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<span class="kw">set </span><font color="Maroon" title="c4">W</font> = <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:111_1_1_1_1"/>
( <font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">G</font> or  not <font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">G</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:111_1_1_1_1_1"/><span class="lab"><font color="Green" title="E99">A1</font></span>: 
<font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> </span><br/><div class="add"><a NAME="E2:111_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glib_001.html#E43"><span class="lab"><font color="Green" title="E35">Lm6</font></span></a></span>;<br/><a NAME="E3:111_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:111_1_1_1_1_1"><span class="lab"><font color="Green" title="E99">A1</font></span></a>, <a class="txt" href="glib_001.html#E43"><span class="lab"><font color="Green" title="E35">Lm6</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:111_1_1_1_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:111_1_1_1_1_1"><span class="lab"><font color="Green" title="E100">A2</font></span></a>, <a class="ref" href="glib_001.html#D24" target="_self" title="GLIB_001:def.24">Def24</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="111_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:111_1_1_1_1_2"/>
not <font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> </span><br/><div class="add"><a NAME="E2:111_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</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="glib_001.html#D5" target="_self" title="GLIB_001:def.5">Def5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:111_1_1_1_1_2"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E2:111_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">x</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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