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<b>let </b><font color="Maroon">f1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font></span>)</span>,<span class="p2">(<span class="default"><a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font></span>)</span></span><a href="mcart_1.html#K12">:]</a></span>, <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>, <font color="Maroon">f2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font></span>)</span>,<span class="p2">(<span class="default"><a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font></span>)</span></span><a href="mcart_1.html#K12">:]</a></span>, <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8_1_2"/><i><font color="Green">E53</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k1</font>,<font color="Olive">k2</font></span><a href="domain_1.html#K1">]</a></span> where <font color="Olive">k1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>, <font color="Olive">k2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font> : <font color="Olive">k1</font> <a href="commacat.html#K3" target="_self">`11</a>  <a href="hidden.html#R1">=</a> <font color="Olive">k2</font> <a href="commacat.html#K4" target="_self">`12</a>  </span>}</span>  &amp; ( for <font color="Olive">k</font>, <font color="Olive">k'</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>  st <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k</font>,<font color="Olive">k'</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k</font>,<font color="Olive">k'</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">k</font> <a href="commacat.html#K5" target="_self">*</a> <font color="Olive">k'</font> ) )
 <b>and </b><br/><a NAME="E2:8_1_2"/><i><font color="Green">E54</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k1</font>,<font color="Olive">k2</font></span><a href="domain_1.html#K1">]</a></span> where <font color="Olive">k1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>, <font color="Olive">k2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font> : <font color="Olive">k1</font> <a href="commacat.html#K3" target="_self">`11</a>  <a href="hidden.html#R1">=</a> <font color="Olive">k2</font> <a href="commacat.html#K4" target="_self">`12</a>  </span>}</span>  &amp; ( for <font color="Olive">k</font>, <font color="Olive">k'</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>  st <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k</font>,<font color="Olive">k'</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> holds <br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k</font>,<font color="Olive">k'</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R1">=</a> <font color="Olive">k</font> <a href="commacat.html#K5" target="_self">*</a> <font color="Olive">k'</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:8_1_2_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">k1</font>,<font color="Olive">k2</font></span><a href="domain_1.html#K1">]</a></span> where <font color="Olive">k1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>, <font color="Olive">k2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font> : <font color="Olive">k1</font> <a href="commacat.html#K3" target="_self">`11</a>  <a href="hidden.html#R1">=</a> <font color="Olive">k2</font> <a href="commacat.html#K4" target="_self">`12</a>  </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font>, <font color="Maroon">k2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="commacat.html#K2" target="_self">commaMorphs</a> <font color="Maroon">F</font>,<font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:8_1_2_1"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">k1</font>,<font color="Maroon">k2</font></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">k1</font> <a href="commacat.html#K3" target="_self">`11</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">k2</font> <a href="commacat.html#K4" target="_self">`12</a>  )
 ;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">k1</font> <a href="commacat.html#K5" target="_self">*</a> <font color="Maroon">k2</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:8_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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