<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/>





<a NAME="E1:55"/>
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="normform.html#T64" target="_self" title="NORMFORM:th.64">Th64</a></i>;<br/>
<a NAME="E2:55"/><b>then </b><i><font color="Green" title="E37">A1</font></i>: 
<span class="p1">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font>
 
<b>by </b><i><a class="ref" href="normform.html#T70" target="_self" title="NORMFORM:th.70">Th70</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">a</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font>;<br/><b>assume </b><a NAME="E1:55_1"/><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font></span>)</span>
 ;<br/><a NAME="E2:55_1"/><b>then </b>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="ref" href="normform.html#T58" target="_self" title="NORMFORM:th.58">Th58</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E4:55_1"/><i><font color="Green" title="E39">A3</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Maroon" title="c4">a</font>
 <b>and </b><br/><a NAME="E5:55_1"/><i><font color="Green" title="E40">A4</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="txt" href="normform.html#E87"><i><font color="Green" title="E35">Lm6</font></i></a></i>;<br/><b>thus </b><a NAME="E6:55_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="txt" href="normform.html#E2:55"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="normform.html#E1:55_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="txt" href="normform.html#E4:55_1"><i><font color="Green" title="E39">A3</font></i></a>, <a class="txt" href="normform.html#E5:55_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="ref" href="normform.html#T58" target="_self" title="NORMFORM:th.58">Th58</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:55"/>
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="txt" href="normform.html#E77"><i><font color="Green" title="E28">Lm5</font></i></a></i>;<br/>


</div>
