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<b>let </b><font color="Maroon">G</font> be   <a href="graph_1.html#NM1">Graph</a>;<br/>

<b>assume </b><a NAME="E1:34_1_1"/>
<font color="Maroon">G</font> is <a href="msscyc_1.html#V2" target="_self">empty</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">G'</font> = <font color="Maroon">G</font> as  <a href="msscyc_1.html#V2" target="_self">empty</a> <a href="graph_1.html#NM1">Graph</a> ;<br/>
<b>let </b><font color="Maroon">v</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>; <i><font color="Red">:: according to </font></i><a class="ref" href="msscyc_1.html#D5" target="_self">MSSCYC_1:def 5</a><br/>

<b>take </b>
0
;<br/>

<b>let </b><font color="Maroon">c</font> be  <a href="graph_1.html#V8">directed</a>  <a href="graph_1.html#M1">Chain</a> of <font color="Maroon">G</font>;<br/>

<b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">c</font> as    <a href="graph_1.html#M1">Chain</a> of <font color="Maroon">G'</font> ;<br/>
<a NAME="E4:34_1_1"/>
<font color="Maroon">c</font> is <a href="xboole_0.html#V1">empty</a>
 
;<br/>
<b>hence </b><a NAME="E5:34_1_1"/>
( not <font color="Maroon">c</font> is <a href="xboole_0.html#V1">empty</a> &amp; <span class="p1">(<span class="default"><a href="graph_2.html#K7">vertex-seq</a> <font color="Maroon">c</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> implies  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 ;<br/>


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