsl:apply-templates mode="noannot" select="*[6]/target/*[1]"/>
+         </m:apply>
+        </m:apply>
+       </xsl:when>
+       <xsl:otherwise>
+        <m:apply helm:xref="{@id}">
+         <m:csymbol>or_ind</m:csymbol>
+         <xsl:apply-templates mode="noannot" select="*[7]"/>
+         <xsl:for-each select="$InnerTypes">
+          <xsl:apply-templates mode="pure" select="key('typeid',$id)/*[1]"/>
+         </xsl:for-each>
+         <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' 
  and name(*[5]/target/*[1])='LAMBDA'"> 
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>ex_ind</m:csymbol>
-      <xsl:apply-templates mode="noannot" select="*[6]"/>
-      <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
-      <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
-      <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/LAMBDA/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
-      <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
-      <xsl:apply-templates mode="noannot" select="*[5]/target/LAMBDA/target/*"/>
-     </m:apply>
+      <m:apply helm:xref="{@id}">
+       <m:csymbol>ex_ind</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[6]"/>
+       <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
+       <xsl:apply-templates mode="pure" select="*[5]/source/*"/>
+       <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="*[5]/target/LAMBDA/target/@binder"/></xsl:with-param></xsl:call-template></m:ci>
+       <xsl:apply-templates mode="pure" select="*[5]/target/LAMBDA/source/*"/>
+       <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>
-    <!-- Threads -->
-    <!-- <xsl:when test="count(*[@id = //InnerTypes/TYPE/@of]) = 1"> -->
-    <xsl:when test="count(*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]) = 1">
+    <!-- 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>thread</m:csymbol>
-      <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
+      <m:csymbol>letin</m:csymbol>
       <m:apply>
-       <m:csymbol>app</m:csymbol>
-       <xsl:apply-templates mode="copy-of-no-prop" select="*[1]"/>
+       <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="thread" select="*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]"/>
+      <xsl:apply-templates mode="proof_transform" select="*[1]/target/*[1]"/>
      </m:apply>
     </xsl:when>
     <xsl:otherwise>
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>proof</m:csymbol>
-      <xsl:apply-templates select="." mode="pure"/>
-      <!-- <xsl:apply-templates select="key('typeid',@id)" mode="pure"/> -->
-      <xsl:apply-templates select="//InnerTypes/TYPE[@of=$id]/*" mode="pure"/>
-     </m:apply>
+     <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 match="*" mode="copy-of-no-prop">
+<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($proof/*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]) = 0))"/>
  <xsl:choose>
-  <!-- <xsl:when test="@id = //InnerTypes/TYPE/@of"> -->
-  <xsl:when test="@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
-   <m:ci>previous</m:ci>
+  <xsl:when test="$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="$proof" mode="pure"/>
+    </xsl:otherwise>
+   </xsl:choose>
   </xsl:when>
   <xsl:otherwise>
-   <xsl:apply-templates select="." mode="pure"/>
+   <xsl:variable name="id" select="@id"/>
+   <m:apply helm:xref="{@id}">
+    <xsl:choose>
+     <xsl:when test="$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="$proof"/>
+    <xsl:for-each select="$InnerTypes">
+     <xsl:apply-templates mode="pure" select="key('typeid',$proof/@id)/*"/>
+    </xsl:for-each>
+   </m:apply>
+   <!-- <xsl:apply-templates select="$proof" mode="noannot"/> -->
   </xsl:otherwise>
  </xsl:choose>
- <xsl:apply-templates mode="copy-of-no-prop" select="following-sibling::*[1]"/>
 </xsl:template>
 
-<xsl:template match="*" mode="thread">
-  <xsl:choose>
-   <xsl:when test="name()= 'APPLY' and CONST[
- attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
- attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) = 7">
-    <xsl:variable name="id" select="@id"/>
-     <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
-     <m:apply>
-      <m:csymbol>rw_step</m:csymbol>
-      <xsl:apply-templates mode="pure" select="*[3]"/>
-      <xsl:apply-templates mode="pure" select="*[6]"/>
-      <xsl:apply-templates mode="pure" select="*[7]"/>
+<xsl:template match="APPLY" mode="letin">
+   <xsl:variable name="no_subproofs">
+    <xsl:variable name="stars">
+     <xsl:for-each select="*[@sort='Prop']">
+      <xsl:variable name="id" select="@id"/>
+      <xsl:variable name="innertype_available">
+       <xsl:for-each select="$InnerTypes">
+        <xsl:if test="key('typeid',$id)/*">
+         <xsl:text>yes</xsl:text>
+        </xsl:if>
+       </xsl:for-each>
+      </xsl:variable>
+      <xsl:if test="name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX' or ((name(.)='REL' or name(.)='VAR' or name(.)='META' or name(.)='CONST' or name(.)='MUTCONSTRUCT') and $innertype_available='yes')">
+       <!-- We generate one star for each subproof -->
+       <xsl:text>*</xsl:text>
+      </xsl:if>
+     </xsl:for-each>
+    </xsl:variable>
+    <xsl:value-of select="string-length($stars)"/>
+   </xsl:variable>
+   <!-- <m:cn><xsl:value-of select="$no_subproofs"/></m:cn> -->
+   <xsl:choose>
+    <xsl:when test="$naturalLanguage='yes' and ($no_subproofs = 1)">
+     <m:apply helm:xref="{@id}">
+      <m:csymbol>letin1</m:csymbol>
+      <xsl:for-each select="*[@sort='Prop']">
+       <xsl:variable name="id" select="@id"/>
+       <xsl:variable name="innertype_available">
+        <xsl:for-each select="$InnerTypes">
+         <xsl:if test="key('typeid',$id)/*">
+          <xsl:text>yes</xsl:text>
+         </xsl:if>
+        </xsl:for-each>
+       </xsl:variable>
+       <xsl:if test="name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX' or ((name(.)='REL' or name(.)='VAR' or name(.)='META' or name(.)='CONST' or name(.)='MUTCONSTRUCT') and $innertype_available='yes')">
+        <xsl:apply-templates mode="noannot" select="."/>
+       </xsl:if>
+      </xsl:for-each>
+      <!-- now re-process the application -->
+      <m:apply helm:xref="{@id}">
+       <m:csymbol>app</m:csymbol>
+       <!-- mode previous looks for siblings: 
+            call with the first child -->
+       <xsl:apply-templates mode="previous" select="*[1]"/>
+      </m:apply>
      </m:apply>
-     <xsl:apply-templates mode="thread" select="*[5]"/>
-   </xsl:when>
-<!--**** Patch temporanea, per il problema dei threads ***-->
-<xsl:when test="(name()= 'APPLY' and 
- (CONST[attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con'] or
-  CONST[attribute::uri='cic:/Coq/Init/Logic_Type/exT_ind.con'] or
-  CONST[attribute::uri='cic:/Coq/Init/Logic/First_order_quantifiers/ex_ind.con'])
- and count(child::*) = 6 
- and name(*[5])='LAMBDA' 
- and name(*[5]/target/*[1])='LAMBDA')
- or
-(name()= 'APPLY' and CONST[
- attribute::uri='cic:/Coq/Init/Logic/Disjunction/or_ind.con'] 
- and count(child::*) = 7)">
- <xsl:apply-templates mode="noannot" select="."/>
-</xsl:when>
-<!--**** Fine Patch temporanea, per il problema dei threads ***-->
-   <xsl:when test="//InnerTypes and count(*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]) = 1">
+    </xsl:when>
+    <xsl:when test="$naturalLanguage='yes' and ($no_subproofs > 1)">
+     <m:apply helm:xref="{@id}">
+      <m:csymbol>letin</m:csymbol>
+      <!-- first process all subproofs (let-in) -->
+      <xsl:call-template name="gen_let"/>
+      <!-- now re-process the application  -->
+      <m:apply helm:xref="{@id}">
+       <m:csymbol>app</m:csymbol>
+       <!-- mode flat looks for siblings: call with the first child -->
+       <xsl:apply-templates mode="flat" select="*[1]"/>
+      </m:apply>
+     </m:apply>
+    </xsl:when>
+    <xsl:otherwise>
+     <xsl:choose>
+     <xsl:when test="@sort='Prop'">
+      <m:apply>
+       <m:csymbol>app</m:csymbol>
+       <xsl:apply-templates mode="erase" select="*[1]"/>
+      </m:apply>
+     </xsl:when>
+     <xsl:otherwise>
+      <xsl:apply-templates mode="pure" select="."/>
+     </xsl:otherwise>
+     </xsl:choose>
+    </xsl:otherwise>
+   </xsl:choose>
+</xsl:template>
+
+<xsl:template name="gen_let">
+ <xsl:param name="init_pos" select="0"/>
+ <xsl:param name="from" select="0"/>
+      <xsl:for-each select="*[position()>$from and @sort='Prop']">
        <xsl:variable name="id" select="@id"/>
-       <m:apply helm:xref="{@id}">
-        <m:csymbol>thread</m:csymbol>
-        <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
+       <xsl:variable name="innertype_available">
+        <xsl:for-each select="$InnerTypes">
+         <xsl:if test="key('typeid',$id)/*">
+          <xsl:text>yes</xsl:text>
+         </xsl:if>
+        </xsl:for-each>
+       </xsl:variable>
+       <xsl:if test="name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX' or ((name(.)='REL' or name(.)='VAR' or name(.)='META' or name(.)='CONST' or name(.)='MUTCONSTRUCT') and $innertype_available='yes')">
         <m:apply>
-         <m:csymbol>app</m:csymbol>
-         <xsl:apply-templates mode="copy-of-no-prop" select="*[1]"/>
+         <m:csymbol>let</m:csymbol>
+         <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',position()+$init_pos)"/></xsl:with-param></xsl:call-template></m:ci>
+         <xsl:apply-templates mode="noannot" select="."/>
         </m:apply>
-        <!-- <xsl:apply-templates mode="thread" select="*[@id = //InnerTypes/TYPE/@of]"/> -->
-        <xsl:apply-templates mode="thread" select="*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]"/>
-       </m:apply>
+       </xsl:if>
+      </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>
-    <xsl:apply-templates mode="noannot" select="."/>
+    <m:ci>.</m:ci>
    </xsl:otherwise>
-  </xsl:choose>
+   </xsl:choose>
+ <xsl:apply-templates mode="erase" select="following-sibling::*[1]"/>
 </xsl:template>
 
+<xsl:template match="*" mode="previous">
+ <xsl:variable name="innertype_available">
+  <xsl:variable name="id" select="@id"/>
+  <xsl:for-each select="$InnerTypes">
+   <xsl:if test="key('typeid',$id)/*">
+    <xsl:text>yes</xsl:text>
+   </xsl:if>
+  </xsl:for-each>
+ </xsl:variable>
+ <xsl:choose>
+  <xsl:when test="@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX' or ((name(.)='REL' or name(.)='VAR' or name(.)='META' or name(.)='CONST' or name(.)='MUTCONSTRUCT') and $innertype_available='yes'))">
+   <m:ci>previous</m:ci>
+  </xsl:when>
+  <xsl:otherwise>
+   <!-- 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]"/>
+</xsl:template>
 
-<!-- Basic proof operators -->
-
-<!-- non del tutto soddisfacente, ma .... -->
-<xsl:template match="APPLY[CONST[
- attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
- attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con']]" mode="appflat">
-    <xsl:choose>
-     <xsl:when test="count(child::*) > 7">
-      <xsl:variable name="id" select="@id"/>
-      <xsl:variable name="ideqp" select="*[7]/@id"/>
-      <xsl:variable name="idsubp" select="*[5]/@id"/>
-<!--
-      <xsl:variable name="leteqp" select="boolean(//InnerTypes/TYPE[@of=$ideqp])"/>
-      <xsl:variable name="letsubp" select="boolean(//InnerTypes/TYPE[@of=$idsubp])"/>
--->
-      <xsl:variable name="leteqp" select="boolean(*[7][@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
-      <xsl:variable name="letsubp" select="boolean(*[5][@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>
-      <m:apply helm:xref="{@id}">
-       <m:csymbol>rewrite_and_apply</m:csymbol>
-       <m:apply>
-        <m:csymbol>rw_step</m:csymbol>
-        <xsl:apply-templates mode="pure" select="*[3]"/>
-        <xsl:apply-templates mode="pure" select="*[6]"/>
-        <xsl:choose>
-         <xsl:when test="$leteqp">
-          <xsl:choose>
-           <xsl:when test="$letsubp">
-            <m:ci>
-             <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="'h2'"/></xsl:with-param></xsl:call-template>
-            </m:ci>
-           </xsl:when>
-           <xsl:otherwise>
-            <m:ci>
-             <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="'h1'"/></xsl:with-param></xsl:call-template>
-            </m:ci>
-           </xsl:otherwise>
-          </xsl:choose>
-         </xsl:when>
-         <xsl:otherwise>
-          <xsl:apply-templates mode="pure" select="*[7]"/>
-         </xsl:otherwise>
-        </xsl:choose>
-       </m:apply>
-      <xsl:choose>
-       <xsl:when test="$letsubp">
-        <m:ci>
-         <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="'h1'"/></xsl:with-param></xsl:call-template>
-        </m:ci>
-       </xsl:when>
-       <xsl:otherwise>
-        <xsl:apply-templates mode="pure" select="*[5]"/>
-       </xsl:otherwise>
-      </xsl:choose>
-      <xsl:apply-templates mode="flat" select="*[8]">
-       <xsl:with-param name="n">
-        <xsl:value-of select="1+$letsubp+$leteqp"/>
-       </xsl:with-param>
-      </xsl:apply-templates>
-     </m:apply>
+<xsl:template match="*" mode="flat">
+ <xsl:param name="n" select="1"/>
+ <xsl:variable name="id" select="@id"/>
+ <xsl:variable name="innertype_available">
+  <xsl:for-each select="$InnerTypes">
+   <xsl:if test="key('typeid',$id)/*">
+    <xsl:text>yes</xsl:text>
+   </xsl:if>
+  </xsl:for-each>
+ </xsl:variable>
+ <xsl:choose>
+  <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX' or ((name(.)='REL' or name(.)='VAR' or name(.)='META' or name(.)='CONST' or name(.)='MUTCONSTRUCT') and $innertype_available='yes'))">
+   <m:ci>
+    <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',$n)"/></xsl:with-param></xsl:call-template>
+   </m:ci>
+   <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
+    <xsl:with-param name="n" select="$n+1"/>
+   </xsl:apply-templates>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:choose>
+    <xsl:when test="name()='REL' or @sort='Prop' or $naturalLanguage='no'">
+     <xsl:apply-templates mode="pure" select="."/>
     </xsl:when>
     <xsl:otherwise>
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>app</m:csymbol>
-      <xsl:apply-templates mode="flat" select="*[1]"/>
-     </m:apply>
+     <m:ci>.</m:ci>
     </xsl:otherwise>
    </xsl:choose>
-</xsl:template> 
+   <!-- <xsl:apply-templates mode="pure" select="."/> -->
+   <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
+    <xsl:with-param name="n" select="$n"/>
+   </xsl:apply-templates>
+  </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
 
-<xsl:template match="APPLY[CONST[
+<!-- 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">
     <xsl:choose>
      <xsl:when test="count(child::*) > 4">
@@ -313,13 +1013,7 @@
       </m:apply>
      </xsl:otherwise>
     </xsl:choose>
-</xsl:template> 
+</xsl:template>  -->
 
 
 </xsl:stylesheet>
-
-
-
-
-
-