X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fstyle%2Fproofs.xsl;h=f61cbe6d90d1ea9fece3bf22847b6a25ab8a357f;hb=1c7fb836e2af4f2f3d18afd0396701f2094265ff;hp=b3596889174ce264678da62bc43b315c02b01599;hpb=5d9c64e007c6eff9447b2ef67d2a680c86c2775d;p=helm.git

diff --git a/helm/style/proofs.xsl b/helm/style/proofs.xsl
index b35968891..f61cbe6d9 100644
--- a/helm/style/proofs.xsl
+++ b/helm/style/proofs.xsl
@@ -39,10 +39,39 @@
 <!-- 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 -->
@@ -50,12 +79,21 @@
 <!-- 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="$naturalLanguage='yes' and @sort='Prop' and name(../..) != 'LAMBDA'">
+  <xsl:when test="$naturalLanguage='yes' and @sort='Prop' and $innertype_available='yes'">
    <m:apply helm:xref="{@id}">
     <m:csymbol>proof</m:csymbol>
     <xsl:apply-templates mode="proof_transform" select="."/>
-    <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
+    <xsl:for-each select="$InnerTypes">
+     <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+    </xsl:for-each>
    </m:apply>
   </xsl:when>
   <xsl:otherwise>
@@ -65,7 +103,7 @@
 </xsl:template>
 
 <!-- ALL these elements have inner type -->
-<xsl:template match="CAST|APPLY|MUTCASE|FIX|COFIX" mode="noannot">
+<xsl:template match="LETIN|CAST|APPLY|MUTCASE|FIX|COFIX" mode="noannot">
  <xsl:variable name="id" select="@id"/>
  <xsl:choose>
   <xsl:when test="$naturalLanguage='yes' and @sort='Prop'">
@@ -73,13 +111,18 @@
     <m:csymbol>proof</m:csymbol>
     <xsl:apply-templates mode="proof_transform" select="."/>
     <!-- <xsl:apply-templates mode="try_inductive" select="."/> -->
-    <xsl:apply-templates mode="pure" select="$InnerTypes/InnerTypes/TYPE[@of=$id]/*"/>
+    <xsl:for-each select="$InnerTypes">
+     <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+    </xsl:for-each>
    </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"/>
@@ -90,7 +133,7 @@
 </xsl:template>
 
 <!-- si presuppone che il tipo induttivo non sia mutuamente 
-     induttivo. Bisognerebbe andare a vedere l'utlimo parametro
+     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
@@ -108,8 +151,9 @@
       <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="$ind_uri"/></xsl:call-template></xsl:variable>
        <xsl:variable name="inductive_def" 
-     select="document(concat(string($absPath),$ind_uri))/InductiveDefinition"/>
+     select="document($InductiveTypeUrl)/InductiveDefinition"/>
        <!-- check if the corresponding inductive definition actually
             exists -->
        <xsl:choose>
@@ -151,12 +195,293 @@
    </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>
+    <!-- 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
@@ -169,7 +494,10 @@
        <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="proof_transform" 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 -->
@@ -189,7 +517,10 @@
           <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>
@@ -223,7 +554,10 @@
              </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">
@@ -246,8 +580,11 @@
              <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">
@@ -299,8 +636,9 @@
         <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]/*"/>
+         <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>
@@ -331,8 +669,9 @@
         <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: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>
@@ -397,7 +736,10 @@
        <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:apply-templates mode="proof_transform" select="target/*[1]/*[7]"/>
+       <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>
@@ -411,15 +753,91 @@
  </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="$proof"/>
+    <xsl:for-each select="$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:template>
 
 <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')])"/>
+   <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 ($no_subproofs = 1)">
      <m:apply helm:xref="{@id}">
       <m:csymbol>letin1</m:csymbol>
-      <xsl:apply-templates mode="noannot" select="*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]"/>
+      <xsl:for-each select="*[@sort='Prop']">
+       <xsl:variable name="id" select="@id"/>
+       <xsl:variable name="innertype_available">
+        <xsl:for-each select="$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 $innertype_available='yes')">
+        <xsl:apply-templates mode="noannot" select="."/>
+       </xsl:if>
+      </xsl:for-each>
       <!-- now re-process the application -->
       <m:apply helm:xref="{@id}">
        <m:csymbol>app</m:csymbol>
@@ -461,12 +879,22 @@
 <xsl:template name="gen_let">
  <xsl:param name="init_pos" select="0"/>
  <xsl:param name="from" select="0"/>
-      <xsl:for-each select="*[position()>$from and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]">
-       <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="concat('h',position()+$init_pos)"/></xsl:with-param></xsl:call-template></m:ci>
-        <xsl:apply-templates mode="noannot" select="."/>
-       </m:apply>
+      <xsl:for-each select="*[position()>$from and @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 $innertype_available='yes')">
+        <m:apply>
+         <m:csymbol>let</m:csymbol>
+         <m:ci><xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',position()+$init_pos)"/></xsl:with-param></xsl:call-template></m:ci>
+         <xsl:apply-templates mode="noannot" select="."/>
+        </m:apply>
+       </xsl:if>
       </xsl:for-each>
 </xsl:template>
 
@@ -479,17 +907,26 @@
     <m:ci>.</m:ci>
    </xsl:otherwise>
    </xsl:choose>
- <xsl:apply-templates mode="previous" select="following-sibling::*[1]"/>
+ <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="$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="@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:when test="@sort='Prop' or $naturalLanguage='no'">
     <xsl:apply-templates mode="pure" select="."/>
    </xsl:when>
    <xsl:otherwise>
@@ -505,10 +942,15 @@
 <xsl:template match="*" mode="flat">
  <xsl:param name="n" select="1"/>
  <xsl:variable name="id" select="@id"/>
+ <xsl:variable name="innertype_available">
+  <xsl:for-each select="$InnerTypes">
+   <xsl:if test="key('typeid',$id)/*">
+    <xsl:text>yes</xsl:text>
+   </xsl:if>
+  </xsl:for-each>
+ </xsl:variable>
  <xsl:choose>
-  <!-- <xsl:when test="key('typeid',@id)"> -->
-  <!-- <xsl:when test="$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')">
+  <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>
@@ -518,12 +960,12 @@
   </xsl:when>
   <xsl:otherwise>
    <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: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]">