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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>assume </b><a NAME="E1:249"/><i><font color="Green" title="E161">A1</font></i>: 
( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c3">x</font> is    <a href="glib_001.html#M2" title="GLIB_001:mode.2">EdgeSeq</a> of <font color="Maroon" title="c1">G1</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">es</font> = <font color="Maroon" title="c3">x</font> as    <a href="glib_001.html#M2" title="GLIB_001:mode.2">EdgeSeq</a> of <font color="Maroon" title="c1">G1</font> ;<br/>
<b>consider </b><font color="Maroon" title="c5">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font><b> such that </b><br/><a NAME="E4:249"/><i><font color="Green" title="E162">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs</font> <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="c4">es</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">es</font> holds <br/><font color="Maroon" title="c4">es</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c5">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c1">G1</font> ) )
 <b>by </b><i><a class="ref" href="glib_001.html#D2" target="_self" title="GLIB_001:def.2">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">es2</font> = <font color="Maroon" title="c4">es</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c2">G2</font> <b>by </b><i><a class="txt" href="glib_001.html#E1:249"><i><font color="Green" title="E161">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="249_1"><b>now </b></a><div class="add"><b>reconsider </b><font color="Maroon" title="c7">vs</font> = <font color="Maroon" title="c5">vs</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c2">G2</font> <b>by </b><i><a class="txt" href="glib_001.html#E1:249"><i><font color="Green" title="E161">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><b>take </b><font color="Maroon" title="c8">vs</font> = <font color="Maroon" title="c7">vs</font>;<br/><b>thus </b><a NAME="E2:249_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">vs</font> <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="c4">es</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E4:249"><i><font color="Green" title="E162">A2</font></i></a></i>;<br/><b>let </b><font color="Maroon" title="c9">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E3:249_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">n</font> &amp; <font color="Maroon" title="c9">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">es2</font> )
 ;<br/><a NAME="E4:249_1"/><b>then </b>
<font color="Maroon" title="c6">es2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">n</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c8">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">n</font>,<font color="Maroon" title="c8">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c1">G1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E4:249"><i><font color="Green" title="E162">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E5:249_1"/>
<font color="Maroon" title="c6">es2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">n</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c8">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">n</font>,<font color="Maroon" title="c8">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">G2</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:249"><i><font color="Green" title="E161">A1</font></i></a>, <a class="ref" href="glib_000.html#T91" title="GLIB_000:th.91">GLIB_000:91</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:249"/>
<font color="Maroon" title="c3">x</font> is    <a href="glib_001.html#M2" title="GLIB_001:mode.2">EdgeSeq</a> of <font color="Maroon" title="c2">G2</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D2" target="_self" title="GLIB_001:def.2">Def2</a></i>;<br/>


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