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<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">C</font> being   <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> holds   <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Olive" title="b1">B</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Olive" title="b2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Olive" title="b2">C</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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></span><br/>





<a NAME="E1:58"/><i><font color="Green" title="E40">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#T64" target="_self" title="NORMFORM:th.64">Th64</a>, <a class="ref" href="normform.html#T70" target="_self" title="NORMFORM:th.70">Th70</a></i>;<br/>
<a NAME="E2:58"/><i><font color="Green" title="E41">A2</font></i>: 
 <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="ref" href="normform.html#T71" target="_self" title="NORMFORM:th.71">Th71</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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"><span class="p2">(<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></span>)</span> implies <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> )</span><br/><b>assume </b><a NAME="E1:58_1"/><i><font color="Green" title="E42">A3</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"><span class="p2">(<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></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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></span><br/><a NAME="E2:58_1"/><b>then </b><i><font color="Green" title="E43">A4</font></i>: 
<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="ref" href="normform.html#T58" target="_self" title="NORMFORM:th.58">Th58</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">b</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">b</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> &amp; <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> implies <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> )</span><br/><b>assume </b><a NAME="E1:58_1_1"/>
<font color="Maroon" title="c5">b</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> implies <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> )</span><br/><b>then consider </b><font color="Maroon" title="c6">c</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="E3:58_1_1"/><i><font color="Green" title="E44">A5</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Maroon" title="c5">b</font>
 <b>and </b><br/><a NAME="E4:58_1_1"/><i><font color="Green" title="E45">A6</font></i>: 
<font color="Maroon" title="c6">c</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>assume </b><a NAME="E5:58_1_1"/><i><font color="Green" title="E46">A7</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font></span><br/><a NAME="E6:58_1_1"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="normform.html#E3:58_1_1"><i><font color="Green" title="E44">A5</font></i></a>, <a class="ref" href="normform.html#T5" target="_self" title="NORMFORM:th.5">Th5</a></i>;<br/><a NAME="E7:58_1_1"/><b>then </b>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="normform.html#E1:58_1"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="normform.html#E4:58_1_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="normform.html#T58" target="_self" title="NORMFORM:th.58">Th58</a></i>;<br/><b>hence </b><a NAME="E8:58_1_1"/>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="normform.html#E3:58_1_1"><i><font color="Green" title="E44">A5</font></i></a>, <a class="txt" href="normform.html#E5:58_1_1"><i><font color="Green" title="E46">A7</font></i></a>, <a class="ref" href="normform.html#T4" target="_self" title="NORMFORM:th.4">Th4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:58_1"/>
<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>
 <b>by </b><i><a class="txt" href="normform.html#E1:58"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="normform.html#E2:58_1"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="normform.html#T61" target="_self" title="NORMFORM:th.61">Th61</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:58"/>
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<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></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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>
 <b>by </b><i><a class="txt" href="normform.html#E77"><i><font color="Green" title="E28">Lm5</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<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></span>)</span></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> implies <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"><span class="p2">(<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></span>)</span> )</span><br/><b>assume </b><a NAME="E1:58_2"/><i><font color="Green" title="E42">A8</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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"><span class="p2">(<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></span>)</span></span><br/><a NAME="E2:58_2"/><b>then </b>
for <font color="Olive" title="b1">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>  st <font color="Olive" title="b1">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> &amp; <font color="Olive" title="b1">b</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Maroon" title="c4">a</font> holds <br/><font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="normform.html#E1:58"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="normform.html#T58" target="_self" title="NORMFORM:th.58">Th58</a></i>;<br/><b>hence </b><a NAME="E3:58_2"/>
<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"><span class="p2">(<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></span>)</span>
 <b>by </b><i><a class="txt" href="normform.html#E2:58"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="normform.html#E1:58_2"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="normform.html#T61" target="_self" title="NORMFORM:th.61">Th61</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:58"/>
 <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>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<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></span>)</span>
 <b>by </b><i><a class="txt" href="normform.html#E77"><i><font color="Green" title="E28">Lm5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
