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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>;<br/><b>let </b><font color="Maroon" title="c2">W1</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">W2</font> be    <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c2">W1</font>;<br/><b>let </b><font color="Maroon" title="c4">W3</font> be    <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c3">W2</font>;<br/>







<b>set </b><font color="Maroon" title="c5">fs</font> = <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">fs1</font> = <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> ;<br/>
<b>set </b><font color="Maroon" title="c7">fs2</font> = <font color="Maroon" title="c4">W3</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> ;<br/>
<a NAME="E1:131"/><i><font color="Green" title="E107">A1</font></i>: 
( <font color="Maroon" title="c4">W3</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  &amp;  ex <font color="Olive" title="b1">fss1</font> being   <a href="graph_2.html#M1" title="GRAPH_2:mode.1">FinSubsequence</a> of <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  st <font color="Maroon" title="c4">W3</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b1">fss1</font> )
 
<b>by </b><i><a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/>
<a NAME="E2:131"/>
( <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  &amp;  ex <font color="Olive" title="b1">fss</font> being   <a href="graph_2.html#M1" title="GRAPH_2:mode.1">FinSubsequence</a> of <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  st <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Olive" title="b1">fss</font> )
 
<b>by </b><i><a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/>
<a NAME="E3:131"/><b>then </b><i><font color="Green" title="E108">A2</font></i>: 
( <font color="Maroon" title="c3">W2</font> <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">W1</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  &amp; <font color="Maroon" title="c3">W2</font> <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">W1</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  )
 
<b>by </b><i><a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">fss1</font> being    <a href="graph_2.html#M1" title="GRAPH_2:mode.1">FinSubsequence</a> of <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> <b> such that </b><br/><a NAME="E5:131"/><i><font color="Green" title="E109">A3</font></i>: 
<font color="Maroon" title="c4">W3</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c8">fss1</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">fss</font> being    <a href="graph_2.html#M1" title="GRAPH_2:mode.1">FinSubsequence</a> of <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> <b> such that </b><br/><a NAME="E7:131"/><i><font color="Green" title="E110">A4</font></i>: 
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c9">fss</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">fss2</font> = <font color="Maroon" title="c9">fss</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">fss</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">fss1</font></span>)</span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">fss2</font> = <font color="Maroon" title="c9">fss</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p4">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c9">fss</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c8">fss1</font></span>)</span></span>)</span></span>)</span> as    <a href="graph_2.html#M1" title="GRAPH_2:mode.1">FinSubsequence</a> of <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <b>by </b><i><a class="ref" href="graph_2.html#T29" title="GRAPH_2:th.29">GRAPH_2:29</a></i>;<br/>
<a NAME="E9:131"/>
<font color="Maroon" title="c4">W3</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c11">fss2</font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E5:131"><i><font color="Green" title="E109">A3</font></i></a>, <a class="txt" href="glib_001.html#E7:131"><i><font color="Green" title="E110">A4</font></i></a>, <a class="ref" href="graph_2.html#T30" title="GRAPH_2:th.30">GRAPH_2:30</a></i>;<br/>
<b>hence </b><a NAME="E10:131"/>
<font color="Maroon" title="c4">W3</font> is    <a href="glib_001.html#M4" title="GLIB_001:mode.4">Subwalk</a> of <font color="Maroon" title="c2">W1</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:131"><i><font color="Green" title="E107">A1</font></i></a>, <a class="txt" href="glib_001.html#E3:131"><i><font color="Green" title="E108">A2</font></i></a>, <a class="ref" href="glib_001.html#D32" target="_self" title="GLIB_001:def.32">Def32</a></i>;<br/>


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