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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E37">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: HEYTING1:25</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> 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 <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="normform.html#K10" title="NORMFORM:func.10">^</a> <span class="p1"><a href="heyting1.html#K2" title="HEYTING1:func.2">{</a><span class="default"><font color="Olive" title="b2">a</font></span><a href="heyting1.html#K2" title="HEYTING1:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/><span class="p1">(<span class="default"><a href="heyting1.html#K4" title="HEYTING1:func.4">Atom</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><a href="heyting1.html#K8" title="HEYTING1:func.8">pseudo_compl</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">u</font></div></div>
