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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="dilworth.html#V3" title="DILWORTH:attr.3">with_finite_clique#</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">R</font> is   <a href="dilworth.html#NM2" title="DILWORTH:NM.2">StableSet</a> of <font color="Maroon" title="c1">R</font> implies  <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E19">A</font></span>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">R</font> is   <a href="dilworth.html#NM2" title="DILWORTH:NM.2">StableSet</a> of <font color="Maroon" title="c1">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<a NAME="E2:41"/><span class="lab"><font color="Green" title="E20">B</font></span>: 
 <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <font color="Maroon" title="c1">R</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<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/>
<span class="kw">consider </span><font color="Maroon" title="c2">A</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 <font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E4:41"/><span class="lab"><font color="Green" title="E21">C</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <font color="Maroon" title="c1">R</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="dilworth.html#D4" target="_self" title="DILWORTH:def.4">Lheight</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:41"/>
 <a href="dilworth.html#K1" title="DILWORTH:func.1">clique#</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E6:41"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">A</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E20">B</font></span></a>, <a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E21">C</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:41"/><span class="lab"><font color="Green" title="E22">D</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E9:41"/><span class="lab"><font color="Green" title="E23">E</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">and </span><br/><a NAME="E10:41"/><span class="lab"><font color="Green" title="E24">F</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#T1" title="GLIB_002:th.1">GLIB_002:1</a></span>;<br/>
<span class="kw">thus </span><a NAME="E11:41"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:41"><span class="lab"><font color="Green" title="E22">D</font></span></a>, <a class="txt" href="#E9:41"><span class="lab"><font color="Green" title="E23">E</font></span></a>, <a class="txt" href="#E10:41"><span class="lab"><font color="Green" title="E24">F</font></span></a>, <a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E19">A</font></span></a>, <a class="ref" href="dilworth.html#T15" target="_self" title="DILWORTH:th.15">ACClique</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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