<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">K</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">F</font> is  <a href="combgras.html#V7" title="COMBGRAS:attr.7">automorphism</a>  &amp; <font color="Olive" title="b2">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  holds <br/>( <font color="Olive" title="b1">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Olive" title="b2">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  &amp; <font color="Olive" title="b1">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Olive" title="b2">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be    <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>  st <font color="Maroon" title="c2">F</font> is  <a href="combgras.html#V7" title="COMBGRAS:attr.7">automorphism</a>  &amp; <font color="Olive" title="b1">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  holds <br/>( <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Olive" title="b1">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Olive" title="b1">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is  <a href="combgras.html#V7" title="COMBGRAS:attr.7">automorphism</a>  &amp; <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  implies ( <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  ) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:37"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="combgras.html#V7" title="COMBGRAS:attr.7">automorphism</a> 
 <span class="kw">and </span><br/><a NAME="E2:37"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
<font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  )</span><br/>

<a NAME="E3:37"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="combgras.html#D9" target="_self" title="COMBGRAS:def.9">Def9</a></span>;<br/>
<a NAME="E4:37"/>
the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c2">F</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="combgras.html#D9" target="_self" title="COMBGRAS:def.9">Def9</a></span>;<br/>
<a NAME="E5:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A4</font></span>: 
the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></span>;<br/>
<a NAME="E6:37"/><span class="lab"><font color="Green" title="E32">A5</font></span>: 
the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T67" title="FUNCT_2:th.67">FUNCT_2:67</a></span>;<br/>
<a NAME="E7:37"/><span class="lab"><font color="Green" title="E33">A6</font></span>: 
for <font color="Olive" title="b1">U</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">U</font> holds <br/><font color="Olive" title="b1">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">U</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">U</font> implies <font color="Maroon" title="c4">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:37_1"/><span class="lab"><font color="Green" title="E34">A7</font></span>: 
<font color="Maroon" title="c4">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 <span class="kw">and </span><br/><a NAME="E2:37_1"/><span class="lab"><font color="Green" title="E35">A8</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">U</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font></span><br/>

<a NAME="E3:37_1"/>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c4">U</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="relat_1.html#T156" title="RELAT_1:th.156">RELAT_1:156</a></span>;<br/>
<a NAME="E4:37_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A9</font></span>: 
<font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c4">U</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="funct_1.html#T147" title="FUNCT_1:th.147">FUNCT_1:147</a></span>;<br/>
<a NAME="E5:37_1"/><span class="lab"><font color="Green" title="E37">A10</font></span>: 
<font color="Maroon" title="c4">U</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c4">U</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="ref" href="funct_1.html#T146" title="FUNCT_1:th.146">FUNCT_1:146</a></span>;<br/>
<a NAME="E6:37_1"/>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c4">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E34">A7</font></span></a>, <a class="ref" href="combgras.html#T20" target="_self" title="COMBGRAS:th.20">Th20</a></span>;<br/>
<a NAME="E7:37_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">U</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E36">A9</font></span></a>, <a class="txt" href="#E5:37_1"><span class="lab"><font color="Green" title="E37">A10</font></span></a>, <a class="ref" href="combgras.html#D3" target="_self" title="COMBGRAS:def.3">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:37_1"/>
<font color="Maroon" title="c4">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37_1"><span class="lab"><font color="Green" title="E35">A8</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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/>


</div><span class="kw">end;</span></div>
<a NAME="E8:37"/><span class="lab"><font color="Green" title="E34">A11</font></span>: 
the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Maroon" title="c2">F</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="combgras.html#D9" target="_self" title="COMBGRAS:def.9">Def9</a></span>;<br/>
<a NAME="E9:37"/><span class="lab"><font color="Green" title="E35">A12</font></span>: 
for <font color="Olive" title="b1">U</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">U</font> holds <br/><font color="Olive" title="b1">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:37_2"/><span class="lab"><font color="Green" title="E36">A13</font></span>: 
<font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E32">A5</font></span></a>, <a class="ref" href="funct_1.html#T146" title="FUNCT_1:th.146">FUNCT_1:146</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">U</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="incsp_1.html#U1" title="INCSP_1:sel.1">Points</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">U</font> implies <font color="Maroon" title="c4">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:37_2"/><span class="lab"><font color="Green" title="E37">A14</font></span>: 
<font color="Maroon" title="c4">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 <span class="kw">and </span><br/><a NAME="E3:37_2"/><span class="lab"><font color="Green" title="E38">A15</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">U</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font></span><br/>

<a NAME="E4:37_2"/>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c4">U</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="ref" href="relat_1.html#T178" title="RELAT_1:th.178">RELAT_1:178</a></span>;<br/>
<a NAME="E5:37_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A16</font></span>: 
<font color="Maroon" title="c3">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c4">U</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_2"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E6:37_2"/>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c4">U</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E2:37_2"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="ref" href="combgras.html#T21" target="_self" title="COMBGRAS:th.21">Th21</a></span>;<br/>
<a NAME="E7:37_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c4">U</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E5:37_2"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="ref" href="combgras.html#D3" target="_self" title="COMBGRAS:def.3">Def3</a></span>;<br/>
<a NAME="E8:37_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">U</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E31">A4</font></span></a>, <a class="ref" href="funct_1.html#T147" title="FUNCT_1:th.147">FUNCT_1:147</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:37_2"/>
<font color="Maroon" title="c4">U</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37_2"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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/>


</div><span class="kw">end;</span></div>
<a NAME="E10:37"/><span class="lab"><font color="Green" title="E36">A17</font></span>: 
<font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="combgras.html#D3" target="_self" title="COMBGRAS:def.3">Def3</a></span>;<br/>
<a NAME="E11:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A18</font></span>: 
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="combgras.html#T20" target="_self" title="COMBGRAS:th.20">Th20</a></span>;<br/>
<a NAME="E12:37"/>
<font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V1" title="COMBGRAS:attr.1">clique</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E36">A17</font></span></a>, <a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="combgras.html#T21" target="_self" title="COMBGRAS:th.21">Th21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:37"/>
( <font color="Maroon" title="c2">F</font> <a href="combgras.html#K4" title="COMBGRAS:func.4">.:</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  &amp; <font color="Maroon" title="c2">F</font> <a href="combgras.html#K5" title="COMBGRAS:func.5">"</a> <font color="Maroon" title="c3">K</font> is  <a href="combgras.html#V2" title="COMBGRAS:attr.2">maximal_clique</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="txt" href="#E9:37"><span class="lab"><font color="Green" title="E35">A12</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E33">A6</font></span></a>, <a class="ref" href="combgras.html#D3" target="_self" title="COMBGRAS:def.3">Def3</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/>


</div>
