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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">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="Olive" title="b2">x</font>,<font color="Olive" title="b2">x</font>,<font color="Maroon" title="c1">G</font> holds <br/><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">e</font>,<font color="Olive" title="b2">x</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a></span><br/><b>let </b><font color="Maroon" title="c2">e</font>, <font color="Maroon" title="c3">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="c2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c1">G</font> implies <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> )</span><br/>





<b>set </b><font color="Maroon" title="c4">W</font> = <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">x</font>;<br/>
<b>assume </b><a NAME="E1:230"/>
<font color="Maroon" title="c2">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">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"> <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a></span><br/>

<a NAME="E2:230"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <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> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<b>by </b><i><a class="ref" href="glib_001.html#T15" target="_self" title="GLIB_001:th.15">Th15</a></i>;<br/>
<a NAME="E3:230"/><b>then </b>
not <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 
<b>by </b><i><a class="txt" href="glib_001.html#E91"><i><font color="Green" title="E83">Lm54</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:230"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K2" title="GLIB_001:func.2">.walkOf</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">x</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D31" target="_self" title="GLIB_001:def.31">Def31</a></i>; <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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