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

<span class="kw">let </span><font color="Maroon" title="c1">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="c1">C</font> is 3 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  implies ( <font color="Maroon" title="c1">C</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:112_2_1"/><span class="lab"><font color="Green" title="E53">A2</font></span>: 
( <font color="Maroon" title="c1">C</font> is 3 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c1">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"> ( <font color="Maroon" title="c1">C</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  )</span><br/>

<a NAME="E2:112_2_1"/><span class="kw">then </span>
( <font color="Maroon" title="c1">C</font> is <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3 <a href="glib_013.html#V3" title="GLIB_013:attr.3">-vertex</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:112_2_1"/><span class="lab"><font color="Green" title="E54">A3</font></span>: 
<font color="Maroon" title="c1">C</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</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="c1">C</font> is  <a href="chord.html#V2" title="CHORD:attr.2">complete</a>  &amp; <font color="Maroon" title="c1">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="112_2_1_1"><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">v</font>, <font color="Olive" title="b2">w</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">C</font>  st <font color="Olive" title="b1">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">w</font> holds <br/><font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">w</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">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"> ( <font color="Maroon" title="c2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">w</font> implies <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:112_2_1_1"/><span class="lab"><font color="Green" title="E55">A4</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">w</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="c2">v</font>,<font color="Maroon" title="c3">w</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> </span><br/>2 = 
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_2_1"><span class="lab"><font color="Green" title="E53">A2</font></span></a>, <a class="ref" href="glib_016.html#D4" onmouseover="rs('glib_016/D4')" onmouseout="rh()">GLIB_016:def 4</a></span>
<br/>.= 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K38" title="GLIB_000:func.38">.allNeighbors()</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:112_2_1"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="ref" href="glib_000.html#T111" onmouseover="rs('glib_000/T111')" onmouseout="rh()">GLIB_000:111</a></span>
;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:112_2_1_1"/><span class="lab"><font color="Green" title="E56">A5</font></span>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">y</font> &amp; <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K38" title="GLIB_000:func.38">.allNeighbors()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T60" onmouseover="rs('card_2/T60')" onmouseout="rh()">CARD_2:60</a></span>;<br/><a NAME="E5:112_2_1_1"/>
( <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> or <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="112_2_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:112_2_1_1_2"/><span class="lab"><font color="Green" title="E57">A6</font></span>: 
( <font color="Maroon" title="c3">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c3">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">y</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"> contradiction</span><br/>

<a NAME="E2:112_2_1_1_2"/><span class="lab"><font color="Green" title="E58">A7</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K38" title="GLIB_000:func.38">.allNeighbors()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:112_2_1"><span class="lab"><font color="Green" title="E54">A3</font></span></a>, <a class="ref" href="glib_000.html#T175" onmouseover="rs('glib_000/T175')" onmouseout="rh()">GLIB_000:175</a></span>;<br/>
<a NAME="E3:112_2_1_1_2"/>
<font color="Maroon" title="c2">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E4:112_2_1_1_2"/><span class="kw">then </span>
 not <font color="Maroon" title="c2">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K38" title="GLIB_000:func.38">.allNeighbors()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112_2_1_1_2"><span class="lab"><font color="Green" title="E58">A7</font></span></a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E5:112_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A8</font></span>: 
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:112_2_1_1"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/>
<a NAME="E6:112_2_1_1_2"/>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:112_2_1_1"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="xboole_1.html#T8" onmouseover="rs('xboole_1/T8')" onmouseout="rh()">XBOOLE_1:8</a></span>;<br/>
<a NAME="E7:112_2_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T5" onmouseover="rs('enumset1/T5')" onmouseout="rh()">ENUMSET1:5</a></span>;<br/>
<a NAME="E8:112_2_1_1_2"/><span class="kw">then </span>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">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="ref" href="card_1.html#T11" onmouseover="rs('card_1/T11')" onmouseout="rh()">CARD_1:11</a></span>;<br/>
<a NAME="E9:112_2_1_1_2"/><span class="kw">then </span>
4 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">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="#E1:112_2_1_1"><span class="lab"><font color="Green" title="E55">A4</font></span></a>, <a class="txt" href="#E4:112_2_1_1"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="txt" href="#E1:112_2_1_1_2"><span class="lab"><font color="Green" title="E57">A6</font></span></a>, <a class="txt" href="#E5:112_2_1_1_2"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="ref" href="card_2.html#T59" onmouseover="rs('card_2/T59')" onmouseout="rh()">CARD_2:59</a></span>;<br/>
<a NAME="E10:112_2_1_1_2"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 4 <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_2_1"><span class="lab"><font color="Green" title="E53">A2</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/>
<span class="kw">hence </span><a NAME="E11:112_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T39" onmouseover="rs('nat_1/T39')" onmouseout="rh()">NAT_1:39</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><a NAME="E6:112_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K38" title="GLIB_000:func.38">.allNeighbors()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:112_2_1_1"><span class="lab"><font color="Green" title="E56">A5</font></span></a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><a NAME="E7:112_2_1_1"/><span class="kw">then </span>
 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="c2">v</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T71" onmouseover="rs('glib_000/T71')" onmouseout="rh()">GLIB_000:71</a></span>;<br/><span class="kw">hence </span><a NAME="E8:112_2_1_1"/>
<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">w</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D3" onmouseover="rs('chord/D3')" onmouseout="rh()">CHORD:def 3</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="E5:112_2_1"/>
<font color="Maroon" title="c1">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#D6" onmouseover="rs('chord/D6')" onmouseout="rh()">CHORD:def 6</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="c1">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="112_2_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">P</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">C</font>  st <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>  holds <br/><font color="Olive" title="b1">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">P</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">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"> ( <font color="Maroon" title="c2">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="c2">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>  implies <font color="Maroon" title="c2">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:112_2_1_2"/><span class="lab"><font color="Green" title="E55">A9</font></span>: 
( <font color="Maroon" title="c2">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="c2">P</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">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"> <font color="Maroon" title="c2">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</a> </span><br/><a NAME="E2:112_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A10</font></span>: 
3 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" onmouseover="rs('nat_1/T44')" onmouseout="rh()">NAT_1:44</a></span>;<br/><a NAME="E3:112_2_1_2"/>
<font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">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="#E1:112_2_1_2"><span class="lab"><font color="Green" title="E55">A9</font></span></a>, <a class="ref" href="glibpre1.html#T26" onmouseover="rs('glibpre1/T26')" onmouseout="rh()">GLIBPRE1:26</a></span>;<br/><a NAME="E4:112_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:112_2_1"><span class="lab"><font color="Green" title="E53">A2</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="E5:112_2_1_2"/><span class="kw">then </span>
3 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:112_2_1_2"><span class="lab"><font color="Green" title="E56">A10</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:112_2_1_2"/>
<font color="Maroon" title="c2">P</font> is  <a href="chord.html#V5" title="CHORD:attr.5">chordal</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"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:112_2_1"/>
<font color="Maroon" title="c1">C</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</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/>


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