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<b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">v1</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">v2</font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font>;<br/><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="E1:55"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="graph_5.html#K4" target="_self">AcyclicPaths</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b>
<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_4.html#V1">Simple</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#R3" target="_self">is_acyclicpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">q</font> being  <a href="graph_1.html#V8">oriented</a> <a href="graph_4.html#V1">Simple</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E4:55"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp; <font color="Maroon">q</font> <a href="graph_5.html#R3" target="_self">is_acyclicpath_of</a> <font color="Maroon">v1</font>,<font color="Maroon">v2</font> )
 ;<br/>
<a NAME="E5:55"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">r</font> where <font color="Olive">r</font> is  <a href="graph_1.html#V8">oriented</a> <a href="graph_4.html#V1">Simple</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font> : verum </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:55"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="graph_5.html#K7" target="_self">AcyclicPaths</a> <font color="Maroon">G</font>
 ;<br/>


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