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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: MYCIELSK:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="mycielsk.html#V1" title="MYCIELSK:attr.1">with_finite_chromatic#</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">C</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="dilworth.html#NM4" title="DILWORTH:NM.4">Coloring</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">c</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">C</font> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mycielsk.html#K2" title="MYCIELSK:func.2">chromatic#</a> <font color="Olive" title="b1">R</font> holds <br/> ex <font color="Olive" title="b4">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> st <br/>( <font color="Olive" title="b4">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">c</font> &amp; (  for <font color="Olive" title="b5">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">C</font>  st <font color="Olive" title="b5">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> holds <br/> ex <font color="Olive" title="b6">w</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> st <br/>( <font color="Olive" title="b6">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="mycielsk.html#K4" title="MYCIELSK:func.4">Adjacent</a> <font color="Olive" title="b4">v</font> &amp; <font color="Olive" title="b6">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">d</font> ) ) )</div></div>
