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

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  iff <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">H</font> =  the   <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font></span>)</span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:11_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span></span><br/><a NAME="E2:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font></span>)</span>
 ;<br/><a NAME="E3:11_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a>  the   <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D33" onmouseover="rs('glib_000/D33')" onmouseout="rh()">GLIB_000:def 33</a></span>;<br/><a NAME="E4:11_1"/>
<font color="Maroon" title="c1">G</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T40" onmouseover="rs('glib_000/T40')" onmouseout="rh()">GLIB_000:40</a></span>;<br/><a NAME="E5:11_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  the   <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E3:11_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="glib_000.html#T86" onmouseover="rs('glib_000/T86')" onmouseout="rh()">GLIB_000:86</a></span>;<br/><a NAME="E6:11_1"/>
 the   <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T6" target="_self" onmouseover="rs('glenum00/T6')" onmouseout="rh()">Th6</a></span>;<br/><span class="kw">hence </span><a NAME="E7:11_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:11_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="glib_000.html#T85" onmouseover="rs('glib_000/T85')" onmouseout="rh()">GLIB_000:85</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:11"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glenum00.html#K2" title="GLENUM00:func.2">createGraph</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:11"/>
<font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_008.html#T52" onmouseover="rs('glib_008/T52')" onmouseout="rh()">GLIB_008:52</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>
