+ <!-- mode lambda is defined in content.xsl -->
+ <xsl:apply-templates select="*[1]" mode="lambda"/>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template match="decl" mode="lambda_prop">
+ <xsl:variable name="id" select="@id"/>
+ <xsl:variable name="innertype_available">
+ <xsl:for-each select="$InnerTypes">
+ <xsl:if test="key('typeid',$id)/*">
+ <xsl:text>yes</xsl:text>
+ </xsl:if>
+ </xsl:for-each>
+ </xsl:variable>
+ <xsl:choose>
+ <xsl:when test="$naturalLanguage='yes' and $innertype_available='yes'">
+ <m:apply helm:xref="{@id}">
+ <m:csymbol>proof</m:csymbol>
+ <m:lambda helm:xref="{@id}">
+ <m:bvar>
+ <m:ci>
+ <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="@binder"/></xsl:with-param></xsl:call-template>
+ </m:ci>
+ <m:type>
+ <xsl:apply-templates select="*[1]" mode="noannot"/>
+ </m:type>
+ </m:bvar>
+ <xsl:apply-templates select="following-sibling::*[1]" mode="lambda_prop"/>
+ </m:lambda>
+ <xsl:for-each select="$InnerTypes">
+ <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+ </xsl:for-each>
+ </m:apply>
+ </xsl:when>
+ <xsl:otherwise>
+ <m:lambda helm:xref="{@id}">
+ <m:bvar>
+ <m:ci>
+ <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="@binder"/></xsl:with-param></xsl:call-template>
+ </m:ci>
+ <m:type>
+ <xsl:apply-templates select="*[1]" mode="noannot"/>
+ </m:type>
+ </m:bvar>
+ <xsl:apply-templates select="following-sibling::*[1]" mode="lambda_prop"/>
+ </m:lambda>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template match="target" mode="lambda_prop">
+ <xsl:apply-templates select="*[1]" mode="noannot"/>
+</xsl:template>
+
+<!-- LETIN -->
+
+<xsl:template match="LETIN" mode="noannot">
+ <xsl:choose>
+ <xsl:when test="@sort='Prop'">
+ <xsl:apply-templates select="*[1]" mode="letin_prop"/>
+ </xsl:when>
+ <xsl:otherwise>
+ <!-- mode letin is defined in content.xsl -->
+ <xsl:apply-templates select="*[1]" mode="letin_pure"/>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template match="def" mode="letin_prop">
+ <xsl:variable name="id" select="@id"/>
+ <xsl:variable name="innertype_available">
+ <xsl:for-each select="$InnerTypes">
+ <xsl:if test="key('typeid',$id)/*">
+ <xsl:text>yes</xsl:text>
+ </xsl:if>
+ </xsl:for-each>
+ </xsl:variable>
+ <xsl:choose>
+ <xsl:when test="$naturalLanguage='yes' and $innertype_available='yes'">
+ <m:apply helm:xref="{@id}">
+ <m:csymbol>proof</m:csymbol>
+ <m:apply helm:xref="{@id}">
+ <m:csymbol>let_in</m:csymbol>
+ <m:bvar>
+ <m:ci>
+ <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="@binder"/></xsl:with-param></xsl:call-template>
+ </m:ci>
+ </m:bvar>
+ <xsl:apply-templates select="*[1]" mode="noannot"/>
+ <xsl:apply-templates select="following-sibling::*[1]" mode="letin_prop"/>
+ </m:apply>
+ <xsl:for-each select="$InnerTypes">
+ <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+ </xsl:for-each>
+ </m:apply>
+ </xsl:when>
+ <xsl:otherwise>
+ <m:apply helm:xref="{@id}">
+ <m:csymbol>let_in</m:csymbol>
+ <m:bvar>
+ <m:ci>
+ <xsl:call-template name="insert_subscript"><xsl:with-param name="node_value"><xsl:value-of select="@binder"/></xsl:with-param></xsl:call-template>
+ </m:ci>
+ </m:bvar>
+ <xsl:apply-templates select="*[1]" mode="noannot"/>
+ <xsl:apply-templates select="following-sibling::*[1]" mode="letin_prop"/>
+ </m:apply>
+ </xsl:otherwise>
+ </xsl:choose>
+</xsl:template>
+
+<xsl:template match="target" mode="letin_prop">
+ <xsl:apply-templates select="*[1]" mode="noannot"/>
+</xsl:template>
+
+<!-- ALL these elements have inner type -->
+<xsl:template match="CAST|APPLY|MUTCASE|FIX|COFIX" mode="noannot">
+ <xsl:variable name="id" select="@id"/>
+ <xsl:choose>
+ <xsl:when test="$naturalLanguage='yes' and @sort='Prop'">
+ <m:apply helm:xref="{@id}">
+ <m:csymbol>proof</m:csymbol>
+ <xsl:apply-templates mode="proof_transform" select="."/>
+ <xsl:for-each select="$InnerTypes">
+ <xsl:apply-templates mode="pure" select="key('typeid',$id)/*"/>
+ </xsl:for-each>
+ </m:apply>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:choose>
+ <xsl:when test="name()='APPLY'">
+ <!-- This is the case of an applicative expression wich is not
+ a proof but could contains proofs...
+ MODE LETIN OR MODE PURE ??? Big question -->
+ <xsl:apply-templates select="." mode="pure"/>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:apply-templates select="." mode="pure"/>
+ </xsl:otherwise>
+ </xsl:choose>