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

<span class="kw">set </span><font color="Maroon" title="c1">G0</font> =  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">v</font> =  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">w</font> =  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">e</font> =  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">G1</font> =  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<a NAME="E1:85_1_1"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
(  not  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp;  not  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )
 
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">v1</font> =  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <font color="Maroon" title="c7">w1</font> =  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="glib_006.html#T68" onmouseover="rs('glib_006/T68')" onmouseout="rh()">GLIB_006:68</a>, <a class="ref" href="glib_006.html#T129" onmouseover="rs('glib_006/T129')" onmouseout="rh()">GLIB_006:129</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">f</font> =  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">G2</font> =  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font>;<br/>
<span class="kw">take </span>
 the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</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"> (  not  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  &amp;  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  )</span><br/>

<a NAME="E3:85_1_1"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="glib_006.html#T70" onmouseover="rs('glib_006/T70')" onmouseout="rh()">GLIB_006:70</a>, <a class="ref" href="glib_006.html#T131" onmouseover="rs('glib_006/T131')" onmouseout="rh()">GLIB_006:131</a></span>;<br/>
<a NAME="E4:85_1_1"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
 not  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>
 
;<br/>
<a NAME="E5:85_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A5</font></span>: 
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c7">w1</font>,<font color="Maroon" title="c6">v1</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#T105" onmouseover="rs('glib_006/T105')" onmouseout="rh()">GLIB_006:105</a></span>;<br/>
<a NAME="E6:85_1_1"/>
 ex <font color="Olive" title="b1">e1</font>, <font color="Olive" title="b2">e2</font>, <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>( <font color="Olive" title="b1">e1</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Olive" title="b2">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Olive" title="b1">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">e2</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="85_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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">  ex <font color="Olive" title="b1">e2</font>, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Olive" title="b1">e2</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e2</font> )</span><br/>

<span class="kw">take </span>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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">  ex <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )</span><br/>

<span class="kw">take </span>
 the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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">  ex <font color="Olive" title="b1">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  st <br/>(  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Olive" title="b1">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Olive" title="b1">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )</span><br/>

<span class="kw">take </span>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )</span><br/>

<span class="kw">thus </span><a NAME="E1:85_1_1_1"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85_1_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</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"> (  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )</span><br/>

<span class="kw">thus </span><a NAME="E2:85_1_1_1"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:85_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</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">  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span><br/>

<span class="kw">thus </span><a NAME="E3:85_1_1_1"/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:85_1_1"/>
 not  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D20" onmouseover="rs('glib_000/D20')" onmouseout="rh()">GLIB_000:def 20</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">  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> </span><br/>

<a NAME="E8:85_1_1"/>
 for <font color="Olive" title="b1">e1</font>, <font color="Olive" title="b2">e2</font>, <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</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="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Olive" title="b2">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Olive" title="b3">v1</font>,<font color="Olive" title="b4">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="85_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">e1</font>, <font color="Maroon" title="c11">e2</font>, <font color="Maroon" title="c12">v1</font>, <font color="Maroon" title="c13">v2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c10">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c12">v1</font>,<font color="Maroon" title="c13">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c11">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c12">v1</font>,<font color="Maroon" title="c13">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> implies <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:85_1_1_2"/><span class="lab"><font color="Green" title="E22">A6</font></span>: 
( <font color="Maroon" title="c10">e1</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c12">v1</font>,<font color="Maroon" title="c13">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c11">e2</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c12">v1</font>,<font color="Maroon" title="c13">v2</font>, the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</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="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</font></span><br/>

<a NAME="E2:85_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A7</font></span>: 
( <font color="Maroon" title="c10">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>  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> &amp; <font color="Maroon" title="c11">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>  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D14" onmouseover="rs('glib_000/D14')" onmouseout="rh()">GLIB_000:def 14</a></span>;<br/>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> = 
<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:85_1_1"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="ref" href="glib_006.html#D11" onmouseover="rs('glib_006/D11')" onmouseout="rh()">GLIB_006:def 11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="glib_006.html#D12" onmouseover="rs('glib_006/D12')" onmouseout="rh()">GLIB_006:def 12</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span>,<span class="p2">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T1" onmouseover="rs('enumset1/T1')" onmouseout="rh()">ENUMSET1:1</a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_2_2"><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="E1:85_1_1_2_2"/><span class="kw">then </span>
( ( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ) or ( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ) or ( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ) or ( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:85_1_1_2"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="tarski.html#D2" onmouseover="rs('tarski/D2')" onmouseout="rh()">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_2_2_1"><span class="kw">suppose </span></a><a NAME="E1:85_1_1_2_2_1"/>
( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:85_1_1_2_2_1"/>
<font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_2_2_2"><span class="kw">suppose </span></a><a NAME="E1:85_1_1_2_2_2"/>
( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</font></span><br/><div class="add"><a NAME="E2:85_1_1_2_2_2"/><span class="kw">then </span>
( <font color="Maroon" title="c12">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c13">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c12">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c13">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85_1_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:85_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E1:85_1_1_2"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="glib_000.html#T125" onmouseover="rs('glib_000/T125')" onmouseout="rh()">GLIB_000:125</a></span>;<br/><a NAME="E3:85_1_1_2_2_2"/><span class="kw">then </span>
(  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp;  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )
 ;<br/><span class="kw">hence </span><a NAME="E4:85_1_1_2_2_2"/>
<font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_2_2_3"><span class="kw">suppose </span></a><a NAME="E1:85_1_1_2_2_3"/>
( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</font></span><br/><div class="add"><a NAME="E2:85_1_1_2_2_3"/><span class="kw">then </span>
( <font color="Maroon" title="c12">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c13">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c12">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c13">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85_1_1"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E5:85_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E1:85_1_1_2"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="glib_000.html#T125" onmouseover="rs('glib_000/T125')" onmouseout="rh()">GLIB_000:125</a></span>;<br/><a NAME="E3:85_1_1_2_2_3"/><span class="kw">then </span>
(  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp;  the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> )
 ;<br/><span class="kw">hence </span><a NAME="E4:85_1_1_2_2_3"/>
<font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="85_1_1_2_2_4"><span class="kw">suppose </span></a><a NAME="E1:85_1_1_2_2_4"/>
( <font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> &amp; <font color="Maroon" title="c11">e2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <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="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:85_1_1_2_2_4"/>
<font color="Maroon" title="c10">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">e2</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E9:85_1_1"/>
 the    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c7">w1</font>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, the   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>, <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a>  the   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>,<font color="Maroon" title="c6">v1</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D21" onmouseover="rs('glib_000/D21')" onmouseout="rh()">GLIB_000:def 21</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>
