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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">R</font> being   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a>  st <br/>(  <a href="dilworth.html#K2" title="DILWORTH:func.2">stability#</a> <font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="mycielsk.html#K3" title="MYCIELSK:func.3">cliquecover#</a> <font color="Olive" title="b1">R</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">R</font> =  <a href="mycielsk.html#K7" title="MYCIELSK:func.7">Mycielskian</a> <font color="Maroon" title="c1">n</font>;<br/>
<a NAME="E1:89"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E2:89"/><span class="kw">then </span>
<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E3:89"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A1</font></span>: 
(  <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K7" title="MYCIELSK:func.7">Mycielskian</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="mycielsk.html#K2" title="MYCIELSK:func.2">chromatic#</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K7" title="MYCIELSK:func.7">Mycielskian</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#T50" target="_self" title="MYCIELSK:th.50">Th50</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c3">S</font> =  <a href="necklace.html#K3" title="NECKLACE:func.3">ComplRelStr</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K7" title="MYCIELSK:func.7">Mycielskian</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="dilworth.html#K2" title="DILWORTH:func.2">stability#</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="mycielsk.html#K3" title="MYCIELSK:func.3">cliquecover#</a> <font color="Maroon" title="c3">S</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font> )</span><br/>

<span class="kw">thus </span><a NAME="E4:89"/>
 <a href="dilworth.html#K2" title="DILWORTH:func.2">stability#</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:89"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="mycielsk.html#T23" target="_self" title="MYCIELSK:th.23">Th23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="mycielsk.html#K3" title="MYCIELSK:func.3">cliquecover#</a> <font color="Maroon" title="c3">S</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font></span><br/>

<span class="kw">thus </span><a NAME="E5:89"/>
 <a href="mycielsk.html#K3" title="MYCIELSK:func.3">cliquecover#</a> <font color="Maroon" title="c3">S</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:89"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="mycielsk.html#T29" target="_self" title="MYCIELSK:th.29">Th29</a></span>; <a class="txt" 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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