X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fstyle%2Fmmlextension.xsl;h=4a801a65402c244e03bbe273c6a4d7a7ba1709a3;hb=1c7fb836e2af4f2f3d18afd0396701f2094265ff;hp=5537076fb7173ef65fb617fda37cbb422f2e31d5;hpb=07fa5c704b876f1e84af3013de37a9fa269c1d86;p=helm.git

diff --git a/helm/style/mmlextension.xsl b/helm/style/mmlextension.xsl
index 5537076fb..4a801a654 100644
--- a/helm/style/mmlextension.xsl
+++ b/helm/style/mmlextension.xsl
@@ -32,11 +32,21 @@
 <!-- Revised: March 21 2000, Irene Schena                                  -->
 <!--***********************************************************************--> 
 
+<!-- NOTE: the namespace declaration has to be done in the stylesheets 
+which generates the toplevel element (see for instance xlink) -->
 <xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
                               xmlns:m="http://www.w3.org/1998/Math/MathML"
-                              xmlns:helm="http://www.cs.unibo.it/helm">
+                              xmlns:helm="http://www.cs.unibo.it/helm"
+                              xmlns:xlink="http://www.w3.org/1999/xlink">
 
-<xsl:import href="mml2mmlv1_0.xsl"/>
+<!-- OLD: <xsl:import href="mml2mmlv1_0.xsl"/> -->
+
+<xsl:import href="mmlnotation.xsl"/>
+
+<xsl:import href="mmltheoryextension.xsl"/>
+
+
+<xsl:param name="explodeall" select="false()"/>
 
 <!--***********************************************************************-->
 <!-- Parameter affecting line-breaking                                     -->
@@ -56,9 +66,19 @@
 <!--        OBJECTS       -->
 <!--**********************-->
 
+<xsl:param name="type" select="'standalone'"/>
+
 <xsl:template match="/">
- <xsl:processing-instruction name="cocoon-format">type="text/xhtml"</xsl:processing-instruction>
- <xsl:apply-templates select="*"/>
+ <xsl:choose>
+  <xsl:when test="$type = 'standalone'">
+   <xsl:apply-templates select="*"/>
+  </xsl:when>
+  <xsl:otherwise>
+   <to_be_embedded>
+    <xsl:apply-templates select="*"/>
+   </to_be_embedded>
+  </xsl:otherwise> 
+ </xsl:choose>
 </xsl:template>
 
 <!-- DEFINITION -->
@@ -161,10 +181,54 @@
       <xsl:for-each select="Conjecture">
       <m:mtr>
        <m:mtd>
-        <m:mrow>
+        <m:mrow helm:xref="{@helm:xref}">
          <m:mphantom><m:mtext>__</m:mtext></m:mphantom>
-         <m:mtext><xsl:value-of select="./@no"/>:</m:mtext>
-         <xsl:apply-templates select="./*[1]"/>
+         <xsl:for-each select="Decl|Def|Hidden">
+          <xsl:choose>
+           <xsl:when test="name(.)='Decl'">
+            <m:mrow helm:xref="{@helm:xref}">
+             <xsl:choose>
+              <xsl:when test="@name">
+               <m:mi><xsl:value-of select="@name"/></m:mi>
+              </xsl:when>
+              <xsl:otherwise>
+               <m:mi>_</m:mi>
+              </xsl:otherwise>
+             </xsl:choose>
+             <m:mo>:</m:mo>
+             <xsl:apply-templates select="./*[1]"/>
+            </m:mrow>
+           </xsl:when>
+           <xsl:when test="name(.)='Def'">
+            <m:mrow helm:xref="{@helm:xref}">
+             <xsl:choose>
+              <xsl:when test="@name">
+               <m:mi><xsl:value-of select="@name"/></m:mi>
+              </xsl:when>
+              <xsl:otherwise>
+               <m:mi>_</m:mi>
+              </xsl:otherwise>
+             </xsl:choose>
+             <m:mo>:=</m:mo>
+             <xsl:apply-templates select="./*[1]"/>
+            </m:mrow>
+           </xsl:when>
+           <xsl:otherwise>
+            <m:mrow helm:xref="{@helm:xref}">
+             <m:mi>_</m:mi>
+             <m:mo>:?</m:mo>
+             <m:mi>_</m:mi>
+            </m:mrow>
+           </xsl:otherwise>
+          </xsl:choose>
+          <xsl:if test="not (position() = last())">
+           <m:mo>;</m:mo>
+          </xsl:if>
+         </xsl:for-each>
+         <m:mo>|-</m:mo>
+         <m:msub><m:mi>?</m:mi><m:mn><xsl:value-of select="@no"/></m:mn></m:msub>
+         <m:mo>:</m:mo>
+         <xsl:apply-templates select="./Goal/*[1]"/>
         </m:mrow>
        </m:mtd>
       </m:mtr>
@@ -172,7 +236,7 @@
       <m:mtr>
        <m:mtd>
         <m:mrow>
-         <m:mtext>CORRESPONDING PROOF:</m:mtext>
+         <m:mtext>PROOF:</m:mtext>
         </m:mrow>
        </m:mtd>
       </m:mtr>
@@ -340,6 +404,61 @@
     </m:math>
 </xsl:template>
 
+<!-- SEQUENT -->
+
+<xsl:template match="Sequent">
+ <xsl:variable name="rowlines">
+  <xsl:for-each select="Decl|Def">
+   <xsl:if test="position() != last()">
+    <xsl:text>none </xsl:text>
+   </xsl:if>
+  </xsl:for-each>
+  <xsl:text>solid</xsl:text>
+ </xsl:variable>
+ <xsl:variable name="no" select="@no"/>
+    <m:math>
+     <m:mi><xsl:text>?</xsl:text><xsl:value-of select="$no"/></m:mi>
+     <m:mo>:</m:mo>
+     <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+     <m:mtable align="baseline 1" equalrows="false" columnalign="left" helm:xref="{@helm:xref}" rowlines="{$rowlines}">
+      <xsl:for-each select="Decl|Def">
+       <m:mtr>
+        <m:mtd>
+         <m:mrow helm:xref="{@helm:xref}">
+          <m:mi><xsl:value-of select="@name"/></m:mi>
+          <xsl:choose>
+           <xsl:when test="name(.) = 'Decl'">
+            <m:mo>:</m:mo>
+           </xsl:when>
+           <xsl:otherwise>
+            <m:mo>:=</m:mo>
+           </xsl:otherwise>
+          </xsl:choose>
+          <xsl:apply-templates select="*[1]"/>
+         </m:mrow>
+        </m:mtd>
+       </m:mtr>
+      </xsl:for-each>
+      <xsl:if test="not(Decl|Def)">
+      <m:mtr>
+       <m:mtd>
+        <m:mrow>
+         <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+        </m:mrow>
+       </m:mtd>
+      </m:mtr>
+      </xsl:if>
+      <m:mtr>
+       <m:mtd>
+        <m:mrow>
+         <xsl:apply-templates select="Goal/*[1]"/>
+        </m:mrow>
+       </m:mtd>
+      </m:mtr>
+     </m:mtable>
+    </m:math>
+</xsl:template>
+
 <!--**********************-->
 <!--        TERMS         -->
 <!--**********************-->
@@ -355,21 +474,27 @@
      <m:mtable align="baseline 1" equalrows="false" columnalign="left">
       <m:mtr>
        <m:mtd>
-        <xsl:apply-templates select="m:ci"/>
-        <m:mo>:</m:mo>
+        <m:mrow>
+         <xsl:apply-templates select="m:ci"/>
+         <m:mo>:</m:mo>
+        </m:mrow>
        </m:mtd>
       </m:mtr>
       <m:mtr>
        <m:mtd>
+        <m:mrow>
          <xsl:apply-templates select="m:type"/>
+        </m:mrow>
        </m:mtd>
       </m:mtr>
      </m:mtable>
     </xsl:when>
     <xsl:otherwise>
-     <xsl:apply-templates select="m:ci"/>
-     <m:mo>:</m:mo>
-     <xsl:apply-templates select="m:type"/>
+     <m:mrow>
+      <xsl:apply-templates select="m:ci"/>
+      <m:mo>:</m:mo>
+      <xsl:apply-templates select="m:type"/>
+     </m:mrow>
     </xsl:otherwise>
    </xsl:choose>
   </xsl:when>
@@ -383,21 +508,35 @@
 <!-- CSYMBOL -->
 
 <xsl:template match="m:apply[m:csymbol]">
+<xsl:param name="nopar" select="0"/>
     <xsl:variable name="name"><xsl:value-of select="m:csymbol"/></xsl:variable>
     <xsl:variable name="charlength"><xsl:apply-templates select="m:csymbol" mode="charcount"/></xsl:variable>
     <m:mrow>
-     <xsl:if test="@helm:xref">
-      <xsl:attribute name="helm:xref"><xsl:value-of select="@helm:xref"/></xsl:attribute>
+     <xsl:if test="@id">
+      <xsl:attribute name="xref"><xsl:value-of select="@id"/></xsl:attribute>
      </xsl:if>
+     <xsl:variable name="id" select="m:csymbol/@id"/>
      <xsl:choose>
+      <!-- META -->
+      <xsl:when test="$name='meta'">
+       <m:mrow>
+        <xsl:apply-templates select="*[position()=2]"/>
+        <m:mfenced open="[" close="]" separators=";">
+         <xsl:apply-templates select="*[position()>2]"/>
+        </m:mfenced>
+       </m:mrow>
+      </xsl:when>
+      <!-- FORALL -->
       <xsl:when test="$name='forall'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
-            <m:mo mathcolor="Blue"><m:mchar name="ForAll"/></m:mo>
+           <m:mrow>
+            <m:mo mathcolor="Blue">&#8704;</m:mo>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -411,7 +550,7 @@
         </m:mtable>
        </xsl:when>
        <xsl:otherwise>
-        <m:mo mathcolor="Blue"><m:mchar name="ForAll"/></m:mo>
+        <m:mo mathcolor="Blue">&#8704;</m:mo>
         <xsl:apply-templates select="m:bvar/m:ci"/>
         <m:mo>:</m:mo>
         <xsl:apply-templates select="m:bvar/m:type"/>
@@ -420,15 +559,18 @@
        </xsl:otherwise>
        </xsl:choose> 
       </xsl:when>
+      <!-- LET-IN -->
       <xsl:when test="$name='let_in'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
+           <m:mrow>
             <m:mo>LET</m:mo>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -463,14 +605,17 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when> 
+      <!-- PROD -->
       <xsl:when test="$name='prod'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
+           <m:mrow>
             <m:mo mathcolor="Blue">&#x03a0;</m:mo>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -493,6 +638,7 @@
        </xsl:otherwise>
        </xsl:choose> 
       </xsl:when>
+      <!-- ARROW -->
       <xsl:when test="$name='arrow'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -500,7 +646,9 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mo stretchy="false">(</m:mo>
+            <xsl:if test="$nopar=0">
+             <m:mo stretchy="false">(</m:mo>
+            </xsl:if>
             <xsl:apply-templates select="*[position()=2]"/>
            </m:mrow>
           </m:mtd>
@@ -509,10 +657,26 @@
           <m:mtd>
            <m:mrow>
             <m:mo mathmathcolor="Blue">&#x2192;</m:mo>
-            <xsl:apply-templates select="*[position()=3]"/>
+            <xsl:choose>
+            <xsl:when test="*[position()=3]/m:csymbol">
+             <xsl:variable name="nextp"><xsl:value-of select="*[position()=3]/m:csymbol"/></xsl:variable>
+             <xsl:choose>
+             <xsl:when test="$nextp='arrow'">
+              <xsl:apply-templates select="*[position()=3]"><xsl:with-param name="nopar" select="1"/></xsl:apply-templates>
+             </xsl:when>
+             <xsl:otherwise>
+              <xsl:apply-templates select="*[position()=3]"/>
+             </xsl:otherwise>
+             </xsl:choose>
+            </xsl:when>
+            <xsl:otherwise>
+             <xsl:apply-templates select="*[position()=3]"/>
+            </xsl:otherwise>
+            </xsl:choose>
            </m:mrow>
           </m:mtd>
          </m:mtr>
+         <xsl:if test="$nopar=0">
          <m:mtr>
           <m:mtd>
            <m:mrow>
@@ -520,17 +684,38 @@
            </m:mrow>
           </m:mtd>
          </m:mtr>
+         </xsl:if>
         </m:mtable>
        </xsl:when>
        <xsl:otherwise>
-        <m:mo stretchy="false">(</m:mo>
+        <xsl:if test="$nopar=0">
+         <m:mo stretchy="false">(</m:mo>
+        </xsl:if>
         <xsl:apply-templates select="*[position()=2]"/>
         <m:mo mathcolor="Blue">&#x2192;</m:mo>
-        <xsl:apply-templates select="*[position()=3]"/>
-        <m:mo stretchy="false">)</m:mo>
+        <xsl:choose>
+        <xsl:when test="*[position()=3]/m:csymbol">
+         <xsl:variable name="nextp"><xsl:value-of select="*[position()=3]/m:csymbol"/></xsl:variable>
+         <xsl:choose>
+         <xsl:when test="$nextp='arrow'">
+          <xsl:apply-templates select="*[position()=3]"><xsl:with-param name="nopar" select="1"/></xsl:apply-templates>
+         </xsl:when>
+         <xsl:otherwise>
+          <xsl:apply-templates select="*[position()=3]"/>
+         </xsl:otherwise>
+         </xsl:choose>
+        </xsl:when>
+        <xsl:otherwise>
+         <xsl:apply-templates select="*[position()=3]"/>
+        </xsl:otherwise>
+        </xsl:choose>
+        <xsl:if test="$nopar=0">
+         <m:mo stretchy="false">)</m:mo>
+        </xsl:if>
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- APP -->
       <xsl:when test="$name='app'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -539,7 +724,10 @@
           <m:mtd>
            <m:mrow>
             <m:mo stretchy="false">(</m:mo>
-            <xsl:apply-templates select="*[position()=2]"/>
+<!-- added precedence to app = FUNCTION_PREC (99) -->
+            <xsl:apply-templates select="*[position()=2]">
+             <xsl:with-param name="IN_PREC" select="$FUNCTION_PREC"/>
+            </xsl:apply-templates>
            </m:mrow>
           </m:mtd>
          </m:mtr>
@@ -548,7 +736,10 @@
           <m:mtd>
            <m:mrow>
             <m:mphantom><m:mtext>(</m:mtext></m:mphantom>
-            <xsl:apply-templates select="."/>
+<!-- added precedence to app = FUNCTION_PREC (99) -->
+            <xsl:apply-templates select=".">
+             <xsl:with-param name="IN_PREC" select="$FUNCTION_PREC"/>
+            </xsl:apply-templates>
            </m:mrow>
           </m:mtd>
          </m:mtr>
@@ -564,15 +755,22 @@
        </xsl:when>
        <xsl:otherwise>
         <m:mo stretchy="false">(</m:mo>
-        <xsl:apply-templates select="*[position()=2]"/>
+<!-- added precedence to app = FUNCTION_PREC (99) -->
+        <xsl:apply-templates select="*[position()=2]">
+         <xsl:with-param name="IN_PREC" select="$FUNCTION_PREC"/>
+        </xsl:apply-templates>
         <xsl:for-each select="*[position()>2]">
          <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-         <xsl:apply-templates select="."/>
+<!-- added precedence to app = FUNCTION_PREC (99) -->
+         <xsl:apply-templates select=".">
+          <xsl:with-param name="IN_PREC" select="$FUNCTION_PREC"/>
+         </xsl:apply-templates>
         </xsl:for-each>
         <m:mo stretchy="false">)</m:mo>
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- CAST -->
       <xsl:when test="$name='cast'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -611,15 +809,19 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- PROP -->
       <xsl:when test="$name='Prop'">
        <m:mo>Prop</m:mo>
       </xsl:when>
+      <!-- SET -->
       <xsl:when test="$name='Set'">
        <m:mo>Set</m:mo>
       </xsl:when>
+      <!-- TYPE -->
       <xsl:when test="$name='Type'">
        <m:mo>Type</m:mo>
       </xsl:when>
+      <!-- MUTCASE -->
       <xsl:when test="$name='mutcase'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -658,8 +860,8 @@
            </m:mrow>
           </m:mtd>
          </m:mtr>
-         <xsl:for-each select="*[position() mod 2 = 0 and position()>3]">
-         <xsl:variable name="charlength"><xsl:apply-templates select="." mode="charcount"><xsl:with-param name="nosibling" select="1"/></xsl:apply-templates></xsl:variable>
+         <xsl:for-each select="m:piecewise/m:piece">
+         <xsl:variable name="charlength"><xsl:apply-templates select="./*[2]" mode="charcount"><xsl:with-param name="nosibling" select="1"/></xsl:apply-templates></xsl:variable>
          <m:mtr>
           <m:mtd>
            <m:mrow>
@@ -672,10 +874,10 @@
             </xsl:otherwise>
             </xsl:choose>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="."/>
+            <xsl:apply-templates select="./*[2]"/>
             <xsl:if test="$framewidth > $charlength">
              <m:mo mathcolor="Green">&#x21d2;</m:mo>
-             <xsl:apply-templates select="following-sibling::*[position()= 1]"/>
+             <xsl:apply-templates select="./*[1]"/>
             </xsl:if>
            </m:mrow>
           </m:mtd>
@@ -686,7 +888,7 @@
            <m:mrow>
             <m:mphantom><m:mtext>|_</m:mtext></m:mphantom>  
             <m:mo mathcolor="Green">&#x21d2;</m:mo>
-            <xsl:apply-templates select="following-sibling::*[position()= 1]"/>
+            <xsl:apply-templates select="./*[1]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
@@ -708,21 +910,22 @@
         <xsl:apply-templates select="*[position()=3]"/>
         <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
         <m:mo>OF</m:mo>
-        <xsl:for-each select="*[position() mod 2 = 0 and position()>3]">
+        <xsl:for-each select="m:piecewise/m:piece">
          <xsl:choose>
          <xsl:when test="position() != 1">
           <m:mo stretchy="false">|</m:mo>
          </xsl:when> 
          </xsl:choose>
-         <xsl:apply-templates select="."/>
+         <xsl:apply-templates select="./*[2]"/>
          <m:mo mathcolor="Green">&#x21d2;</m:mo>
-         <xsl:apply-templates select="following-sibling::*[position()= 1]"/>
+         <xsl:apply-templates select="./*[1]"/>
         </xsl:for-each>
         <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
         <m:mo>END</m:mo>
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- FIX -->
       <xsl:when test="$name='fix'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -812,6 +1015,7 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- COFIX -->
       <xsl:when test="$name='cofix'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -904,7 +1108,178 @@
       <!-- ***************************************** -->
       <!-- *********** PROOF ELEMENTS ************** -->
       <!-- ***************************************** -->
+      <!-- PROOF -->
       <xsl:when test="$name='proof'">
+        <!-- CSC: $explodeall until the annotationHelper can handle mactions -->
+        <xsl:variable name="test" select="(not($explodeall)) and
+	   (not(preceding-sibling::*[1]/text()='letin1')) and
+	   (not(preceding-sibling::*[1]/text()='rw_step')) and
+	   (not(name(..)='m:lambda'))"/>
+        <xsl:variable name="hidden_details">
+         <xsl:if test="$test">
+          <!-- Details hided (default) -->
+          <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+           <m:mtr>
+            <m:mtd>
+             <m:mrow>
+              <m:mtext mathcolor="Red">We&#x00a0;can&#x00a0;prove</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <!-- the last child is either the expected type, if provided,-->
+              <!-- or the synthesized type.                                -->
+              <xsl:apply-templates select="*[position()=last()]"/>
+              <m:mrow>
+               <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+               <m:mtext mathcolor="Green">(explain)</m:mtext>
+              </m:mrow>
+             </m:mrow>
+            </m:mtd>
+           </m:mtr>
+          </m:mtable>
+         </xsl:if>
+        </xsl:variable>
+        <xsl:variable name="shown_details">
+         <!-- Show details -->
+         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <xsl:apply-templates select="*[position()=2]"/>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+          <xsl:variable name="hidedetails">
+            <m:mrow>
+             <m:mphantom>
+              <m:mtext>_</m:mtext>
+             </m:mphantom>
+             <xsl:if test="$test">
+              <m:mtext mathcolor="Green">(hide&#x00a0;details)</m:mtext>
+             </xsl:if>
+            </m:mrow>
+          </xsl:variable>
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <m:mtext mathcolor="Red">we&#x00a0;proved</m:mtext>
+             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+             <xsl:apply-templates select="*[position()=3]"/>
+             <xsl:if test="not(*[4])">
+              <xsl:copy-of select="$hidedetails"/>
+             </xsl:if>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+          <xsl:if test="*[4]">
+           <m:mtr>
+            <m:mtd>
+             <m:mrow>
+              <m:mtext mathcolor="Red">that&#x00a0;is&#x00a0;equivalent&#x00a0;to</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[position()=4]"/>
+              <xsl:copy-of select="$hidedetails"/>
+             </m:mrow>
+            </m:mtd>
+           </m:mtr>
+          </xsl:if>
+         </m:mtable>
+        </xsl:variable>
+        <xsl:choose>
+         <xsl:when test="$test">
+          <m:maction actiontype="toggle">
+           <xsl:copy-of select="$hidden_details"/>
+           <xsl:copy-of select="$shown_details"/>
+          </m:maction>
+         </xsl:when>
+         <xsl:otherwise>
+          <xsl:copy-of select="$shown_details"/>
+         </xsl:otherwise>
+        </xsl:choose>
+      </xsl:when>
+      <!-- SIDE_PROOF -->
+      <xsl:when test="$name='side_proof'">
+        <xsl:variable name="test" select="(not($explodeall))"/>
+        <xsl:variable name="hidden_details">
+         <xsl:if test="$test">
+          <!-- Details hided (default) -->
+          <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+           <m:mtr>
+            <m:mtd>
+             <m:mrow>
+              <m:mtext mathcolor="Red">We&#x00a0;can&#x00a0;prove</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <!-- the last child is either the expected type, if provided,-->
+              <!-- or the synthesized type.                                -->
+              <xsl:apply-templates select="*[position()=last()]"/>
+              <m:mrow>
+               <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+               <m:mtext mathcolor="Green">(explain)</m:mtext>
+              </m:mrow>
+             </m:mrow>
+            </m:mtd>
+           </m:mtr>
+          </m:mtable>
+         </xsl:if>
+        </xsl:variable>
+        <xsl:variable name="shown_details">
+         <!-- Show details -->
+         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <xsl:apply-templates select="*[position()=2]"/>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+          <xsl:variable name="hidedetails">
+            <m:mrow>
+             <m:mphantom>
+              <m:mtext>_</m:mtext>
+             </m:mphantom>
+             <xsl:if test="$test">
+              <m:mtext mathcolor="Green">(hide&#x00a0;details)</m:mtext>
+             </xsl:if>
+            </m:mrow>
+          </xsl:variable>
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <m:mtext mathcolor="Red">we&#x00a0;proved</m:mtext>
+             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+             <xsl:apply-templates select="*[position()=3]"/>
+             <xsl:if test="not(*[4])">
+              <xsl:copy-of select="$hidedetails"/>
+             </xsl:if>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+          <xsl:if test="*[4]">
+           <m:mtr>
+            <m:mtd>
+             <m:mrow>
+              <m:mtext mathcolor="Red">that&#x00a0;is&#x00a0;equivalent&#x00a0;to</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[position()=4]"/>
+              <xsl:copy-of select="$hidedetails"/>
+             </m:mrow>
+            </m:mtd>
+           </m:mtr>
+          </xsl:if>
+         </m:mtable>
+        </xsl:variable>
+        <xsl:choose>
+         <xsl:when test="$test">
+          <m:maction actiontype="toggle">
+           <xsl:copy-of select="$hidden_details"/>
+           <xsl:copy-of select="$shown_details"/>
+          </m:maction>
+         </xsl:when>
+         <xsl:otherwise>
+          <xsl:copy-of select="$shown_details"/>
+         </xsl:otherwise>
+        </xsl:choose>
+      </xsl:when>
+      <!-- LETIN1 -->
+      <xsl:when test="$name='letin1'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
@@ -916,14 +1291,146 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext mathcolor="Maroon">we proved </m:mtext>
-            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="*[position()=3]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <xsl:when test="$name='by_induction'">
+       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtext mathcolor="Red">We&#x00a0;prove</m:mtext>
+           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+           <xsl:apply-templates select="../*[3]"/>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtext mathcolor="Red">by&#x00a0;induction&#x00a0;on</m:mtext>
+           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+           <xsl:apply-templates 
+            select="*[position()=last()]/*[position()=last()]"/>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+            <xsl:for-each select="*[position()>3 and not(position()=last())]">
+             <m:mtr>
+              <m:mtd>
+               <m:mrow>
+                <xsl:apply-templates select="."/>
+               </m:mrow>
+              </m:mtd>
+             </m:mtr>
+            </xsl:for-each>
+           </m:mtable>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+       </m:mtable>
+      </xsl:when>
+      <!-- inductive_case -->
+      <xsl:when test="$name='inductive_case'">
+       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtext mathcolor="Red">Case</m:mtext>
+           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+           <xsl:apply-templates select="*[2]"/>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+           <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+            <xsl:if test="*[3]/*[position()>1]">
+             <m:mtr>
+              <m:mtd>
+               <m:mrow>
+                <m:mtext mathcolor="Red">By&#x00a0;induction&#x00a0;hypothesis,&#x00a0;we&#x00a0;have:</m:mtext>
+               </m:mrow>
+              </m:mtd>
+             </m:mtr>
+             <m:mtr>
+              <m:mtd>
+               <m:mrow>
+                <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+                <xsl:for-each select="*[3]/*[position()>1]">
+                 <m:mo stretchy="false">(</m:mo>
+                 <xsl:apply-templates select="m:ci"/>
+                 <m:mo stretchy="false">) </m:mo>
+                 <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+                 <xsl:apply-templates select="m:type"/>
+                </xsl:for-each>
+               </m:mrow>
+              </m:mtd>
+             </m:mtr>
+            </xsl:if>
+            <m:mtr>
+             <m:mtd>
+              <m:mrow>
+               <xsl:apply-templates select="*[4]"/>
+              </m:mrow>
+             </m:mtd>
+            </m:mtr>
+           </m:mtable>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+       </m:mtable>
+      </xsl:when>
+      <!-- case_lhs  -->
+      <xsl:when test="$name='case_lhs'">
+       <m:mrow>
+        <xsl:choose>
+         <xsl:when test="count(*)=2">
+          <xsl:apply-templates select="*[2]"/>
+         </xsl:when>
+         <xsl:otherwise>
+          <m:mo stretchy="false">(</m:mo>
+          <xsl:apply-templates select="*[2]"/>
+          <xsl:for-each select="m:bvar">
+           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+           <xsl:apply-templates select="*[1]"/>
+           <m:mtext>:</m:mtext>
+           <xsl:apply-templates select="m:type/*[1]"/>
+          </xsl:for-each>
+          <m:mo stretchy="false">)</m:mo>
+         </xsl:otherwise>
+        </xsl:choose>
+       </m:mrow>
+      </xsl:when>
+      <!-- false_ind  -->
+      <xsl:when test="$name='false_ind'">
+       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <xsl:apply-templates select="*[3]"/>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtext mathcolor="Red">Contradiction.</m:mtext>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+       </m:mtable>
+      </xsl:when>
+      <!-- LET-IN -->
       <xsl:when test="$name='letin'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <!-- <xsl:for-each select="APPLY[m:csymbol and (string(m:csymbol)='let')]"> -->
@@ -945,98 +1452,136 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- LET -->
       <xsl:when test="$name='let'">
        <m:mtext>(</m:mtext>
        <xsl:apply-templates select="m:ci"/>
        <m:mtext>) </m:mtext>
        <xsl:apply-templates select="*[3]"/>
       </xsl:when>
-      <xsl:when test="$name='thread'">
+      <!-- RW_STEP -->
+      <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>
-            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[position()>3]"/>
+            <xsl:apply-templates select="*[5]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
-       </m:mtable>
-      </xsl:when> 
-      <xsl:when test="$name='and_ind'">
+        </m:mtable>
+      </xsl:when>
+      <!-- not existing any more
+      <xsl:when test="$name='thread'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
            <m:mrow>
             <xsl:choose>
-             <xsl:when test="name(*[2])='m:apply'">
-              <xsl:apply-templates select="*[2]"/>
+             <xsl:when test="name(*[last()])='m:apply'">
+              <xsl:apply-templates select="*[last()]"/>
              </xsl:when>
              <xsl:otherwise>
-              <m:mtext>Consider </m:mtext>
-              <xsl:apply-templates select="*[2]"/>
+              <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>
+      --> 
+      <!-- REWRITE_AND_APPLY -->
+      <xsl:when test="$name='rewrite_and_apply'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
-           <m:mtext>In particular, we have</m:mtext>
+           <m:mrow>
+            <xsl:apply-templates select="*[2]"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>(</m:mtext>
-            <xsl:apply-templates select="*[3]"/>
-            <m:mtext>)</m:mtext>
+            <m:mtext>Then&#x00a0;apply&#x00a0;it&#x00a0;to</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[4]"/>
-            </m:mrow>
+            <xsl:apply-templates select="*[position()>2]"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
+       </m:mtable>
+      </xsl:when>
+      <!-- AND_IND -->
+      <xsl:when test="$name='and_ind'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>(</m:mtext>
+            <xsl:choose>
+             <xsl:when test="name(*[2])='m:apply'">
+              <xsl:apply-templates select="*[2]"/>
+             </xsl:when>
+             <xsl:otherwise>
+              <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>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>In&#x00a0;particular,&#x00a0;we&#x00a0;have</m:mtext>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>(</m:mtext>
+            <xsl:apply-templates select="*[3]"/>
+            <m:mtext>)</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[4]"/>
+            </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>(</m:mtext>
             <xsl:apply-templates select="*[5]"/>
             <m:mtext>)</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
@@ -1053,6 +1598,78 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- full_or_ind -->
+      <xsl:when test="$name='full_or_ind'">
+        <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:choose>
+             <xsl:when test="name(*[2])='m:apply'">
+              <xsl:apply-templates select="*[2]"/>
+             </xsl:when>
+             <xsl:otherwise>
+              <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>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>We&#x00a0;proceed&#x00a0;by&#x00a0;cases&#x00a0;to&#x00a0;prove</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[3]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>Left:&#x00a0;suppose</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mo stretchy="false">(</m:mo>
+            <xsl:apply-templates select="*[4]/m:bvar/m:ci"/>
+            <m:mo stretchy="false">)</m:mo>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[4]/m:bvar/m:type/*[1]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[4]/*[3]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>Right:&#x00a0;suppose</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mo stretchy="false">(</m:mo>
+            <xsl:apply-templates select="*[5]/m:bvar/m:ci"/>
+            <m:mo stretchy="false">)</m:mo>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[5]/m:bvar/m:type/*[1]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:apply-templates select="*[5]/*[3]"/>
+           </m:mrow>
+          </m:mtd>
+         </m:mtr>
+        </m:mtable>
+      </xsl:when>
+      <!-- OR_IND -->
       <xsl:when test="$name='or_ind'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1073,17 +1690,19 @@
          </m:mtr>
          <m:mtr>
           <m:mtd>
-           <m:mtext>We prove</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>by cases:</m:mtext>
+           <m:mrow>
+            <m:mtext>We&#x00a0;prove</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>by&#x00a0;cases:</m:mtext>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>*</m:mtext>
+            <m:mtext>Left</m:mtext>
             <xsl:apply-templates select="*[4]"/>
            </m:mrow>
           </m:mtd>
@@ -1091,13 +1710,14 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>*</m:mtext>
+            <m:mtext>Right</m:mtext>
             <xsl:apply-templates select="*[5]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- EX_IND -->
       <xsl:when test="$name='ex_ind'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1108,7 +1728,8 @@
               <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>
@@ -1117,19 +1738,21 @@
          </m:mtr>
          <m:mtr>
           <m:mtd>
-           <m:mtext>Let</m:mtext>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <xsl:apply-templates select="*[3]"/>
-           <m:mtext>:</m:mtext>
-           <xsl:apply-templates select="*[4]"/>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <m:mtext>such that</m:mtext>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <m:mtext>(</m:mtext>
-            <xsl:apply-templates select="*[5]"/>
-           <m:mtext>)</m:mtext>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <xsl:apply-templates select="*[6]"/>
+           <m:mrow>
+            <m:mtext>Let</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[3]"/>
+            <m:mtext>:</m:mtext>
+            <xsl:apply-templates select="*[4]"/>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mtext>such&#x00a0;that</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mtext>(</m:mtext>
+             <xsl:apply-templates select="*[5]"/>
+            <m:mtext>)</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[6]"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -1141,13 +1764,226 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- EQ_CHAIN -->
+      <xsl:when test="$name='eq_chain'">
+       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtext mathcolor="Red">We&#x00a0;have&#x00a0;the&#x00a0;following&#x00a0;equality&#x00a0;chain:</m:mtext>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <xsl:for-each select="*[position() mod 2 = 0]">
+        <xsl:variable name="pos" select="position()"/>
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <xsl:choose>
+           <xsl:when test="$pos = 1">
+            <xsl:apply-templates select="."/>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mo>=</m:mo>
+           </xsl:when>
+           <xsl:otherwise>
+            <m:mo>=</m:mo>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="."/>
+           </xsl:otherwise>
+           </xsl:choose>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <xsl:if test="$pos != last()">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mphantom><m:mtext>__</m:mtext></m:mphantom>
+           <xsl:apply-templates select="../*[position()=2*$pos +1]"/>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        </xsl:if>
+        </xsl:for-each>
+       </m:mtable>
+      </xsl:when>
+      <!-- DISEQ_CHAIN -->
+      <xsl:when test="$name='diseq_chain'">
+       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mtext mathcolor="Red">We&#x00a0;have&#x00a0;the&#x00a0;following&#x00a0;disequality&#x00a0;chain:</m:mtext>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <xsl:for-each select="*[position() mod 3 = 2]">
+        <xsl:variable name="pos" select="position()"/>
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <xsl:choose>
+           <xsl:when test="$pos = 1">
+            <xsl:apply-templates select="."/>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <mo><xsl:apply-templates select="../*[position()=3*$pos]"/></mo>
+           </xsl:when>
+           <xsl:otherwise>
+            <mo><xsl:apply-templates select="../*[position()=3*($pos - 1)]"/></mo>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="."/>
+           </xsl:otherwise>
+           </xsl:choose>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        <xsl:if test="$pos != last()">
+        <m:mtr>
+         <m:mtd>
+          <m:mrow>
+           <m:mphantom><m:mtext>__</m:mtext></m:mphantom>
+           <xsl:apply-templates select="../*[position()=3*$pos +1]"/>
+          </m:mrow>
+         </m:mtd>
+        </m:mtr>
+        </xsl:if>
+        </xsl:for-each>
+       </m:mtable>
+      </xsl:when>
+      <!-- ***************************************** -->
+      <!-- *********** NOTATIONS ******************* -->
+      <!-- ***************************************** -->
+      <!-- subst -->
+      <xsl:when test="$name='subst'">
+        <xsl:apply-templates select="*[3]"/>
+<!-- no font for ApplyFunction: <m:mo>&#xe8a0;</m:mo> -->
+        <m:mo stretchy="false">[</m:mo>
+        <xsl:apply-templates select="*[4]"/>
+        <m:mo mathcolor="Green">
+         <xsl:if test="$id != ''">
+          <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+         </xsl:if>&#8592;</m:mo>
+        <xsl:apply-templates select="*[2]"/>
+        <m:mo stretchy="false">]</m:mo>
+      </xsl:when>
+      <!-- lift -->
+      <xsl:when test="$name='lift'">
+        <m:msup>
+         <m:mo mathcolor="Green">
+          <xsl:if test="$id != ''">
+           <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+          </xsl:if>&#8593;</m:mo>
+	 <xsl:apply-templates select="*[2]"/>
+        </m:msup>
+	<m:mrow>
+	 <m:mo stretchy="false">(</m:mo>
+         <xsl:apply-templates select="*[3]"/>
+	 <m:mo stretchy="false">)</m:mo>
+        </m:mrow>
+      </xsl:when>
+      <!-- lift_with_base -->
+      <xsl:when test="$name='lift_with_base'">
+        <m:msubsup>
+         <m:mo mathcolor="Green">
+          <xsl:if test="$id != ''">
+           <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+          </xsl:if>&#8593;</m:mo>
+	 <xsl:apply-templates select="*[3]"/>
+	 <xsl:apply-templates select="*[4]"/>
+        </m:msubsup>
+	<m:mrow>
+	 <m:mo stretchy="false">(</m:mo>
+         <xsl:apply-templates select="*[2]"/>
+	 <m:mo stretchy="false">)</m:mo>
+        </m:mrow>	
+      </xsl:when>
+      <!-- beta_red1 -->
+      <xsl:when test="$name='beta_red1'">
+        <xsl:apply-templates select="*[2]"/>
+        <m:munder>
+         <m:mo mathcolor="Green">
+          <xsl:if test="$id != ''">
+           <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+          </xsl:if>&#8594;</m:mo>
+          <m:mi mathcolor="Green">&#946;</m:mi>
+        </m:munder>
+        <xsl:apply-templates select="*[3]"/>
+      </xsl:when>
+      <!-- beta_red -->
+      <xsl:when test="$name='beta_red'">
+        <xsl:apply-templates select="*[2]"/>
+        <m:munderover>
+         <m:mo mathcolor="Green">
+          <xsl:if test="$id != ''">
+           <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+          </xsl:if>&#8594;</m:mo>
+          <m:mi mathcolor="Green">&#946;</m:mi>
+          <m:mi mathcolor="Green">*</m:mi>
+        </m:munderover>
+        <xsl:apply-templates select="*[3]"/>
+      </xsl:when>
+      <!-- par_beta_red1 -->
+      <xsl:when test="$name='par_beta_red1'">
+        <xsl:apply-templates select="*[2]"/>
+        <m:munder>
+         <m:mo mathcolor="Green">
+          <xsl:if test="$id != ''">
+           <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+          </xsl:if>&#8658;</m:mo>
+          <m:mi mathcolor="Green">&#946;</m:mi>
+        </m:munder>
+        <xsl:apply-templates select="*[3]"/>
+      </xsl:when>
+      <!-- par_beta_red -->
+      <xsl:when test="$name='par_beta_red'">
+        <xsl:apply-templates select="*[2]"/>
+        <m:munderover>
+         <m:mo mathcolor="Green">
+          <xsl:if test="$id != ''">
+           <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+          </xsl:if>&#8658;</m:mo>
+          <m:mi mathcolor="Green">&#946;</m:mi>
+          <m:mi mathcolor="Green">*</m:mi>
+        </m:munderover>
+        <xsl:apply-templates select="*[3]"/>
+      </xsl:when>
+      <!-- forgetful -->
+      <xsl:when test="$name='forgetful'">
+       <m:mfenced open="|" close="|">
+        <xsl:if test="$id != ''">
+         <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+        </xsl:if>
+        <xsl:apply-templates select="*[2]"/>
+       </m:mfenced>
+      </xsl:when>
+      <!-- isomorphic -->
+      <xsl:when test="$name='isomorphic'">
+        <xsl:apply-templates select="*[2]"/>
+        <m:mo mathcolor="Green">
+         <xsl:if test="$id != ''">
+          <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+         </xsl:if>&#8773;</m:mo>
+        <xsl:apply-templates select="*[3]"/>
+      </xsl:when>
+      <!-- interp -->
+      <xsl:when test="$name='forgetful'">
+       <m:mfenced open="[" close="]">
+        <xsl:if test="$id != ''">
+         <xsl:attribute name="xref"><xsl:value-of select="$id"/></xsl:attribute>
+        </xsl:if>
+        <xsl:apply-templates select="*[2]"/>
+       </m:mfenced>
+      </xsl:when> 
+
+      <!-- ERROR -->
       <xsl:otherwise>
-       <m:ci>ERROR</m:ci>
+       <m:mi>ERROR</m:mi>
       </xsl:otherwise>
      </xsl:choose>
     </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>
@@ -1172,7 +2008,7 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext mathcolor="Maroon">we get</m:mtext>
+            <m:mtext mathcolor="Red">we&#x00a0;get</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="."/>
            </m:mrow>
@@ -1190,7 +2026,7 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext mathcolor="Maroon">we get</m:mtext>
+            <m:mtext mathcolor="Red">we&#x00a0;get</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="."/>
            </m:mrow>
@@ -1200,20 +2036,27 @@
    </xsl:choose>
          <xsl:apply-templates mode="thread" select="preceding-sibling::*[position()=2]"/>
 </xsl:template>
-
+-->
 
 <!-- LAMBDA -->
 
 <xsl:template match="m:lambda">
     <xsl:variable name="charlength"><xsl:apply-templates select="*[position()=1]" mode="charcount"/></xsl:variable>
-    <m:mrow helm:xref="{@helm:xref}">
+    <m:mrow>
+     <xsl:if test="@id">
+      <xsl:attribute name="xref">
+       <xsl:value-of select="@id"/>
+      </xsl:attribute>
+     </xsl:if>
      <xsl:choose>
      <xsl:when test="$charlength >= $framewidth">
       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
         <m:mtr>
           <m:mtd>
+           <m:mrow>
             <m:mo mathcolor="Red">&#x03bb;</m:mo>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
        <m:mtr>
@@ -1238,229 +2081,6 @@
     </m:mrow>
 </xsl:template>
 
-<!-- *********************************** -->
-<!-- BASE SET OF MATHML CONTENT ELEMENTS -->
-<!-- *********************************** -->
-
-<!-- Logic -->
-
-<xsl:template match = "m:apply[m:eq[1]]">
- <xsl:variable name="charlength">
-  <xsl:apply-templates select="*[1]" mode="charcount"/>
- </xsl:variable>
- <xsl:choose>
-  <xsl:when test="$charlength >= $framewidth">
-   <m:mtable align="baseline 1" equalrows="false" columnalign="left">
-    <xsl:if test="@helm:xref">
-     <xsl:attribute name="helm:xref">
-      <xsl:value-of select="@helm:xref"/>
-     </xsl:attribute>
-    </xsl:if>    
-    <m:mtr>
-     <m:mtd>
-      <m:mo stretchy="false">(</m:mo>
-      <xsl:apply-templates select="*[position()=2]"/>
-     </m:mtd>
-    </m:mtr>
-    <xsl:for-each select = "*[position()>2]">
-     <m:mtr>
-      <m:mtd>
-       <m:mphantom><m:mtext>__</m:mtext></m:mphantom>
-       <m:mo helm:xref="m:in/@helm:xref"> 
-        =
-       </m:mo>
-       <xsl:apply-templates select="."/>
-      </m:mtd>
-     </m:mtr>
-    </xsl:for-each>
-    <m:mtr>
-     <m:mtd>
-      <m:mo stretchy="false">)</m:mo>
-     </m:mtd>
-    </m:mtr>
-   </m:mtable>
-  </xsl:when>
-  <xsl:otherwise>
-   <xsl:apply-imports/>
-  </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
-
-<xsl:template match = "m:apply[m:and[1]|m:or[1]
-          |m:geq[1]|m:leq[1]|m:gt[1]|m:lt[1]
-          |m:in[1]|m:intesect[1]|m:union[1]|m:subset[1]
-          |m:prsubset|m:setdiff[1]]">
- <xsl:variable name="symbol">
-  <xsl:choose>
-   <xsl:when test="m:and[1]">
-    <xsl:value-of select="'wedge'"/>
-   </xsl:when>
-   <xsl:when test="m:or[1]">
-    <xsl:value-of select="'vee'"/>
-   </xsl:when>
-   <xsl:when test="m:geq[1]">
-    <xsl:value-of select="'geq'"/>
-   </xsl:when>
-   <xsl:when test="m:leq[1]">
-    <xsl:value-of select="'leq'"/>
-   </xsl:when>
-   <xsl:when test="m:gt[1]">
-    <xsl:value-of select="'gt'"/>
-   </xsl:when>
-   <xsl:when test="m:lt[1]">
-    <xsl:value-of select="'lt'"/>
-   </xsl:when>
-   <xsl:when test="m:eq[1]">
-    <xsl:value-of select="'Equal'"/>
-   </xsl:when>
-   <xsl:when test="m:in[1]">
-    <xsl:value-of select="'Element'"/>
-   </xsl:when>
-   <xsl:when test="m:subset[1]">
-    <xsl:value-of select="'SubsetEqual'"/>
-   </xsl:when>
-   <xsl:when test="m:prsubset[1]">
-    <xsl:value-of select="'subset'"/>
-   </xsl:when>
-   <xsl:when test="m:intersect[1]">
-    <xsl:value-of select="'Intersection'"/>
-   </xsl:when>
-   <xsl:when test="m:union[1]">
-    <xsl:value-of select="'Union'"/>
-   </xsl:when>
-   <xsl:when test="m:setdiff[1]">
-    <xsl:value-of select="'Backslash'"/>
-   </xsl:when>
-  </xsl:choose>
- </xsl:variable>
- <xsl:variable name="charlength">
-  <xsl:apply-templates select="*[1]" mode="charcount"/>
- </xsl:variable>
- <xsl:choose>
-  <xsl:when test="$charlength >= $framewidth">
-   <m:mtable align="baseline 1" equalrows="false" columnalign="left">
-    <xsl:if test="@helm:xref">
-     <xsl:attribute name="helm:xref">
-      <xsl:value-of select="@helm:xref"/>
-     </xsl:attribute>
-    </xsl:if>    
-    <m:mtr>
-     <m:mtd>
-      <m:mo stretchy="false">(</m:mo>
-      <xsl:apply-templates select="*[position()=2]"/>
-     </m:mtd>
-    </m:mtr>
-    <xsl:for-each select = "*[position()>2]">
-     <m:mtr>
-      <m:mtd>
-       <m:mphantom><m:mtext>__</m:mtext></m:mphantom>
-       <m:mo helm:xref="{*[1]/@helm:xref}"> 
-        <m:mchar name="{$symbol}"/>
-       </m:mo>
-       <xsl:apply-templates select="."/>
-      </m:mtd>
-     </m:mtr>
-    </xsl:for-each>
-    <m:mtr>
-     <m:mtd>
-      <m:mo stretchy="false">)</m:mo>
-     </m:mtd>
-    </m:mtr>
-   </m:mtable>
-  </xsl:when>
-  <xsl:otherwise>
-   <xsl:apply-imports/>
-  </xsl:otherwise>
- </xsl:choose>
-</xsl:template>
-
-<xsl:template match = "m:set">
- <xsl:choose>
-  <xsl:when test="count(child::*) = 0">
-   <m:mi> 
-    <m:mchar name="emptyset"/>
-   </m:mi>
-  </xsl:when>
-  <xsl:otherwise>
-   <xsl:variable name="charlength">
-    <xsl:apply-templates select="*[1]" mode="charcount"/>
-   </xsl:variable>
-   <xsl:choose>
-    <xsl:when test="$charlength >= $framewidth">
-     <xsl:choose>
-      <xsl:when test="name(*[1]) = 'm:bvar'">
-       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
-        <m:mtr>
-         <m:mtd>
-          <m:mo stretchy="false">{</m:mo>
-          <xsl:apply-templates select="*[position()=1]"/>
-         </m:mtd>
-        </m:mtr>
-        <m:mtr>
-         <m:mtd>
-          <m:mphantom><m:mtext>{</m:mtext></m:mphantom>
-          <m:mo stretchy="false">|</m:mo>
-          <xsl:apply-templates select="m:condition/*[1]"/>
-         </m:mtd>
-        </m:mtr>
-        <m:mtr>
-         <m:mtd>
-          <m:mo stretchy="false">}</m:mo>
-         </m:mtd>
-        </m:mtr>
-       </m:mtable>
-      </xsl:when>
-      <xsl:otherwise>
-       <m:mtable align="baseline 1" equalrows="false" columnalign="left">
-        <m:mtr>
-         <m:mtd>
-          <m:mo stretchy="false">{</m:mo>
-          <xsl:apply-templates select="*[position()=1]"/>
-          <xsl:if test="position() != last()">
-           <mo>,</mo>
-          </xsl:if>
-         </m:mtd>
-        </m:mtr>
-        <xsl:for-each select = "*[position()>2]">
-         <m:mtr>
-          <m:mtd>
-           <m:mphantom><m:mtext>{</m:mtext></m:mphantom>
-           <xsl:apply-templates select="."/>
-           <xsl:if test="position() != last()">
-            <mo>,</mo>
-           </xsl:if>
-          </m:mtd>
-         </m:mtr>
-        </xsl:for-each>
-        <m:mtr>
-         <m:mtd>
-          <m:mo stretchy="false">}</m:mo>
-         </m:mtd>
-        </m:mtr>
-       </m:mtable>
-      </xsl:otherwise>
-     </xsl:choose>
-    </xsl:when>
-    <xsl:otherwise>
-     <xsl:apply-imports/>
-    </xsl:otherwise>
-   </xsl:choose>
-  </xsl:otherwise>
- </xsl:choose>
-</xsl:template>      
-
-<xsl:template match = "m:apply[m:card[1]]">
- <m:mo stretchy="false">|</m:mo>
-  <xsl:apply-templates select="*[2]"/>
- <m:mo stretchy="false">|</m:mo>
-</xsl:template>
-
-<!-- *********************************** -->
-<!--          PROOF ELEMENTS             -->
-<!-- *********************************** -->
-
-
 
 <!--**********************-->
 <!--       COUNTING       -->
@@ -1518,7 +2138,16 @@
 <xsl:param name="nosibling" select="0"/>
  <xsl:choose>
   <xsl:when test="count(child::*) = 0">
-   <xsl:value-of select="$incurrent_length"/>
+   <!-- tremendous bug fixed. An empty element can still have siblings!!! -->
+   <xsl:variable name="siblength"><xsl:apply-templates select="following-sibling::*[position()=1]" mode="charcount"><xsl:with-param name="incurrent_length" select="$incurrent_length"/></xsl:apply-templates></xsl:variable>
+   <xsl:choose>
+    <xsl:when test="string($siblength) = &quot;&quot;">
+     <xsl:value-of select="$incurrent_length"/>
+    </xsl:when>
+    <xsl:otherwise>
+      <xsl:value-of select="number($siblength)"/>
+    </xsl:otherwise>
+   </xsl:choose>
   </xsl:when>
   <xsl:otherwise>
     <xsl:variable name="childlength"><xsl:apply-templates select="*[position()=1]" mode="charcount"><xsl:with-param name="incurrent_length" select="$incurrent_length"/><xsl:with-param name="nosibling" select="0"/></xsl:apply-templates></xsl:variable>
@@ -1532,7 +2161,7 @@
      <xsl:otherwise>
       <xsl:value-of select="number($siblength)"/>
      </xsl:otherwise>
-     </xsl:choose>>
+     </xsl:choose>
     </xsl:when>
     <xsl:otherwise>
      <xsl:value-of select="number($childlength)"/>
@@ -1544,4 +2173,3 @@
 
 </xsl:stylesheet> 
 
-