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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">sc'</font> be  <a href="graph_1.html#V8">oriented</a> <a href="graph_4.html#V1" target="_self">Simple</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font>;<br/>



<b>consider </b><font color="Maroon">vs</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E2:29"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">vs</font> <a href="graph_4.html#R3" target="_self">is_oriented_vertex_seq_of</a> <font color="Maroon">sc'</font> &amp; ( for <font color="Olive">n</font>, <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m</font> &amp; <font color="Olive">m</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">vs</font> &amp; <font color="Maroon">vs</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">vs</font> <a href="funct_1.html#K1">.</a> <font color="Olive">m</font> holds <br/>( <font color="Olive">n</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Olive">m</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">vs</font> ) ) )
 <b>by </b><i/>;<br/>
<a NAME="E3:29"/>
<font color="Maroon">vs</font> <a href="graph_2.html#R1">is_vertex_seq_of</a> <font color="Maroon">sc'</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:29"/>
<font color="Maroon">sc'</font> is  <a href="graph_1.html#V8">oriented</a> <a href="graph_2.html#V3">simple</a>  <a href="graph_1.html#M2">Chain</a> of <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="graph_2.html#D10">GRAPH_2:def 10</a></i>;<br/>


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