<?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">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">B</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> <font color="Maroon" title="c2">X</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">X</font>,<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>







<b>set </b><font color="Maroon" title="c6">J</font> =  <a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font>;<br/>
<a NAME="E1:28"/><i><font color="Green" title="E21">A1</font></i>: 
(  <a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  &amp; <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p1">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="normform.html#T37" target="_self" title="NORMFORM:th.37">Th37</a>, <a class="ref" href="normform.html#T38" target="_self" title="NORMFORM:th.38">Th38</a></i>;<br/>
<b>assume </b><a NAME="E2:28"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c3">B</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1"/>
( <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><b>hence </b> <a href="normform.html#K6" title="NORMFORM:func.6">FinPairUnion</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">f</font> = 
<span class="p1">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c4">f</font>

<br/>.= 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="normform.html#E1:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="setwiseo.html#T40" title="SETWISEO:th.40">SETWISEO:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</a> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c5">g</font>
<b>by </b><i><a class="txt" href="normform.html#E1:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="setwiseo.html#T40" title="SETWISEO:th.40">SETWISEO:40</a></i>
<br/>.= 
 <a href="normform.html#K6" title="NORMFORM:func.6">FinPairUnion</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c5">g</font>
<b>by </b><i><a class="txt" href="normform.html#E1:28_1_1_1"><i><font color="Green" title="E23">A3</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_2"/><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:28_1_1_2"/><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="normform.html#E2:28"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="lattice2.html#T16" title="LATTICE2:th.16">LATTICE2:16</a></i>;<br/><b>thus </b><a NAME="E3:28_1_1_2"/>
 <a href="normform.html#K6" title="NORMFORM:func.6">FinPairUnion</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K6" title="NORMFORM:func.6">FinPairUnion</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c5">g</font>
 <b>by </b><i><a class="txt" href="normform.html#E1:28_1_1_2"><i><font color="Green" title="E23">A4</font></i></a>, <a class="txt" href="normform.html#E2:28_1_1_2"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="setwiseo.html#T35" title="SETWISEO:th.35">SETWISEO:35</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:28"/>
 <a href="normform.html#K6" title="NORMFORM:func.6">FinPairUnion</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K6" title="NORMFORM:func.6">FinPairUnion</a> <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c5">g</font>
 ;<br/>


</div>
