<?xml version="1.0"?>
<div class="add">

<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">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> is <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> is <a href="glib_001.html#V4" title="GLIB_001:attr.4">Trail-like</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Olive" title="b1">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> )</span><br/><b>let </b><font color="Maroon" title="c2">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V4" title="GLIB_001:attr.4">Trail-like</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> )</span><br/>



<b>set </b><font color="Maroon" title="c3">W</font> = <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font>;<br/>
<a NAME="E1:38"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<b>hence </b><a NAME="E2:38"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</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" target="_self" title="GLIB_001:def.24">Def24</a></i>; <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V4" title="GLIB_001:attr.4">Trail-like</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</font> be  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><b>assume </b><a NAME="E1:38_1"/>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><a NAME="E2:38_1"/><b>then </b>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/><b>hence </b><a NAME="E3:38_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:38"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V2" title="GLIB_001:attr.2">directed</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D25" target="_self" title="GLIB_001:def.25">Def25</a></i>; <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V4" title="GLIB_001:attr.4">Trail-like</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> )</span><br/>

<a NAME="E5:38"/>
 <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E6:38"/><b>then </b>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="glib_001.html#D15" target="_self" title="GLIB_001:def.15">Def15</a></i>;<br/>
<a NAME="E7:38"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<b>hence </b><a NAME="E8:38"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</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#D26" target="_self" title="GLIB_001:def.26">Def26</a></i>; <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V4" title="GLIB_001:attr.4">Trail-like</a> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a> )</span><br/>

<a NAME="E9:38"/>
 <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="glib_001.html#D15" target="_self" title="GLIB_001:def.15">Def15</a></i>;<br/>
<a NAME="E10:38"/><b>then </b>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/>
<a NAME="E11:38"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <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="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E12:38"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
;<br/>
<b>hence </b><a NAME="E13:38"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V4" title="GLIB_001:attr.4">Trail-like</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D27" target="_self" title="GLIB_001:def.27">Def27</a></i>; <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</font>, <font color="Maroon" title="c5">m</font> be  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> &amp; <font color="Maroon" title="c5">m</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> implies ( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> ) )</span><br/><b>assume </b><a NAME="E1:38_2"/>
( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> &amp; <font color="Maroon" title="c5">m</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> implies ( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> ) )</span><br/><a NAME="E2:38_2"/><b>then </b>
( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">m</font> &amp; <font color="Maroon" title="c5">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 )
 <b>by </b><i><a class="ref" href="finseq_1.html#T57" title="FINSEQ_1:th.57">FINSEQ_1:57</a></i>;<br/><a NAME="E3:38_2"/><b>then </b>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E4:38_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">m</font> implies ( <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E15:38"/>
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c2">v</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 <b>by </b><i><a class="txt" href="#E13:38"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</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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