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<b>let </b><font color="Maroon" title="c3">W</font> be    <a href="lexbfs.html#M1" title="LEXBFS:mode.1">Walk</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a></span><br/>

<a NAME="E1:24_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">W</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a>  <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">V</font>
 
<b>by </b><i><a class="ref" href="lexbfs.html#D6" target="_self" title="LEXBFS:def.6">Def6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">m</font>, <font color="Maroon" title="c5">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">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> <font color="Maroon" title="c3">W</font> &amp; <font color="Maroon" title="c5">n</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> <font color="Maroon" title="c3">W</font> &amp; <font color="Maroon" title="c3">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> implies <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">n</font> )</span><br/><b>assume </b><b>that </b><br/><a NAME="E1:24_1_1_1"/><i><font color="Green" title="E18">A2</font></i>: 
( <font color="Maroon" title="c4">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> <font color="Maroon" title="c3">W</font> &amp; <font color="Maroon" title="c5">n</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> <font color="Maroon" title="c3">W</font> )
 <b>and </b><br/><a NAME="E2:24_1_1_1"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c3">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">n</font></span><br/><b>set </b><font color="Maroon" title="c6">mk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2;<br/><b>set </b><font color="Maroon" title="c7">nk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2;<br/><a NAME="E3:24_1_1_1"/><i><font color="Green" title="E20">A4</font></i>: 
( <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"><span class="p3">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">m</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 <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> <font color="Maroon" title="c2">V</font> )
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:24_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="lexbfs.html#E1:24_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="glib_001.html#T69" title="GLIB_001:th.69">GLIB_001:69</a></i>;<br/><a NAME="E4:24_1_1_1"/><i><font color="Green" title="E21">A5</font></i>: 
( <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"><span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 <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> <font color="Maroon" title="c2">V</font> )
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:24_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="lexbfs.html#E1:24_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="glib_001.html#T69" title="GLIB_001:th.69">GLIB_001:69</a></i>;<br/><a NAME="E5:24_1_1_1"/>
<font color="Maroon" title="c3">W</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> <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="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:24_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="lexbfs.html#E1:24_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="glib_001.html#T73" title="GLIB_001:th.73">GLIB_001:73</a></i>;<br/><a NAME="E6:24_1_1_1"/><b>then </b><i><font color="Green" title="E22">A6</font></i>: 
<font color="Maroon" title="c3">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> <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="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:24_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="glib_001.html#D8" title="GLIB_001:def.8">GLIB_001:def 8</a></i>;<br/><a NAME="E7:24_1_1_1"/>
<font color="Maroon" title="c3">W</font> <a href="glib_001.html#K5" title="GLIB_001:func.5">.vertexAt</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> <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="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:24_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="lexbfs.html#E1:24_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="glib_001.html#T73" title="GLIB_001:th.73">GLIB_001:73</a></i>;<br/><a NAME="E8:24_1_1_1"/><b>then </b><i><font color="Green" title="E23">A7</font></i>: 
<font color="Maroon" title="c3">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">V</font> <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="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:24_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="glib_001.html#D8" title="GLIB_001:def.8">GLIB_001:def 8</a></i>;<br/><a NAME="E9:24_1_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">V</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">V</font> )
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:24_1_1_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="lexbfs.html#E4:24_1_1_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E10:24_1_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">n</font>
 <b>by </b><i><a class="txt" href="lexbfs.html#E2:24_1_1_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="lexbfs.html#E3:24_1_1_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="lexbfs.html#E4:24_1_1_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="lexbfs.html#E6:24_1_1_1"><i><font color="Green" title="E22">A6</font></i></a>, <a class="txt" href="lexbfs.html#E8:24_1_1_1"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</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="E3:24_1_1"/>
<font color="Maroon" title="c3">W</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 <b>by </b><i><a class="ref" href="glib_001.html#T147" title="GLIB_001:th.147">GLIB_001:147</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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