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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="graph_1.html#NM1">Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of the <a href="graph_1.html#U1">Vertices</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:49"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K3">len</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b><a NAME="E2:49"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="graph_2.html#D7" target="_self">GRAPH_2:def 7</a><br/>

<b>thus </b><a NAME="E3:49"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <a href="xboole_0.html#K1">{}</a>  holds <br/><a href="xboole_0.html#K1">{}</a>  <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="graph_1.html#R2">joins</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font>,<span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E1:49"><i><font color="Green">E42</font></i></a></i>;<br/>


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