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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
 ex <font color="Olive">C</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> st <br/>( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">C</font> &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> &amp; <font color="Olive">a</font> <a href="normform.html#R1" target="_self">c=</a> <font color="Olive">b</font> holds <br/><font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> ) )
 
;<br/>
<b>hence </b><a NAME="E3:40"/>
(  not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> or  not <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> or  not <font color="Maroon">a</font> <a href="normform.html#R1" target="_self">c=</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/>


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