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<b>let </b><font color="Maroon" title="c1">V</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">G</font> being  <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a><br/> for <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> being   <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="Olive" title="b1">G</font> holds   <a href="graph_5.html#K5" title="GRAPH_5:func.5">AcyclicPaths</a> <font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Maroon" title="c1">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_5.html#K7" title="GRAPH_5:func.7">AcyclicPaths</a> <font color="Olive" title="b1">G</font></span><br/><b>let </b><font color="Maroon" title="c2">G</font> be   <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">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">v1</font>, <font color="Olive" title="b2">v2</font> being   <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="c2">G</font> holds   <a href="graph_5.html#K5" title="GRAPH_5:func.5">AcyclicPaths</a> <font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">v2</font>,<font color="Maroon" title="c1">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_5.html#K7" title="GRAPH_5:func.7">AcyclicPaths</a> <font color="Maroon" title="c2">G</font></span><br/><b>let </b><font color="Maroon" title="c3">v1</font>, <font color="Maroon" title="c4">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="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="graph_5.html#K5" title="GRAPH_5:func.5">AcyclicPaths</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c1">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graph_5.html#K7" title="GRAPH_5:func.7">AcyclicPaths</a> <font color="Maroon" title="c2">G</font></span><br/><b>let </b><font color="Maroon" title="c5">e</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K5" title="GRAPH_5:func.5">AcyclicPaths</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c1">V</font> or <font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K7" title="GRAPH_5:func.7">AcyclicPaths</a> <font color="Maroon" title="c2">G</font> )</span><br/>









<b>assume </b><a NAME="E1:59"/>
<font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K5" title="GRAPH_5:func.5">AcyclicPaths</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c1">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="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K7" title="GRAPH_5:func.7">AcyclicPaths</a> <font color="Maroon" title="c2">G</font></span><br/>

<b>then consider </b><font color="Maroon" title="c6">q</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="c2">G</font><b> such that </b><br/><a NAME="E3:59"/><i><font color="Green" title="E47">A1</font></i>: 
( <font color="Maroon" title="c5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c6">q</font> <a href="graph_5.html#R4" title="GRAPH_5:pred.4">is_acyclicpath_of</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">v2</font>,<font color="Maroon" title="c1">V</font> )
 ;<br/>
<b>thus </b><a NAME="E4:59"/>
<font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graph_5.html#K7" title="GRAPH_5:func.7">AcyclicPaths</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="graph_5.html#E3:59"><i><font color="Green" title="E47">A1</font></i></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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