+ <!-- by_induction -->
+ <xsl:when test="$name='by_induction'">
+ <FONT color="red">We prove </FONT>
+ <xsl:apply-templates select="../*[3]">
+ <xsl:with-param name="current_indent" select="$current_indent+18"/>
+ </xsl:apply-templates>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <FONT color="red">by induction on </FONT>
+ <xsl:apply-templates select="*[position()=last()]/*[position()=last()]">
+ <xsl:with-param name="current_indent" select="$current_indent+30"/>
+ </xsl:apply-templates>
+ <!--
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <xsl:text>The induction property is</xsl:text>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <xsl:apply-templates select="*[3]">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:apply-templates>
+ -->
+ <xsl:apply-templates
+ select="*[position()>3 and not(position()=last())]">
+ <xsl:with-param name="current_indent" select="$current_indent+4"/>
+ </xsl:apply-templates>
+ <!-- <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <xsl:text>End induction</xsl:text> -->
+ </xsl:when>
+ <!-- inductive_case -->
+ <xsl:when test="$name='inductive_case'">
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <FONT color="red">Case </FONT>
+ <xsl:apply-templates select="*[2]">
+ <xsl:with-param name="current_indent" select="$current_indent +10"/>
+ </xsl:apply-templates>
+ <xsl:if test="*[3]/*[position()>1]">
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent+4"/>
+ </xsl:call-template>
+ <FONT color="red">By induction hypothesis, we have:</FONT>
+ <xsl:for-each select="*[3]/*[position()>1]">
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent + 4"/>
+ </xsl:call-template>
+ <xsl:text>(</xsl:text>
+ <xsl:apply-templates select="m:ci"/>
+ <xsl:text>) </xsl:text>
+ <xsl:apply-templates select="m:type">
+ <xsl:with-param name="current_indent" select="$current_indent + 8"/>
+ </xsl:apply-templates>
+ </xsl:for-each>
+ </xsl:if>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent + 4"/>
+ </xsl:call-template>
+ <xsl:apply-templates select="*[4]">
+ <xsl:with-param name="current_indent" select="$current_indent +4"/>
+ </xsl:apply-templates>
+ <!-- <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <xsl:text>End Case</xsl:text> -->
+ </xsl:when>
+ <!-- case_lhs -->
+ <xsl:when test="$name='case_lhs'">
+ <xsl:choose>
+ <xsl:when test="count(*)=2">
+ <xsl:apply-templates mode="inline" select="*[2]"/>
+ </xsl:when>
+ <xsl:otherwise>
+ <xsl:text>(</xsl:text>
+ <xsl:apply-templates mode="inline" select="*[2]"/>
+ <xsl:for-each select="m:bvar">
+ <xsl:text> </xsl:text>
+ <xsl:apply-templates mode="inline" select="*[1]"/>
+ <xsl:text>:</xsl:text>
+ <xsl:apply-templates mode="inline" select="m:type/*[1]"/>
+ </xsl:for-each>
+ <xsl:text>)</xsl:text>
+ </xsl:otherwise>
+ </xsl:choose>
+ </xsl:when>
+ <!-- nat_ind -->
+ <xsl:when test="$name='nat_ind_complete'">
+ <FONT color="red">By induction on </FONT>
+ <xsl:apply-templates select="*[2]"/>:
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <xsl:text>0 </xsl:text>
+ <FONT FACE="Symbol" mathcolor="green">Þ</FONT>
+ <xsl:apply-templates select="*[3]">
+ <xsl:with-param name="current_indent" select="$current_indent + 8"/>
+ </xsl:apply-templates>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <xsl:text>S(</xsl:text>
+ <xsl:apply-templates select="*[4]"/>
+ <xsl:text>) </xsl:text>
+ <FONT FACE="Symbol" mathcolor="green">Þ</FONT>
+ <FONT color="red">Assume by induction</FONT>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent +10"/>
+ </xsl:call-template>
+ <xsl:text>(</xsl:text>
+ <xsl:apply-templates select="*[5]"/>
+ <xsl:text>)</xsl:text>
+ <xsl:apply-templates select="*[6]">
+ <xsl:with-param name="current_indent" select="$current_indent + 14"/>
+ </xsl:apply-templates>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent +10"/>
+ </xsl:call-template>
+ <xsl:apply-templates select="*[7]">
+ <xsl:with-param name="current_indent" select="$current_indent + 10"/>
+ </xsl:apply-templates>
+ </xsl:when>
+ <!-- false_ind -->
+ <xsl:when test="$name='false_ind'">
+ <xsl:apply-templates select="*[3]">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:apply-templates>
+ <br/>
+ <xsl:call-template name="make_indent">
+ <xsl:with-param name="current_indent" select="$current_indent"/>
+ </xsl:call-template>
+ <FONT color="red">Contradiction.</FONT>
+ </xsl:when>