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

<span class="kw">let </span><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</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">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> implies  for <font color="Olive" title="b1">u1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">u2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u2</font> holds <br/> for <font color="Olive" title="b3">H1</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span><br/>  for <font color="Olive" title="b4">H2</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Olive" title="b3">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b4">H2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:65"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</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">  for <font color="Olive" title="b1">u1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">u2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">u2</font> holds <br/> for <font color="Olive" title="b3">H1</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span><br/>  for <font color="Olive" title="b4">H2</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Olive" title="b3">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b4">H2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">u1</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</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">  for <font color="Olive" title="b1">u2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u2</font> holds <br/> for <font color="Olive" title="b2">H1</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span><br/>  for <font color="Olive" title="b3">H2</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Olive" title="b2">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b3">H2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">u2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</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="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u2</font> implies  for <font color="Olive" title="b1">H1</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span><br/>  for <font color="Olive" title="b2">H2</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Olive" title="b1">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b2">H2</font> )</span><br/>



<span class="kw">assume </span><a NAME="E2:65"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">u2</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">  for <font color="Olive" title="b1">H1</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span><br/>  for <font color="Olive" title="b2">H2</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Olive" title="b1">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b2">H2</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">G2Adj</font> = <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">G1Adj</font> = <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<a NAME="E3:65"/><span class="lab"><font color="Green" title="E57">A3</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</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="#E1:65"><span class="lab"><font color="Green" title="E55">A1</font></span></a>, <a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="ref" href="chord.html#T51" target="_self" onmouseover="rs('chord/T51')" onmouseout="rh()">Th50</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">H1</font> be    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.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">  for <font color="Olive" title="b1">H2</font> being    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds  <font color="Maroon" title="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Olive" title="b1">H2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">H2</font> be    <a href="chord.html#M1" title="CHORD:mode.1">AdjGraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.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="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c8">H2</font></span><br/>



<a NAME="E4:65"/><span class="lab"><font color="Green" title="E58">A4</font></span>: 
<font color="Maroon" title="c7">H1</font> is   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D5" target="_self" onmouseover="rs('chord/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<a NAME="E5:65"/><span class="lab"><font color="Green" title="E59">A5</font></span>: 
<font color="Maroon" title="c8">H2</font> is   <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c2">G2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="chord.html#D5" target="_self" onmouseover="rs('chord/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:65_1"/>
(  not <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G1</font></span>)</span> or <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G1</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1"><span class="kw">suppose </span></a><a NAME="E1:65_1_1"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is  not   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G1</font></span>)</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="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c8">H2</font></span><br/><div class="add"><a NAME="E2:65_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E3:65_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A7</font></span>: 
<font color="Maroon" title="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>;<br/><a NAME="E4:65_1_1"/>
<font color="Maroon" title="c8">H2</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E1:65_1_1"><span class="lab"><font color="Green" title="E60">A6</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><span class="kw">hence </span><a NAME="E5:65_1_1"/>
<font color="Maroon" title="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c8">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1_1"><span class="lab"><font color="Green" title="E61">A7</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_2"><span class="kw">suppose </span></a><a NAME="E1:65_1_2"/><span class="lab"><font color="Green" title="E60">A8</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <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">G1</font></span>)</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="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c8">H2</font></span><br/><div class="add"><a NAME="E2:65_1_2"/><span class="kw">then </span>
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</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="#E4:65"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E3:65_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A9</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c7">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c8">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E4:65_1_2"/>
<font color="Maroon" title="c1">G1</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E55">A1</font></span></a>, <a class="ref" href="glib_000.html#T87" onmouseover="rs('glib_000/T87')" onmouseout="rh()">GLIB_000:87</a></span>;<br/><a NAME="E5:65_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A10</font></span>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T76" onmouseover="rs('glib_000/T76')" onmouseout="rh()">GLIB_000:76</a></span>;<br/><a NAME="E6:65_1_2"/><span class="lab"><font color="Green" title="E63">A11</font></span>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="txt" href="#E1:65_1_2"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E7:65_1_2"/>
<font color="Maroon" title="c2">G2</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E55">A1</font></span></a>, <a class="ref" href="glib_000.html#T87" onmouseover="rs('glib_000/T87')" onmouseout="rh()">GLIB_000:87</a></span>;<br/><a NAME="E8:65_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A12</font></span>: 
<font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">u1</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T76" onmouseover="rs('glib_000/T76')" onmouseout="rh()">GLIB_000:76</a></span>;<br/><a NAME="E9:65_1_2"/>
<font color="Maroon" title="c2">G2</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65"><span class="lab"><font color="Green" title="E55">A1</font></span></a>, <a class="ref" href="glib_000.html#T87" onmouseover="rs('glib_000/T87')" onmouseout="rh()">GLIB_000:87</a></span>;<br/><a NAME="E10:65_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A13</font></span>: 
<font color="Maroon" title="c8">H2</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T43" onmouseover="rs('glib_000/T43')" onmouseout="rh()">GLIB_000:43</a></span>;<br/><a NAME="E11:65_1_2"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">u2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E1:65_1_2"><span class="lab"><font color="Green" title="E60">A8</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E12:65_1_2"/><span class="kw">then </span>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c7">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c8">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E6:65_1_2"><span class="lab"><font color="Green" title="E63">A11</font></span></a>, <a class="txt" href="#E5:65_1_2"><span class="lab"><font color="Green" title="E62">A10</font></span></a>, <a class="txt" href="#E8:65_1_2"><span class="lab"><font color="Green" title="E64">A12</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E13:65_1_2"/>
<font color="Maroon" title="c7">H1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c8">H2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1_2"><span class="lab"><font color="Green" title="E61">A9</font></span></a>, <a class="txt" href="#E10:65_1_2"><span class="lab"><font color="Green" title="E65">A13</font></span></a>, <a class="ref" href="glib_000.html#T86" onmouseover="rs('glib_000/T86')" onmouseout="rh()">GLIB_000:86</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></div><span class="kw">end;</span></div>

</div>
