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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">e</font>, <font color="Olive" title="b3">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Olive" title="b1">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">G</font> holds <br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Olive" title="b2">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span><br/><b>let </b><font color="Maroon" title="c2">W</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">e</font>, <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<font color="Olive" title="b2">x</font>,<font color="Maroon" title="c1">G</font> holds <br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Olive" title="b1">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span><br/><b>let </b><font color="Maroon" title="c3">e</font>, <font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c1">G</font> implies  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 )</span><br/>





<b>set </b><font color="Maroon" title="c5">W2</font> = <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span>,<font color="Maroon" title="c3">e</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c3">e</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:71"/><i><font color="Green" title="E67">A1</font></i>: 
<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">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span><br/>

<b>then reconsider </b><font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c4">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="glib_000.html#T16" title="GLIB_000:th.16">GLIB_000:16</a></i>;<br/>
<a NAME="E3:71"/><i><font color="Green" title="E68">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x'</font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:71"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="glib_000.html#T69" title="GLIB_000:th.69">GLIB_000:69</a></i>;<br/>
<a NAME="E4:71"/><b>then </b><i><font color="Green" title="E69">A3</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span>,<font color="Maroon" title="c3">e</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c4">x</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:71"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="glib_001.html#D5" target="_self" title="GLIB_001:def.5">Def5</a></i>;<br/>
<a NAME="E5:71"/>
<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> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span>,<font color="Maroon" title="c3">e</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c3">e</font></span>)</span></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">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 
<b>by </b><i><a class="txt" href="glib_001.html#E1:71"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="glib_001.html#E3:71"><i><font color="Green" title="E68">A2</font></i></a>, <a class="txt" href="glib_001.html#E43"><i><font color="Green" title="E35">Lm6</font></i></a></i>;<br/>
<a NAME="E6:71"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Maroon" title="c3">e</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span>,<font color="Maroon" title="c3">e</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K30" title="GLIB_000:func.30">.adj</a> <font color="Maroon" title="c3">e</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="glib_001.html#E46"><i><font color="Green" title="E38">Lm9</font></i></a></i>;<br/>
<a NAME="E7:71"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Maroon" title="c3">e</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 
<b>by </b><i><a class="txt" href="glib_001.html#E4:71"><i><font color="Green" title="E69">A3</font></i></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>
<b>hence </b><a NAME="E8:71"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <font color="Maroon" title="c3">e</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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