X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fstyle%2Fmmlextension.xsl;h=7e9bd1e5f085b1711a8a64458e66c7d9db7f211c;hb=4c9123ced31cede42e5cc1e19d701a6f6e5e9d6b;hp=86675e553e48abf02c18c78ecf1043341445b65f;hpb=26f5337108946df050f07c68ebe9bc07b1fde173;p=helm.git

diff --git a/helm/style/mmlextension.xsl b/helm/style/mmlextension.xsl
index 86675e553..7e9bd1e5f 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 -->
@@ -355,21 +375,27 @@
      <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>
@@ -387,18 +413,22 @@
     <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="m:xref"><xsl:value-of select="@id"/></xsl:attribute>
      </xsl:if>
+     <xsl:variable name="id" select="m:csymbol/@id"/>
      <xsl:choose>
+      <!-- FORALL -->
       <xsl:when test="$name='forall'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
-            <m:mo mathcolor="Blue"><m:mchar name="ForAll"/></m:mo>
+           <m:mrow>
+            <m:mo mathcolor="Blue">&#8704;</m:mo>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -412,7 +442,7 @@
         </m:mtable>
        </xsl:when>
        <xsl:otherwise>
-        <m:mo mathcolor="Blue"><m:mchar name="ForAll"/></m:mo>
+        <m:mo mathcolor="Blue">&#8704;</m:mo>
         <xsl:apply-templates select="m:bvar/m:ci"/>
         <m:mo>:</m:mo>
         <xsl:apply-templates select="m:bvar/m:type"/>
@@ -421,15 +451,18 @@
        </xsl:otherwise>
        </xsl:choose> 
       </xsl:when>
+      <!-- LET-IN -->
       <xsl:when test="$name='let_in'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
+           <m:mrow>
             <m:mo>LET</m:mo>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -464,14 +497,17 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when> 
+      <!-- PROD -->
       <xsl:when test="$name='prod'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
+           <m:mrow>
             <m:mo mathcolor="Blue">&#x03a0;</m:mo>
             <xsl:apply-templates select="m:bvar"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -494,6 +530,7 @@
        </xsl:otherwise>
        </xsl:choose> 
       </xsl:when>
+      <!-- ARROW -->
       <xsl:when test="$name='arrow'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -570,6 +607,7 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- APP -->
       <xsl:when test="$name='app'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -578,7 +616,10 @@
           <m:mtd>
            <m:mrow>
             <m:mo stretchy="false">(</m:mo>
-            <xsl:apply-templates select="*[position()=2]"/>
+<!-- added precedence to app = FUNCTION_PREC (99) -->
+            <xsl:apply-templates select="*[position()=2]">
+             <xsl:with-param name="IN_PREC" select="$FUNCTION_PREC"/>
+            </xsl:apply-templates>
            </m:mrow>
           </m:mtd>
          </m:mtr>
@@ -587,7 +628,10 @@
           <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="$FUNCTION_PREC"/>
+            </xsl:apply-templates>
            </m:mrow>
           </m:mtd>
          </m:mtr>
@@ -603,15 +647,22 @@
        </xsl:when>
        <xsl:otherwise>
         <m:mo stretchy="false">(</m:mo>
-        <xsl:apply-templates select="*[position()=2]"/>
+<!-- added precedence to app = FUNCTION_PREC (99) -->
+        <xsl:apply-templates select="*[position()=2]">
+         <xsl:with-param name="IN_PREC" select="$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 >= $framewidth">
@@ -650,15 +701,19 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- PROP -->
       <xsl:when test="$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 >= $framewidth">
@@ -697,8 +752,8 @@
            </m:mrow>
           </m:mtd>
          </m:mtr>
-         <xsl:for-each select="*[position() mod 2 = 0 and position()>3]">
-         <xsl:variable name="charlength"><xsl:apply-templates select="." mode="charcount"><xsl:with-param name="nosibling" select="1"/></xsl:apply-templates></xsl:variable>
+         <xsl:for-each select="piecewise/piece">
+         <xsl:variable name="charlength"><xsl:apply-templates select="./*[2]" mode="charcount"><xsl:with-param name="nosibling" select="1"/></xsl:apply-templates></xsl:variable>
          <m:mtr>
           <m:mtd>
            <m:mrow>
@@ -711,10 +766,10 @@
             </xsl:otherwise>
             </xsl:choose>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="."/>
+            <xsl:apply-templates select="./*[2]"/>
             <xsl:if test="$framewidth > $charlength">
              <m:mo mathcolor="Green">&#x21d2;</m:mo>
-             <xsl:apply-templates select="following-sibling::*[position()= 1]"/>
+             <xsl:apply-templates select="./*[1]"/>
             </xsl:if>
            </m:mrow>
           </m:mtd>
@@ -725,7 +780,7 @@
            <m:mrow>
             <m:mphantom><m:mtext>|_</m:mtext></m:mphantom>  
             <m:mo mathcolor="Green">&#x21d2;</m:mo>
-            <xsl:apply-templates select="following-sibling::*[position()= 1]"/>
+            <xsl:apply-templates select="./*[1]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
@@ -747,21 +802,22 @@
         <xsl:apply-templates select="*[position()=3]"/>
         <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
         <m:mo>OF</m:mo>
-        <xsl:for-each select="*[position() mod 2 = 0 and position()>3]">
+        <xsl:for-each select="piecewise/piece">
          <xsl:choose>
          <xsl:when test="position() != 1">
           <m:mo stretchy="false">|</m:mo>
          </xsl:when> 
          </xsl:choose>
-         <xsl:apply-templates select="."/>
+         <xsl:apply-templates select="./*[2]"/>
          <m:mo mathcolor="Green">&#x21d2;</m:mo>
-         <xsl:apply-templates select="following-sibling::*[position()= 1]"/>
+         <xsl:apply-templates select="./*[1]"/>
         </xsl:for-each>
         <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
         <m:mo>END</m:mo>
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- FIX -->
       <xsl:when test="$name='fix'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -851,6 +907,7 @@
        </xsl:otherwise>
        </xsl:choose>
       </xsl:when>
+      <!-- COFIX -->
       <xsl:when test="$name='cofix'">
        <xsl:choose>
        <xsl:when test="$charlength >= $framewidth">
@@ -943,7 +1000,140 @@
       <!-- ***************************************** -->
       <!-- *********** PROOF ELEMENTS ************** -->
       <!-- ***************************************** -->
+      <!-- PROOF -->
       <xsl:when test="$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="$test">
+          <!-- Details hided (default) -->
+          <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+           <m:mtr>
+            <m:mtd>
+             <m:mrow>
+              <m:mtext mathcolor="Red">We&#x00a0;can&#x00a0;prove</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[position()=3]"/>
+              <m:mrow>
+               <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+               <m:mtext mathcolor="Green">(explain)</m:mtext>
+              </m:mrow>
+             </m:mrow>
+            </m:mtd>
+           </m:mtr>
+          </m:mtable>
+         </xsl:if>
+        </xsl:variable>
+        <xsl:variable name="shown_details">
+         <!-- Show details -->
+         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <xsl:apply-templates select="*[position()=2]"/>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <m:mtext mathcolor="Red">we&#x00a0;proved</m:mtext>
+             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+             <xsl:apply-templates select="*[position()=3]"/>
+             <m:mrow>
+              <m:mphantom>
+               <m:mtext>_</m:mtext>
+              </m:mphantom>
+              <xsl:if test="$test">
+               <m:mtext mathcolor="Green">(hide&#x00a0;details)</m:mtext>
+              </xsl:if>
+             </m:mrow>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+         </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="$test">
+          <!-- Details hided (default) -->
+          <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+           <m:mtr>
+            <m:mtd>
+             <m:mrow>
+              <m:mtext mathcolor="Red">We&#x00a0;can&#x00a0;prove</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[position()=3]"/>
+              <m:mrow>
+               <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+               <m:mtext mathcolor="Green">(explain)</m:mtext>
+              </m:mrow>
+             </m:mrow>
+            </m:mtd>
+           </m:mtr>
+          </m:mtable>
+         </xsl:if>
+        </xsl:variable>
+        <xsl:variable name="shown_details">
+         <!-- Show details -->
+         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <xsl:apply-templates select="*[position()=2]"/>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+          <m:mtr>
+           <m:mtd>
+            <m:mrow>
+             <m:mtext mathcolor="Red">we&#x00a0;proved</m:mtext>
+             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+             <xsl:apply-templates select="*[position()=3]"/>
+             <m:mrow>
+              <m:mphantom>
+               <m:mtext>_</m:mtext>
+              </m:mphantom>
+              <xsl:if test="$test">
+               <m:mtext mathcolor="Green">(hide&#x00a0;details)</m:mtext>
+              </xsl:if>
+             </m:mrow>
+            </m:mrow>
+           </m:mtd>
+          </m:mtr>
+         </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="$name='letin1'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
@@ -955,32 +1145,146 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext mathcolor="Maroon">we proved </m:mtext>
-            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="*[position()=3]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
         </m:mtable>
       </xsl:when>
-      <xsl:when test="$name='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 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="$name='letin'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <!-- <xsl:for-each select="APPLY[m:csymbol and (string(m:csymbol)='let')]"> -->
@@ -1002,12 +1306,14 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- LET -->
       <xsl:when test="$name='let'">
        <m:mtext>(</m:mtext>
        <xsl:apply-templates select="m:ci"/>
        <m:mtext>) </m:mtext>
        <xsl:apply-templates select="*[3]"/>
       </xsl:when>
+      <!-- RW_STEP -->
       <xsl:when test="$name='rw_step'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1045,6 +1351,7 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- not existing any more
       <xsl:when test="$name='thread'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1065,7 +1372,9 @@
          </m:mtr>
 	 <xsl:apply-templates mode="thread" select="*[(last()-2)]"/> 
         </m:mtable>
-      </xsl:when> 
+      </xsl:when>
+      --> 
+      <!-- REWRITE_AND_APPLY -->
       <xsl:when test="$name='rewrite_and_apply'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1078,7 +1387,7 @@
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>Then apply it to</m:mtext>
+            <m:mtext>Then&#x00a0;apply&#x00a0;it&#x00a0;to</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
             <xsl:apply-templates select="*[position()>2]"/>
            </m:mrow>
@@ -1086,34 +1395,65 @@
          </m:mtr>
        </m:mtable>
       </xsl:when>
-      <!-- NAT_IND -->
-      <xsl:when test="$name='nat_ind'">
+      <!-- AND_IND -->
+      <xsl:when test="$name='and_ind'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
-           <m:mtext>By induction</m:mtext>
+           <m:mrow>
+            <xsl:choose>
+             <xsl:when test="name(*[2])='m:apply'">
+              <xsl:apply-templates select="*[2]"/>
+             </xsl:when>
+             <xsl:otherwise>
+              <m:mtext>Consider</m:mtext>
+              <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+              <xsl:apply-templates select="*[2]"/>
+             </xsl:otherwise>
+            </xsl:choose>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>base case:</m:mtext>
-            <xsl:apply-templates select="*[2]"/>
+            <m:mtext>In&#x00a0;particular,&#x00a0;we&#x00a0;have</m:mtext>
            </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <m:mtext>inductive case:</m:mtext>
+            <m:mtext>(</m:mtext>
             <xsl:apply-templates select="*[3]"/>
+            <m:mtext>)</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[4]"/>
+            </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <m:mtext>(</m:mtext>
+            <xsl:apply-templates select="*[5]"/>
+            <m:mtext>)</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[6]"/>
+            </m:mrow>
+          </m:mtd>
+         </m:mtr>
+         <m:mtr>
+          <m:mtd>
+           <m:mrow>
+            <xsl:apply-templates select="*[7]"/>
            </m:mrow>
           </m:mtd>
          </m:mtr>
         </m:mtable>
       </xsl:when>
-      <!-- AND_IND -->
-      <xsl:when test="$name='and_ind'">
+      <!-- full_or_ind -->
+      <xsl:when test="$name='full_or_ind'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
           <m:mtd>
@@ -1133,40 +1473,57 @@
          </m:mtr>
          <m:mtr>
           <m:mtd>
-           <m:mtext>In particular, we have</m:mtext>
+           <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>(</m:mtext>
-            <xsl:apply-templates select="*[3]"/>
-            <m:mtext>)</m:mtext>
+            <m:mtext>Left:&#x00a0;suppose</m:mtext>
             <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-            <xsl:apply-templates select="*[4]"/>
-            </m:mrow>
+            <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: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>
+            <xsl:apply-templates select="*[4]/*[3]"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
           <m:mtd>
            <m:mrow>
-            <xsl:apply-templates select="*[7]"/>
+            <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>
@@ -1187,17 +1544,19 @@
          </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>
@@ -1205,13 +1564,14 @@
          <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="$name='ex_ind'">
         <m:mtable align="baseline 1" equalrows="false" columnalign="left">
          <m:mtr>
@@ -1232,19 +1592,21 @@
          </m:mtr>
          <m:mtr>
           <m:mtd>
-           <m:mtext>Let</m:mtext>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <xsl:apply-templates select="*[3]"/>
-           <m:mtext>:</m:mtext>
-           <xsl:apply-templates select="*[4]"/>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <m:mtext>such that</m:mtext>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <m:mtext>(</m:mtext>
-            <xsl:apply-templates select="*[5]"/>
-           <m:mtext>)</m:mtext>
-           <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
-           <xsl:apply-templates select="*[6]"/>
+           <m:mrow>
+            <m:mtext>Let</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[3]"/>
+            <m:mtext>:</m:mtext>
+            <xsl:apply-templates select="*[4]"/>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mtext>such&#x00a0;that</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <m:mtext>(</m:mtext>
+             <xsl:apply-templates select="*[5]"/>
+            <m:mtext>)</m:mtext>
+            <m:mphantom><m:mtext>_</m:mtext></m:mphantom>
+            <xsl:apply-templates select="*[6]"/>
+           </m:mrow>
           </m:mtd>
          </m:mtr>
          <m:mtr>
@@ -1256,8 +1618,220 @@
          </m:mtr>
         </m:mtable>
       </xsl:when>
+      <!-- EQ_CHAIN -->
+      <xsl:when test="$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="$id != ''">
+          <xsl:attribute name="m:xref"><xsl:value-of select="$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="m: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="$id != ''">
+           <xsl:attribute name="m:xref"><xsl:value-of select="$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="m: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="$id != ''">
+           <xsl:attribute name="m:xref"><xsl:value-of select="$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="m: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="$id != ''">
+           <xsl:attribute name="m:xref"><xsl:value-of select="$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="m: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="$id != ''">
+          <xsl:attribute name="m:xref"><xsl:value-of select="$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="m: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>
@@ -1288,7 +1862,7 @@
          <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>
@@ -1306,7 +1880,7 @@
          <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>
@@ -1322,14 +1896,21 @@
 
 <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="m: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>
@@ -1354,227 +1935,6 @@
     </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 >= $framewidth">
-   <m:mtable align="baseline 1" equalrows="false" columnalign="left">
-    <xsl:if test="@helm:xref">
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-
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-          |m:in[1]|m:intesect[1]|m:union[1]|m:subset[1]
-          |m:prsubset|m:setdiff[1]]">
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-   <xsl:when test="m:geq[1]">
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-<xsl:template match = "m:set">
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-    <xsl:apply-templates select="*[1]" mode="charcount"/>
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-    <xsl:when test="$charlength >= $framewidth">
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-          <m:mo stretchy="false">{</m:mo>
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-          <xsl:apply-templates select="m:condition/*[1]"/>
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-            <mo>,</mo>
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-    <xsl:otherwise>
-     <xsl:apply-imports/>
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-   </xsl:choose>
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- </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       -->
@@ -1658,5 +2018,3 @@
 
 </xsl:stylesheet> 
 
-
-