<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">Th20</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: HEYTING1:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">a</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="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K11" title="NORMFORM:func.11">NormForm</a> <font color="Olive" title="b1">A</font></span>)</span>  st (  for <font color="Olive" title="b5">c</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="Olive" title="b1">A</font>  st <font color="Olive" title="b5">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">u</font> holds <br/> ex <font color="Olive" title="b6">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="Olive" title="b1">A</font> st <br/>( <font color="Olive" title="b6">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">v</font> &amp; <font color="Olive" title="b6">b</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b5">c</font> <a href="normform.html#K1" title="NORMFORM:func.1">\/</a> <font color="Olive" title="b2">a</font> ) ) holds <br/> ex <font color="Olive" title="b5">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="Olive" title="b1">A</font> st <br/>( <font color="Olive" title="b5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Olive" title="b3">u</font></span>)</span> <a href="heyting1.html#K7" title="HEYTING1:func.7">=&gt;&gt;</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Olive" title="b4">v</font></span>)</span> &amp; <font color="Olive" title="b5">b</font> <a href="normform.html#R1" title="NORMFORM:pred.1">c=</a> <font color="Olive" title="b2">a</font> )</div></div>
