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<span class="kw">let </span><font color="Maroon" title="c1">X</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">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</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="b2">y</font> <a href="tarski.html#R2" title="TARSKI: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="b1">x</font> <a href="tarski.html#R2" title="TARSKI: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="b2">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI: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="b2">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="b1">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="b1">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="b2">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">x</font>, <font color="Maroon" title="c3">y</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" 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"> ( <font color="Maroon" title="c3">y</font> <a href="tarski.html#R2" title="TARSKI: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="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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="c3">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">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="c2">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">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="E1:27"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="tarski.html#R2" title="TARSKI: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="E2:27"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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" 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"> ( <font color="Maroon" title="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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="c3">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">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="c2">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">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="E3:27"/><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="c3">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="c2">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="c3">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="c2">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="c3">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="c2">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">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="c3">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="c2">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">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="c3">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="c2">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">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="c3">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">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="c2">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">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" onmouseover="rs('xboole_1/T23')" onmouseout="rh()">XBOOLE_1:23</a></span>;<br/>
<a NAME="E4:27"/>
<font color="Maroon" title="c2">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="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="txt" href="#E2:27"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="normform.html#T23" target="_self" onmouseover="rs('normform/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E5:27"/><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="c2">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="c2">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> 
 
;<br/>
<a NAME="E6:27"/>
<font color="Maroon" title="c3">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="c3">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="#E1:27"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="normform.html#T23" target="_self" onmouseover="rs('normform/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E7:27"/><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="c3">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="c3">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> 
 
;<br/>
<a NAME="E8:27"/><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="c3">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="c2">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">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="c3">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">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="c2">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">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" onmouseover="rs('xboole_1/T23')" onmouseout="rh()">XBOOLE_1:23</a></span>;<br/>
<a NAME="E9:27"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">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="c3">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="c2">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="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">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="c3">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="c2">x</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a></span>)</span> )
 
;<br/>
<span class="kw">thus </span><a NAME="E10:27"/>
( <font color="Maroon" title="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">X</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">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">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="c2">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">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="#E7:27"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E9:27"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="xboole_0.html#D7" onmouseover="rs('xboole_0/D7')" onmouseout="rh()">XBOOLE_0:def 7</a>, <a class="ref" href="normform.html#T23" target="_self" onmouseover="rs('normform/T23')" onmouseout="rh()">Th23</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"><span class="p2">(<span class="default"><font color="Maroon" title="c3">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">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="c2">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">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="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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/>

<span class="kw">assume </span><a NAME="E11:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">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">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="c2">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">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" 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"> <font color="Maroon" title="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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="E12:27"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">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="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">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="#E7:27"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E5:27"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E3:27"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E8:27"><span class="lab"><font color="Green" title="E24">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:27"/>
<font color="Maroon" title="c3">y</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI: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" 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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