From 26f5337108946df050f07c68ebe9bc07b1fde173 Mon Sep 17 00:00:00 2001
From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Wed, 7 Feb 2001 16:15:46 +0000
Subject: [PATCH] New version of proof.xsl Main modif: - removed "thread" mode
 - proof management (let-in) moved from content.xsl to proofs.xsl

---
 helm/style/content.xsl      |  53 +----
 helm/style/mmlextension.xsl | 125 +++++++++---
 helm/style/proofs.xsl       | 393 +++++++++++++++++++++---------------
 3 files changed, 327 insertions(+), 244 deletions(-)

diff --git a/helm/style/content.xsl b/helm/style/content.xsl
index 6f2226bbf..5aafef63f 100644
--- a/helm/style/content.xsl
+++ b/helm/style/content.xsl
@@ -139,63 +139,12 @@ Amaya o da chi di dovere in /really_very_local/helm/PARSER/example/.../]
 </xsl:template>
 
 <xsl:template match="APPLY" mode="pure">
-   <xsl:choose>
-    <!-- <xsl:when test="//InnerTypes and boolean(key('typeid',*/@id))"> -->
-    <!-- start looking for subproofs -->
-    <!-- <xsl:when test="((*/@id) = (//InnerTypes/TYPE/@of))"> -->
-    <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')]) > 0">
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>letin</m:csymbol>
-      <!-- <xsl:for-each select="*[boolean(key('typeid',@id))]"> -->
-      <!-- first process all subproofs (let-in) -->
-      <xsl:for-each select="*[@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())"/></xsl:with-param></xsl:call-template></m:ci>
-        <xsl:apply-templates mode="noannot" select="."/>
-       </m:apply>
-      </xsl:for-each>
-      <!-- now re-process the application in mode appflat -->
-      <xsl:apply-templates mode="appflat" select="."/> 
-     </m:apply>
-    </xsl:when>
-    <xsl:otherwise>
-     <xsl:apply-templates mode="appflat" select="."/>
-    </xsl:otherwise>
-   </xsl:choose>
-</xsl:template>
-
-<xsl:template match="APPLY" mode="appflat">
       <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]"/>
+       <xsl:apply-templates mode="noannot" select="*"/>
       </m:apply>
 </xsl:template>
 
-<xsl:template match="*" mode="flat">
- <xsl:param name="n" select="1"/>
- <xsl:variable name="id" select="@id"/>
- <xsl:choose>
-  <!-- <xsl:when test="key('typeid',@id)"> -->
-  <!-- <xsl:when test="//InnerTypes/TYPE[@of=$id]"> -->
-  <xsl:when test="//InnerTypes and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
-   <m:ci>
-    <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',$n)"/></xsl:with-param></xsl:call-template>
-   </m:ci>
-   <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
-    <xsl:with-param name="n" select="$n+1"/>
-   </xsl:apply-templates>
-  </xsl:when>
-  <xsl:otherwise>
-   <xsl:apply-templates mode="pure" select="."/>
-   <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
-    <xsl:with-param name="n" select="$n"/>
-   </xsl:apply-templates>
-  </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
 <xsl:template match="VAR" mode="pure">
     <m:ci helm:xref="{@id}">
      <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="substring-after(@relUri,&quot;,&quot;)"/></xsl:with-param></xsl:call-template>
diff --git a/helm/style/mmlextension.xsl b/helm/style/mmlextension.xsl
index 90f8cca10..86675e553 100644
--- a/helm/style/mmlextension.xsl
+++ b/helm/style/mmlextension.xsl
@@ -963,6 +963,24 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <xsl:when test="$name='letin1'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:apply-templates select="*[2]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:apply-templates select="*[3]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+        </m:mtable>
+      </xsl:when>
       <xsl:when test="$name='letin'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <!-- <xsl:for-each select="APPLY[m:csymbol and (string(m:csymbol)='let')]"> -->
@@ -990,55 +1008,111 @@
        <m:mtext>) </m:mtext>
        <xsl:apply-templates select="*[3]"/>
       </xsl:when>
-      <xsl:when test="$name='thread'">
+      <xsl:when test="$name='rw_step'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
            <m:mrow>
             <xsl:choose>
-             <xsl:when test="name(*[last()])='m:apply'">
-              <xsl:apply-templates select="*[last()]"/>
+             <xsl:when test="name(*[2])='m:apply'">
+              <xsl:apply-templates select="*[2]"/>
              </xsl:when>
              <xsl:otherwise>
-              <m:mtext>Consider </m:mtext>
-              <xsl:apply-templates select="*[last()]"/>
+              <m:mtext>Consider</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[2]"/>
              </xsl:otherwise>
             </xsl:choose>
            </m:mrow>
           </m:mtd>
          </m:mtr>
-	 <xsl:apply-templates mode="thread" select="*[(last()-2)]"/> 
-        </m:mtable>
-      </xsl:when> 
-      <xsl:when test="$name='rewrite_and_apply'">
-        <m:mtable>
          <m:mtr>
           <m:mtd>
            <m:mrow>
             <m:mtext>Rewrite</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[2]/*[2]"/>
+            <xsl:apply-templates select="*[3]"/>
 	    <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
 	    <m:mtext>with</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[2]/*[3]"/>
+            <xsl:apply-templates select="*[4]"/>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <m:mtext>by</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[2]/*[4]"/>
-            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <m:mtext>in</m:mtext>
-            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[3]"/>
-            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <m:mtext>and apply to</m:mtext>
+            <xsl:apply-templates select="*[5]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+        </m:mtable>
+      </xsl:when>
+      <xsl:when test="$name='thread'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:choose>
+             <xsl:when test="name(*[last()])='m:apply'">
+              <xsl:apply-templates select="*[last()]"/>
+             </xsl:when>
+             <xsl:otherwise>
+              <m:mtext>Consider</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[last()]"/>
+             </xsl:otherwise>
+            </xsl:choose>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+	 <xsl:apply-templates mode="thread" select="*[(last()-2)]"/> 
+        </m:mtable>
+      </xsl:when> 
+      <xsl:when test="$name='rewrite_and_apply'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:apply-templates select="*[2]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>Then apply it to</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[position()>3]"/>
+            <xsl:apply-templates select="*[position()>2]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
        </m:mtable>
-      </xsl:when> 
+      </xsl:when>
+      <!-- NAT_IND -->
+      <xsl:when test="$name='nat_ind'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+         <m:mtr>
+          <m:mtd>
+           <m:mtext>By induction</m:mtext>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>base case:</m:mtext>
+            <xsl:apply-templates select="*[2]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>inductive case:</m:mtext>
+            <xsl:apply-templates select="*[3]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+        </m:mtable>
+      </xsl:when>
+      <!-- AND_IND -->
       <xsl:when test="$name='and_ind'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1049,7 +1123,8 @@
               <xsl:apply-templates select="*[2]"/>
              </xsl:when>
              <xsl:otherwise>
-              <m:mtext>Consider </m:mtext>
+              <m:mtext>Consider</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
               <xsl:apply-templates select="*[2]"/>
              </xsl:otherwise>
             </xsl:choose>
@@ -1147,7 +1222,8 @@
               <xsl:apply-templates select="*[2]"/>
              </xsl:when>
              <xsl:otherwise>
-              <m:mtext>Consider </m:mtext>
+              <m:mtext>Consider</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
               <xsl:apply-templates select="*[2]"/>
              </xsl:otherwise>
             </xsl:choose>
@@ -1187,6 +1263,7 @@
     </m:mrow>
 </xsl:template>
 
+<!-- Il modo Thread non esiste piu' 
 <xsl:template match="*" mode="thread">
  <xsl:variable name="name"><xsl:value-of select="following-sibling::*[position()=1]/m:csymbol"/></xsl:variable>
  <xsl:choose>
@@ -1239,7 +1316,7 @@
    </xsl:choose>
          <xsl:apply-templates mode="thread" select="preceding-sibling::*[position()=2]"/>
 </xsl:template>
-
+-->
 
 <!-- LAMBDA -->
 
diff --git a/helm/style/proofs.xsl b/helm/style/proofs.xsl
index 760511fd2..6f23e3254 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                 -->
 <!--******************************************************************-->
 
@@ -34,7 +34,6 @@
                               xmlns:m="http://www.w3.org/1998/Math/MathML"
                               xmlns:helm="http://www.cs.unibo.it/helm">
 
-
 <!-- ************************* LOGIC *********************************-->
 
 <!-- Proof objects -->
@@ -46,13 +45,18 @@
 <xsl:apply-templates select="." mode="pure"/>
 </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:choose>
   <xsl:when test="//InnerTypes and @sort='Prop' and name(../..) != 'LAMBDA'">
-  <!-- <xsl:when test="@sort='Prop' and //InnerTypes/TYPE[@of=$id]"> -->
-   <xsl:call-template name="has_inner_type"/>
+   <m:apply helm:xref="{@id}">
+    <m:csymbol>proof</m:csymbol>
+    <xsl:apply-templates mode="proof_transform" select="."/>
+    <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
+   </m:apply>
   </xsl:when>
   <xsl:otherwise>
    <xsl:apply-templates select="." mode="pure"/>
@@ -60,37 +64,148 @@
  </xsl:choose>
 </xsl:template>
 
-<!-- ALL this elements have inner type -->
+<!-- ALL these elements have inner type -->
 <xsl:template match="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=$id]"> -->
   <xsl:when test="//InnerTypes and @sort='Prop'">
-   <xsl:call-template name="has_inner_type"/>
+   <m:apply helm:xref="{@id}">
+    <m:csymbol>proof</m:csymbol>
+    <xsl:apply-templates mode="proof_transform" select="."/>
+    <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
+   </m:apply>
   </xsl:when>
   <xsl:otherwise>
-   <xsl:apply-templates select="." mode="pure"/>
+   <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:otherwise>
  </xsl:choose>
 </xsl:template>
 
-<xsl:template name="has_inner_type">
+<xsl:template mode="proof_transform" match="*">
    <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">
+     <m:apply>
+      <m:csymbol>nat_ind</m:csymbol>
+      <xsl:apply-templates mode="noannot" select="*[3]"/>
+      <xsl:apply-templates mode="noannot" select="*[4]"/>
+     </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">
+     <m:apply>
+      <m:csymbol>nat_ind</m:csymbol>
+      <xsl:apply-templates mode="noannot" select="*[3]"/>
+      <xsl:apply-templates mode="noannot" select="*[4]"/>
+     </m:apply>
+    </xsl:when>
+    <!-- EQUALITY -->
     <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">
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>thread</m:csymbol>
-      <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
       <m:apply>
        <m:csymbol>rw_step</m:csymbol>
+       <xsl:apply-templates mode="noannot" select="*[5]"/>
        <xsl:apply-templates mode="pure" select="*[3]"/>
        <xsl:apply-templates mode="pure" select="*[6]"/>
        <xsl:apply-templates mode="pure" select="*[7]"/>
       </m:apply>
-      <xsl:apply-templates mode="thread" select="*[5]"/>
-     </m:apply>
+    </xsl:when>
+    <!-- EQUALITY with extra-parameters -->
+    <xsl:when test="name()= 'APPLY' and CONST[
+ attribute::uri='cic:/Coq/Init/Logic_Type/eqT_ind.con' or
+ attribute::uri='cic:/Coq/Zarith/auxiliary/eqT_ind_r.con'] and count(child::*) > 7">
+      <xsl:variable name="no_extraproofs" select="count(*[position()>7 and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')])"/>      
+      <xsl:choose>
+       <xsl:when test="$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: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: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: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>
     <!-- gestire meglio il caso di and_ind quando la prova 
          non e' della forma \x.\y.M -->
@@ -99,15 +214,15 @@
  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[
  attribute::uri='cic:/Coq/Init/Logic/Disjunction/or_ind.con'] 
@@ -121,179 +236,121 @@
      </m:apply>
     </xsl:when>
     <!-- ex_ind, exT_ind -->
-    <xsl:when test="name()= 'APPLY' 
+      <xsl:when test="name()= 'APPLY' 
  and (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="proof_transform" select="*[5]/target/LAMBDA/target/*"/>
+      </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: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')])"/>
+   <!-- <m:cn><xsl:value-of select="$no_subproofs"/></m:cn> -->
+   <xsl:choose>
+    <xsl:when test="//InnerTypes and ($no_subproofs = 1)">
      <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: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')]"/>
+      <!-- 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: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">
+    <xsl:when test="//InnerTypes and ($no_subproofs > 1)">
      <m:apply helm:xref="{@id}">
-      <m:csymbol>thread</m:csymbol>
-      <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
-      <m:apply>
+      <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>
-       <xsl:apply-templates mode="copy-of-no-prop" select="*[1]"/>
+       <!-- mode flat looks for siblings: call with the first child -->
+       <xsl:apply-templates mode="flat" select="*[1]"/>
       </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')]"/>
      </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 mode="pure" select="."/>
     </xsl:otherwise>
    </xsl:choose>
 </xsl:template>
 
-<xsl:template match="*" mode="copy-of-no-prop">
+<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>
+</xsl:template>
+
+<xsl:template match="*" mode="previous">
  <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')">
+  <xsl:when test="//InnerTypes 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"/>
   </xsl:otherwise>
  </xsl:choose>
- <xsl:apply-templates mode="copy-of-no-prop" select="following-sibling::*[1]"/>
+ <xsl:apply-templates mode="previous" 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=$id]/*"/>
-     <m:apply>
-      <m:csymbol>rw_step</m:csymbol>
-      <xsl:apply-templates mode="pure" select="*[3]"/>
-      <xsl:apply-templates mode="pure" select="*[6]"/>
-      <xsl:apply-templates mode="pure" select="*[7]"/>
-     </m:apply>
-     <xsl:apply-templates mode="thread" select="*[5]"/>
-   </xsl:when>
-<!--**** Patch temporanea, per il problema dei threads ***-->
-<xsl:when test="(name()= 'APPLY' and 
- (CONST[attribute::uri='cic:/Coq/Init/Logic/Conjunction/and_ind.con'] or
-  CONST[attribute::uri='cic:/Coq/Init/Logic_Type/exT_ind.con'] or
-  CONST[attribute::uri='cic:/Coq/Init/Logic/First_order_quantifiers/ex_ind.con'])
- and count(child::*) = 6 
- and name(*[5])='LAMBDA' 
- and name(*[5]/target/*[1])='LAMBDA')
- or
-(name()= 'APPLY' and CONST[
- attribute::uri='cic:/Coq/Init/Logic/Disjunction/or_ind.con'] 
- and count(child::*) = 7)">
- <xsl:apply-templates mode="noannot" select="."/>
-</xsl:when>
-<!--**** Fine Patch temporanea, per il problema dei threads ***-->
-   <xsl:when test="//InnerTypes and count(*[@sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')]) = 1">
-       <xsl:variable name="id" select="@id"/>
-       <m:apply helm:xref="{@id}">
-        <m:csymbol>thread</m:csymbol>
-        <xsl:apply-templates mode="pure" select="//InnerTypes/TYPE[@of=$id]/*"/>
-        <m:apply>
-         <m:csymbol>app</m:csymbol>
-         <xsl:apply-templates mode="copy-of-no-prop" select="*[1]"/>
-        </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:when>
-   <xsl:otherwise>
-    <xsl:apply-templates mode="noannot" select="."/>
-   </xsl:otherwise>
-  </xsl:choose>
+<xsl:template match="*" mode="flat">
+ <xsl:param name="n" select="1"/>
+ <xsl:variable name="id" select="@id"/>
+ <xsl:choose>
+  <!-- <xsl:when test="key('typeid',@id)"> -->
+  <!-- <xsl:when test="//InnerTypes/TYPE[@of=$id]"> -->
+  <xsl:when test="//InnerTypes and @sort='Prop' and (name(.)='LAMBDA' or name(.)='LETIN' or name(.)='APPLY' or name(.)='MUTCASE' or name(.)='FIX' or name(.)='COFIX')">
+   <m:ci>
+    <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="concat('h',$n)"/></xsl:with-param></xsl:call-template>
+   </m:ci>
+   <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
+    <xsl:with-param name="n" select="$n+1"/>
+   </xsl:apply-templates>
+  </xsl:when>
+  <xsl:otherwise>
+   <xsl:apply-templates mode="pure" select="."/>
+   <xsl:apply-templates mode="flat" select="following-sibling::*[1]">
+    <xsl:with-param name="n" select="$n"/>
+   </xsl:apply-templates>
+  </xsl:otherwise>
+ </xsl:choose>
 </xsl:template>
 
 
-<!-- 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:when>
-    <xsl:otherwise>
-     <m:apply helm:xref="{@id}">
-      <m:csymbol>app</m:csymbol>
-      <xsl:apply-templates mode="flat" select="*[1]"/>
-     </m:apply>
-    </xsl:otherwise>
-   </xsl:choose>
-</xsl:template> 
-
-<xsl:template match="APPLY[CONST[
+<!-- <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">
@@ -313,7 +370,7 @@
       </m:apply>
      </xsl:otherwise>
     </xsl:choose>
-</xsl:template> 
+</xsl:template>  -->
 
 
 </xsl:stylesheet>
-- 
2.39.2