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<span class="kw">let </span><font color="Maroon" title="c2">C</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  implies (  not <font color="Maroon" title="c2">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  &amp;  not <font color="Maroon" title="c2">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:113_1_1"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
( <font color="Maroon" title="c2">C</font> is <font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  &amp;  not <font color="Maroon" title="c2">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  )</span><br/>

<a NAME="E2:113_1_1"/>
 ex <font color="Olive" title="b1">P</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">C</font> st <br/>( <font color="Olive" title="b1">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 &amp; <font color="Olive" title="b1">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>  &amp;  not <font color="Olive" title="b1">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>  )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="113_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c3">P</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">C</font><span class="kw"> such that </span><br/><a NAME="E2:113_1_1_1"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c3">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:113_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="glib_002.html#D2" onmouseover="rs('glib_002/D2')" onmouseout="rh()">GLIB_002:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">P</font> = <font color="Maroon" title="c3">P</font> as   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c2">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:113_1_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">P</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3 &amp; <font color="Maroon" title="c4">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>  &amp;  not <font color="Maroon" title="c4">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>  )</span><br/>

<span class="lab"><font color="Green" title="E55">A3</font></span>: <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  = 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glpacy00.html#T2" target="_self" onmouseover="rs('glpacy00/T2')" onmouseout="rh()">Th4</a></span>
<br/>.= 
<font color="Maroon" title="c2">C</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:113_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:113_1_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="glpacy00.html#T31" target="_self" onmouseover="rs('glpacy00/T31')" onmouseout="rh()">Th39</a></span>
<br/>.= 
<font color="Maroon" title="c2">C</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:113_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="glpacy00.html#T32" target="_self" onmouseover="rs('glpacy00/T32')" onmouseout="rh()">Th40</a></span>
<br/>.= 
<font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:113_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="glib_013.html#D3" onmouseover="rs('glib_013/D3')" onmouseout="rh()">GLIB_013:def 3</a></span>
;<br/>
<a NAME="E5:113_1_1_1"/>
<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#K1" title="NAT_1:func.1">+</a> 3 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" onmouseover="rs('xreal_1/T8')" onmouseout="rh()">XREAL_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:113_1_1_1"/>
<font color="Maroon" title="c4">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:113_1_1_1"><span class="lab"><font color="Green" title="E55">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>  &amp;  not <font color="Maroon" title="c4">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>  )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="113_1_1_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">n</font> &amp; <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font> &amp;  ex <font color="Olive" title="b3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font>,<font color="Maroon" title="c2">C</font> holds <br/> ex <font color="Olive" title="b3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; <font color="Olive" title="b3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font>,<font color="Maroon" title="c2">C</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">m</font>, <font color="Maroon" title="c6">n</font> be   <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font> &amp; <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font> &amp;  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font> implies  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font> ) )</span><br/><span class="kw">assume </span><a NAME="E1:113_1_1_1_2"/>
( <font color="Maroon" title="c5">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">n</font> &amp; <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font> implies  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font> ) )</span><br/><span class="kw">given </span><font color="Maroon" title="c7">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><a NAME="E3:113_1_1_1_2"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
<font color="Maroon" title="c7">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c8">e</font> = <font color="Maroon" title="c7">e</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; <font color="Maroon" title="c8">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font> )</span><br/><a NAME="E4:113_1_1_1_2"/>
<font color="Maroon" title="c8">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:113_1_1_1_2"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="glib_000.html#D13" onmouseover="rs('glib_000/D13')" onmouseout="rh()">GLIB_000:def 13</a></span>;<br/><span class="kw">hence </span><a NAME="E5:113_1_1_1_2"/>
<font color="Maroon" title="c8">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:113_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E2:113_1_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="glpacy00.html#T31" target="_self" onmouseover="rs('glpacy00/T31')" onmouseout="rh()">Th39</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font></span><br/><span class="kw">thus </span><a NAME="E6:113_1_1_1_2"/>
<font color="Maroon" title="c8">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font>,<font color="Maroon" title="c4">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">n</font>,<font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:113_1_1_1_2"><span class="lab"><font color="Green" title="E56">A4</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E8:113_1_1_1"/>
( <font color="Maroon" title="c4">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>  &amp;  not <font color="Maroon" title="c4">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:113_1_1_1"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="ref" href="chord.html#D10" onmouseover="rs('chord/D10')" onmouseout="rh()">CHORD:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E3:113_1_1"/>
(  not <font color="Maroon" title="c2">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  &amp;  not <font color="Maroon" title="c2">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D11" onmouseover="rs('chord/D11')" onmouseout="rh()">CHORD:def 11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
