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

<b>set </b><font color="Maroon">PT</font> = <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is  <a href="graph_1.html#V8">oriented</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font> : <font color="Olive">p</font> <a href="graph_5.html#R1" target="_self">is_orientedpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> </span>}</span> ;<br/>
<a NAME="E1:40_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is  <a href="graph_1.html#V8">oriented</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font> : <font color="Olive">p</font> <a href="graph_5.html#R1" target="_self">is_orientedpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:40_1_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is  <a href="graph_1.html#V8">oriented</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font> : <font color="Olive">p</font> <a href="graph_5.html#R1" target="_self">is_orientedpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being  <a href="graph_1.html#V8">oriented</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:40_1_1_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="graph_5.html#R1" target="_self">is_orientedpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> )
 ;<br/>
<b>thus </b><a NAME="E4:40_1_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> 
 <b>by </b><i><a class="ref" href="graph_5.html#T1" target="_self">Th1</a>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:40_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is  <a href="graph_1.html#V8">oriented</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font> : <font color="Olive">p</font> <a href="graph_5.html#R1" target="_self">is_orientedpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> </span>}</span>  is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default">the <a href="graph_1.html#U2">Edges</a> of <font color="Maroon">G</font> <a href="finseq_2.html#K3">*</a> </span>)</span>
 ;<br/>


</div>
