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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">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">s</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>, <font color="Maroon">t</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>;<br/>





<b>assume </b><a NAME="E1:11"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U3">Source</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> the <a href="graph_1.html#U4">Target</a> of <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> )
 ;<br/>

<b>set </b><font color="Maroon">vs</font> = <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">c</font> = <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span>;<br/>
<a NAME="E2:11"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<b>hence </b><a NAME="E3:11"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="graph_2.html#D7">GRAPH_2:def 7</a><br/>

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E4:11"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span> )
 ;<br/>

<a NAME="E5:11"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>
<a NAME="E6:11"/>
( <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> &amp; <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<b>hence </b><a NAME="E7:11"/>
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">e</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="graph_1.html#R2">joins</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font>,<span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">t</font></span><a href="lang1.html#K4">*&gt;</a></span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="graph_1.html#D9">GRAPH_1:def 9</a></i>;<br/>


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