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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E107">Th91</font></span>: <a NAME="T91"><span class="comment"><font color="firebrick">:: SCMYCIEL:91</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="scmyciel.html#NM1" title="SCMYCIEL:NM.1">SimpleGraph</a> holds   <a href="scmyciel.html#NK3" title="SCMYCIEL:NK.3">Edges</a> <span class="p1">(<span class="default"><a href="scmyciel.html#K12" title="SCMYCIEL:func.12">Mycielskian</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmyciel.html#NK3" title="SCMYCIEL:NK.3">Edges</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"> { <span class="default"> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b2">x</font>,<span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">y</font>,<span class="p5">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">G</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> where <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">G</font> : <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="scmyciel.html#NK3" title="SCMYCIEL:NK.3">Edges</a> <font color="Olive" title="b1">G</font> </span> } </span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">G</font></span>)</span>,<span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b2">y</font>,<span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">G</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> where <font color="Olive" title="b2">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">G</font> : <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b1">G</font> </span> } </span> </div></div>
