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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>,   <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> = <font color="Maroon">a<sub>1</sub></font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">M</font> = <span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span> ;<br/>
<a NAME="E1:41_2_1"/><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E2:41_2_1"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">s</font> <a href="normform.html#K1" target="_self">\/</a> <font color="Olive">t</font></span>)</span> where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E3:41_2_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">B</font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<a NAME="E4:41_2_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">C</font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<a NAME="E5:41_2_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span>  is <a href="finset_1.html#V1">finite</a>
 
<b>from </b><i><a class="ref" href="fraenkel.html#S22">FRAENKEL:sch 22</a>(, <a class="ref" href="normform.html#D6" target="_self">Def6</a>);<br/></i>
<a NAME="E6:41_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span>  is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>
<b>hence </b><a NAME="E7:41_2_1"/>
<span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">A</font> : ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) </span>}</span>  is    <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>
 <b>by </b><i><a class="ref" href="normform.html#T28" target="_self">Th28</a>, <a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/>


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