<?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_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">G9</font> =  the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> ;<br/>
<a NAME="E1:250"/>
<font color="Maroon" title="c1">G</font> is    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K1" title="GLENUM00:func.1">.allSG()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T35" target="_self" onmouseover="rs('glenum00/T35')" onmouseout="rh()">Th35</a></span>;<br/>
<a NAME="E2:250"/><span class="kw">then </span><span class="lab"><font color="Green" title="E149">A1</font></span>: 
 the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  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="glibpre1.html#T119" onmouseover="rs('glibpre1/T119')" onmouseout="rh()">GLIBPRE1:119</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E150">A2</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="250_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  ex <font color="Olive" title="b2">H9</font> being    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  st <font color="Olive" title="b1">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Olive" title="b2">H9</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H9</font> being    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  st <font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Olive" title="b1">H9</font></span><br/><span class="kw">set </span><font color="Maroon" title="c4">H9</font> =  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>  <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c3">v</font></span>)</span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c5">H9</font> =  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>  <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c3">v</font></span>)</span> as    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T189" target="_self" onmouseover="rs('glenum00/T189')" onmouseout="rh()">Th189</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c6">H9</font> = <font color="Maroon" title="c5">H9</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c6">H9</font></span><br/><a NAME="E2:250_1"/>
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c6">H9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c3">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><span class="kw">hence </span><a NAME="E3:250_1"/>
<font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c6">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#T9" onmouseover="rs('glib_002/T9')" onmouseout="rh()">GLIB_002:9</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="250_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of  the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="250_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:250_2_1"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  or  not <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="250_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:250_2_1_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> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of  the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:250_2_1_1"/>
<font color="Maroon" title="c1">G</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of  the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:250"><span class="lab"><font color="Green" title="E150">A2</font></span></a>, <a class="ref" href="glenum00.html#T22" target="_self" onmouseover="rs('glenum00/T22')" onmouseout="rh()">Th22</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="250_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:250_2_1_2"/>
 not <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> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of  the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> </span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">G0</font> = <font color="Maroon" title="c1">G</font> as   non  <a href="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/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="250_2_1_2_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">e</font> being   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c3">G0</font>  ex <font color="Olive" title="b2">H9</font> being    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  st  <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Olive" title="b1">e</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Olive" title="b2">H9</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">e</font> be   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c3">G0</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">H9</font> being    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  st  <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Olive" title="b1">H9</font></span><br/><span class="kw">set </span><font color="Maroon" title="c5">v</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>;<br/><span class="kw">set </span><font color="Maroon" title="c6">w</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>;<br/><a NAME="E1:250_2_1_2_1"/>
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>, <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T14" target="_self" onmouseover="rs('glenum00/T14')" onmouseout="rh()">Th14</a></span>;<br/><a NAME="E2:250_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>, <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T16" onmouseover="rs('glib_000/T16')" onmouseout="rh()">GLIB_000:16</a></span>;<br/><a NAME="E3:250_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E151">A3</font></span>: 
<font color="Maroon" title="c4">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T72" onmouseover="rs('glib_000/T72')" onmouseout="rh()">GLIB_000:72</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">v</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font>, <font color="Maroon" title="c8">w</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">e</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T13" onmouseover="rs('glib_000/T13')" onmouseout="rh()">GLIB_000:13</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c9">H9</font> =  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>  <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c7">v</font></span>)</span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">H9</font> =  the   <a href="glib_009.html#V1" title="GLIB_009:attr.1">plain</a>  <a href="glib_000.html#NM5" title="GLIB_000:NM.5">inducedSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c7">v</font></span>)</span> as    <a href="glenum00.html#M1" title="GLENUM00:mode.1">Element</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T189" target="_self" onmouseover="rs('glenum00/T189')" onmouseout="rh()">Th189</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c11">H9</font> = <font color="Maroon" title="c10">H9</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">  <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c11">H9</font></span><br/><a NAME="E6:250_2_1_2_1"/><span class="lab"><font color="Green" title="E152">A4</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c11">H9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_002.html#K1" title="GLIB_002:func.1">.reachableFrom</a> <font color="Maroon" title="c7">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E7:250_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E153">A5</font></span>: 
<font color="Maroon" title="c7">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#T9" onmouseover="rs('glib_002/T9')" onmouseout="rh()">GLIB_002:9</a></span>;<br/><a NAME="E8:250_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E154">A6</font></span>: 
<font color="Maroon" title="c8">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:250_2_1_2_1"><span class="lab"><font color="Green" title="E151">A3</font></span></a>, <a class="txt" href="#E6:250_2_1_2_1"><span class="lab"><font color="Green" title="E152">A4</font></span></a>, <a class="ref" href="glib_002.html#T10" onmouseover="rs('glib_002/T10')" onmouseout="rh()">GLIB_002:10</a></span>;<br/><a NAME="E9:250_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c11">H9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:250_2_1_2_1"><span class="lab"><font color="Green" title="E151">A3</font></span></a>, <a class="txt" href="#E7:250_2_1_2_1"><span class="lab"><font color="Green" title="E153">A5</font></span></a>, <a class="ref" href="glib_000.html#T32" onmouseover="rs('glib_000/T32')" onmouseout="rh()">GLIB_000:32</a></span>;<br/><a NAME="E10:250_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:250_2_1_2_1"><span class="lab"><font color="Green" title="E152">A4</font></span></a>, <a class="ref" href="glib_000.html#D37" onmouseover="rs('glib_000/D37')" onmouseout="rh()">GLIB_000:def 37</a></span>;<br/><a NAME="E11:250_2_1_2_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" onmouseover="rs('zfmisc_1/T31')" onmouseout="rh()">ZFMISC_1:31</a></span>;<br/><a NAME="E12:250_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E155">A7</font></span>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T13" target="_self" onmouseover="rs('glenum00/T13')" onmouseout="rh()">Th13</a></span>;<br/><a NAME="E13:250_2_1_2_1"/>
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c7">v</font>,<font color="Maroon" title="c8">w</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:250_2_1_2_1"><span class="lab"><font color="Green" title="E153">A5</font></span></a>, <a class="txt" href="#E8:250_2_1_2_1"><span class="lab"><font color="Green" title="E154">A6</font></span></a>, <a class="ref" href="zfmisc_1.html#T32" onmouseover="rs('zfmisc_1/T32')" onmouseout="rh()">ZFMISC_1:32</a></span>;<br/><a NAME="E14:250_2_1_2_1"/><span class="kw">then </span>
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T13" target="_self" onmouseover="rs('glenum00/T13')" onmouseout="rh()">Th13</a></span>;<br/><span class="kw">hence </span><a NAME="E15:250_2_1_2_1"/>
 <a href="glenum00.html#K4" title="GLENUM00:func.4">createGraph</a> <font color="Maroon" title="c4">e</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c11">H9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:250_2_1_2_1"><span class="lab"><font color="Green" title="E155">A7</font></span></a>, <a class="ref" href="glib_000.html#T44" onmouseover="rs('glib_000/T44')" onmouseout="rh()">GLIB_000:44</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:250_2_1_2"/>
<font color="Maroon" title="c1">G</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of  the    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:250"><span class="lab"><font color="Green" title="E150">A2</font></span></a>, <a class="ref" href="glenum00.html#T23" target="_self" onmouseover="rs('glenum00/T23')" onmouseout="rh()">Th23</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:250"/>
<font color="Maroon" title="c1">G</font> is    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:250"><span class="lab"><font color="Green" title="E149">A1</font></span></a>, <a class="ref" href="glib_000.html#T87" onmouseover="rs('glib_000/T87')" onmouseout="rh()">GLIB_000:87</a>, <a class="ref" href="glib_014.html#T22" onmouseover="rs('glib_014/T22')" onmouseout="rh()">GLIB_014:22</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>
