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<div class="add">

<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">  <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font>;<br/>
<a NAME="E1:65"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">n</font>
 
;<br/>
<a NAME="E2:65"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#D7" target="_self" title="MYCIELSK:def.7">Def7</a></span>;<br/>
<a NAME="E3:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A2</font></span>: 
 ex <font color="Olive" title="b1">C</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="dilworth.html#NM1" title="DILWORTH:NM.1">Clique</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> st  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="card_1.html#T40" title="CARD_1:th.40">CARD_1:40</a></span>;<br/>
<a NAME="E4:65"/>
 for <font color="Olive" title="b1">T</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="dilworth.html#NM1" title="DILWORTH:NM.1">Clique</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> holds   <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">T</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">T</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="dilworth.html#NM1" title="DILWORTH:NM.1">Clique</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</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="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">T</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font></span><br/>

<a NAME="E1:65_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="card_1.html#T40" title="CARD_1:th.40">CARD_1:40</a></span>;<br/>
<a NAME="E2:65_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A3</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#D7" target="_self" title="MYCIELSK:def.7">Def7</a></span>;<br/>
<a NAME="E3:65_1"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">T</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dilworth.html#D4" title="DILWORTH:def.4">DILWORTH:def 4</a></span>;<br/>
<a NAME="E4:65_1"/>
 <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="mycielsk.html#T11" target="_self" title="MYCIELSK:th.11">Th11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:65_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">T</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:65"/>
 <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <span class="p1">(<span class="default"><a href="mycielsk.html#K5" title="MYCIELSK:func.5">CompleteRelStr</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="dilworth.html#D4" title="DILWORTH:def.4">DILWORTH:def 4</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/>


</div>
