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

<span class="kw">let </span><font color="Maroon" title="c1">G1</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">  for <font color="Olive" title="b1">G2</font> being   <a href="glib_007.html#NM2" title="GLIB_007:NM.2">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">G3</font> being    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b3">G4</font> being   <a href="glib_007.html#NM2" title="GLIB_007:NM.2">reverseEdgeDirections</a> of <font color="Olive" title="b2">G3</font> holds  <font color="Olive" title="b3">G4</font> is    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Olive" title="b1">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G2</font> be   <a href="glib_007.html#NM2" title="GLIB_007:NM.2">reverseEdgeDirections</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">G3</font> being    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">G4</font> being   <a href="glib_007.html#NM2" title="GLIB_007:NM.2">reverseEdgeDirections</a> of <font color="Olive" title="b1">G3</font> holds  <font color="Olive" title="b2">G4</font> is    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Maroon" title="c2">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">G3</font> be    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</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">G4</font> being   <a href="glib_007.html#NM2" title="GLIB_007:NM.2">reverseEdgeDirections</a> of <font color="Maroon" title="c3">G3</font> holds  <font color="Olive" title="b1">G4</font> is    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Maroon" title="c2">G2</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">G4</font> be   <a href="glib_007.html#NM2" title="GLIB_007:NM.2">reverseEdgeDirections</a> of <font color="Maroon" title="c3">G3</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">G4</font> is    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Maroon" title="c2">G2</font></span><br/>







<span class="lab"><font color="Green" title="E41">A1</font></span>:  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c4">G4</font> = 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c3">G3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>
<br/>.= 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D6" target="_self" onmouseover="rs('glib_012/D6')" onmouseout="rh()">Def6</a></span>
<br/>.= 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>
;<br/>
<a NAME="E2:88"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G3</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#D6" target="_self" onmouseover="rs('glib_012/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<a NAME="E3:88"/><span class="kw">then </span>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G4</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/>
<a NAME="E4:88"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A2</font></span>: 
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c4">G4</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c2">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="88_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">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="c2">G2</font> holds <br/> ( (  ex <font color="Olive" title="b3">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b3">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c2">G2</font> implies  for <font color="Olive" title="b3">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b3">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c4">G4</font> ) &amp; ( (  for <font color="Olive" title="b3">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b3">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c4">G4</font> ) implies  ex <font color="Olive" title="b3">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b3">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">w</font>,<font color="Maroon" title="c2">G2</font> ) )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">w</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"> ( (  ex <font color="Olive" title="b1">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font> implies  for <font color="Olive" title="b1">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b1">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</font> ) &amp; ( (  for <font color="Olive" title="b1">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b1">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</font> ) implies  ex <font color="Olive" title="b1">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font> ) )</span><br/><a NAME="E1:88_2"/><span class="lab"><font color="Green" title="E43">A3</font></span>: 
( <font color="Maroon" title="c5">v</font> is   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> &amp; <font color="Maroon" title="c6">w</font> is   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/><div><span class="kw">hereby </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">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b1">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</font> ) implies  ex <font color="Olive" title="b1">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font> )</span>
<div class="add"><span class="kw">given </span><font color="Maroon" title="c7">e2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><a NAME="E2:88_2_1"/><span class="lab"><font color="Green" title="E44">A4</font></span>: 
<font color="Maroon" title="c7">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<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">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b1">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</font></span><br/><a NAME="E3:88_2_1"/>
<font color="Maroon" title="c7">e2</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">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88_2_1"><span class="lab"><font color="Green" title="E44">A4</font></span></a>, <a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><a NAME="E4:88_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">e2</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="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/><a NAME="E5:88_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A5</font></span>: 
<font color="Maroon" title="c7">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88_2_1"><span class="lab"><font color="Green" title="E44">A4</font></span></a>, <a class="ref" href="glib_007.html#T7" onmouseover="rs('glib_007/T7')" onmouseout="rh()">GLIB_007:7</a></span>;<br/><span class="kw">given </span><font color="Maroon" title="c8">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><a NAME="E7:88_2_1"/><span class="lab"><font color="Green" title="E46">A6</font></span>: 
<font color="Maroon" title="c8">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</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="E8:88_2_1"/>
<font color="Maroon" title="c8">e4</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="c4">G4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:88_2_1"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><a NAME="E9:88_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">e4</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="c3">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" onmouseover="rs('glib_007/T4')" onmouseout="rh()">GLIB_007:4</a></span>;<br/><a NAME="E10:88_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c3">G3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:88_2_1"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="glib_007.html#T7" onmouseover="rs('glib_007/T7')" onmouseout="rh()">GLIB_007:7</a></span>;<br/><span class="kw">hence </span><a NAME="E11:88_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:88_2_1"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="ref" href="glib_012.html#T46" target="_self" onmouseover="rs('glib_012/T46')" onmouseout="rh()">Th46</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">assume </span><a NAME="E3:88_2"/><span class="lab"><font color="Green" title="E44">A7</font></span>: 
 for <font color="Olive" title="b1">e4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b1">e4</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</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">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font></span><br/><a NAME="E4:88_2"/>
 for <font color="Olive" title="b1">e3</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   holds  not <font color="Olive" title="b1">e3</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c3">G3</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="88_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">given </span><font color="Maroon" title="c7">e3</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><a NAME="E2:88_2_2"/><span class="lab"><font color="Green" title="E45">A8</font></span>: 
<font color="Maroon" title="c7">e3</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c3">G3</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="E3:88_2_2"/>
<font color="Maroon" title="c7">e3</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="c3">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88_2_2"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/>
<a NAME="E4:88_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">e3</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c4">G4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:88_2_2"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="ref" href="glib_007.html#T7" onmouseover="rs('glib_007/T7')" onmouseout="rh()">GLIB_007:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:88_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:88_2"><span class="lab"><font color="Green" title="E44">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><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">e1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E6:88_2"/><span class="lab"><font color="Green" title="E45">A9</font></span>: 
<font color="Maroon" title="c7">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88_2"><span class="lab"><font color="Green" title="E43">A3</font></span></a>, <a class="ref" href="glib_012.html#D6" target="_self" onmouseover="rs('glib_012/D6')" onmouseout="rh()">Def6</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c8">e1</font> = <font color="Maroon" title="c7">e1</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">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font></span><br/><a NAME="E7:88_2"/>
<font color="Maroon" title="c8">e1</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="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:88_2"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/><span class="kw">hence </span><a NAME="E8:88_2"/>
<font color="Maroon" title="c8">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:88_2"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="glib_007.html#T7" onmouseover="rs('glib_007/T7')" onmouseout="rh()">GLIB_007:7</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="E6:88"/>
<font color="Maroon" title="c4">G4</font> is    <a href="glib_012.html#M2" title="GLIB_012:mode.2">DLGraphComplement</a> of <font color="Maroon" title="c2">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="txt" href="#E4:88"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="ref" href="glib_012.html#D6" target="_self" onmouseover="rs('glib_012/D6')" onmouseout="rh()">Def6</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>
