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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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> holds   <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> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b1">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Maroon" title="c2">x</font></span><br/>



<a NAME="E1:45"/>
<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="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a>  <a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#T36" target="_self" title="NORMFORM:th.36">Th36</a></span>;<br/>
<a NAME="E2:45"/><span class="kw">then </span>
 <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_1.html#D8" title="BINOP_1:def.8">BINOP_1:def 8</a></span>;<br/>
<a NAME="E3:45"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p2">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p2">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:45"/>
( <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p2">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  &amp; <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <span class="p2">(<span class="default"><a href="normform.html#K5" title="NORMFORM:func.5">FinPairUnion</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="normform.html#D1" target="_self" title="NORMFORM:def.1">NORMFORM:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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