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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c3">v2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>







<b>assume </b><a NAME="E1:52"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K4" title="GRAPH_5:func.4">AcyclicPaths</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">p</font> being  <a href="graph_1.html#V8" title="GRAPH_1:attr.8">oriented</a> <a href="graph_4.html#V1" title="GRAPH_4:attr.1">Simple</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:52"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p</font> &amp; <font color="Maroon" title="c5">p</font> <a href="graph_5.html#R3" title="GRAPH_5:pred.3">is_acyclicpath_of</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font> )
 ;<br/>
<a NAME="E4:52"/>
<font color="Maroon" title="c5">p</font> <a href="graph_5.html#R1" title="GRAPH_5:pred.1">is_orientedpath_of</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font>
 
<b>by </b><i><a class="txt" href="graph_5.html#E3:52"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="graph_5.html#D6" target="_self" title="GRAPH_5:def.6">Def6</a></i>;<br/>
<b>hence </b><a NAME="E5:52"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K3" title="GRAPH_5:func.3">OrientedPaths</a> <font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">v2</font>
 <b>by </b><i><a class="txt" href="graph_5.html#E3:52"><i><font color="Green" title="E41">A1</font></i></a></i>;<br/>


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