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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="graph_1.html#V6" title="GRAPH_1:attr.6">finite</a> <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">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">P</font> being <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font> holds   <a href="graph_5.html#K6" title="GRAPH_5:func.6">AcyclicPaths</a> <font color="Olive" title="b1">P</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/><b>let </b><font color="Maroon" title="c2">P</font> be  <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">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#K6" title="GRAPH_5:func.6">AcyclicPaths</a> <font color="Maroon" title="c2">P</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/>



<a NAME="E1:84"/>
 <a href="graph_5.html#K6" title="GRAPH_5:func.6">AcyclicPaths</a> <font color="Maroon" title="c2">P</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="c1">G</font>
 
<b>by </b><i><a class="ref" href="graph_5.html#T42" target="_self" title="GRAPH_5:th.42">Th42</a></i>;<br/>
<b>hence </b><a NAME="E2:84"/>
 <a href="graph_5.html#K6" title="GRAPH_5:func.6">AcyclicPaths</a> <font color="Maroon" title="c2">P</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <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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