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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>assume </b><a NAME="E1:27"/><i><font color="Green" title="E24">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>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">W1</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c4">W2</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c2">G2</font>;<br/>



<b>assume </b><a NAME="E2:27"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c3">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">W2</font>
 ;<br/>

<b>assume </b><a NAME="E3:27"/><i><font color="Green" title="E26">A3</font></i>: 
<font color="Maroon" title="c3">W1</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>
 ;<br/>

<a NAME="E4:27"/>
<font color="Maroon" title="c3">W1</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 
<b>by </b><i><a class="txt" href="chord.html#E3:27"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E5:27"/><b>then </b><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c4">W2</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 
<b>by </b><i><a class="txt" href="chord.html#E1:27"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="chord.html#E2:27"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="glib_001.html#T182" title="GLIB_001:th.182">GLIB_001:182</a></i>;<br/>
<a NAME="E6:27"/>
not <font color="Maroon" title="c3">W1</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 
<b>by </b><i><a class="txt" href="chord.html#E3:27"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E7:27"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">W2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="txt" href="chord.html#E2:27"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="glib_001.html#T127" title="GLIB_001:th.127">GLIB_001:127</a></i>;<br/>
<a NAME="E8:27"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
not <font color="Maroon" title="c4">W2</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 
<b>by </b><i><a class="ref" href="glib_001.html#T127" title="GLIB_001:th.127">GLIB_001:127</a></i>;<br/>
<a NAME="E9:27"/>
<font color="Maroon" title="c3">W1</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 
<b>by </b><i><a class="txt" href="chord.html#E3:27"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>
<a NAME="E10:27"/><b>then </b>
<font color="Maroon" title="c3">W1</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="c3">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#D24" title="GLIB_001:def.24">GLIB_001:def 24</a></i>;<br/>
<a NAME="E11:27"/><b>then </b>
<font color="Maroon" title="c4">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="c4">W2</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 
<b>by </b><i><a class="txt" href="chord.html#E2:27"><i><font color="Green" title="E25">A2</font></i></a></i>;<br/>
<a NAME="E12:27"/><b>then </b>
<font color="Maroon" title="c4">W2</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 
<b>by </b><i><a class="ref" href="glib_001.html#D24" title="GLIB_001:def.24">GLIB_001:def 24</a></i>;<br/>
<b>hence </b><a NAME="E13:27"/>
<font color="Maroon" title="c4">W2</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>
 <b>by </b><i><a class="txt" href="chord.html#E8:27"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="chord.html#E5:27"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/>


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