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<span class="kw">let </span><font color="Maroon" title="c1">X</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">y</font>, <font color="Olive" title="b2">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">X</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">X</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> holds <br/>( <font color="Olive" title="b1">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> iff <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">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">X</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">X</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"> ( <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> implies ( <font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> iff <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:51"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E2:51"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> iff <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>

<a NAME="E3:51"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></span>;<br/>
<a NAME="E4:51"/>
<font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">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="txt" href="#E2:51"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="normform.html#T42" target="_self" title="NORMFORM:th.42">Th42</a></span>;<br/>
<a NAME="E5:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <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="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E6:51"/>
<font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="normform.html#T42" target="_self" title="NORMFORM:th.42">Th42</a></span>;<br/>
<a NAME="E7:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <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="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E8:51"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span></span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></span>;<br/>
<a NAME="E9:51"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font></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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font></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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> )
 
<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/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:51_1"/>
<font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><a NAME="E2:51_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font></span>)</span> <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="normform.html#T42" target="_self" title="NORMFORM:th.42">Th42</a></span>;<br/><span class="kw">hence </span><a NAME="E3:51_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <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="txt" href="#E7:51"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E8:51"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E11:51"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a> </span>)</span> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E12:51"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:51"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E5:51"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E9:51"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E8:51"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:51"/>
<font color="Maroon" title="c2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
