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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">W1</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>, <font color="Maroon">W2</font> be    <a href="glib_001.html#M3" target="_self">Walk</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:132"/>
<font color="Maroon">W1</font> is    <a href="glib_001.html#M4" target="_self">Subwalk</a> of <font color="Maroon">W2</font>
 ;<br/>

<b>then consider </b><font color="Maroon">es</font> being    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">W2</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> <b> such that </b><br/><a NAME="E3:132"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">W1</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a>  <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">es</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:132"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:132"/><b>then </b>
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E6:132"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W1</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E7:132"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">W2</font> <a href="glib_001.html#K12" target="_self">.edgeSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:132"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">W1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W2</font>
 <b>by </b><i/>;<br/>


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