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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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  <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="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<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>,<font color="Olive" title="b1">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<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>,<font color="Maroon" title="c2">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font></span><br/><span class="kw">thus </span><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="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<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>,<font color="Maroon" title="c2">x</font>) = 
<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="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normform.html#D6" target="_self" onmouseover="rs('normform/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T21" onmouseover="rs('mcart_1/T21')" onmouseout="rh()">MCART_1:21</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:18"/>
<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="binop_1.html#T4" onmouseover="rs('binop_1/T4')" onmouseout="rh()">BINOP_1:4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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