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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">  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">B</font> where <font color="Olive" title="b1">B</font> is    <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> <span class="p1">(<span class="default"><a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font></span>)</span> :  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b2">a</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b3">b</font> holds <br/><font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> </span> } </span> </span><br/>

<a NAME="E1:31"/>
(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is    <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> <span class="p1">(<span class="default"><a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp; (  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">a</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b2">b</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finsub_1.html#T7" onmouseover="rs('finsub_1/T7')" onmouseout="rh()">FINSUB_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:31"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">B</font> where <font color="Olive" title="b1">B</font> is    <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> <span class="p1">(<span class="default"><a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font></span>)</span> :  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b2">a</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b3">b</font> holds <br/><font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> </span> } </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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