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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E13</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U1">Vertices</a> of <span class="p1">(<span class="default"><a href="jgraph_1.html#K1" target="_self">PGraph</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<a NAME="E3:15"/>
<font color="Maroon">c<sub>3</sub></font> <a href="graph_4.html#R3">is_oriented_vertex_seq_of</a>  <a href="jgraph_1.html#K4" target="_self">PairF</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_1.html#E1:15"><i><font color="Green">E13</font></i></a>, <a class="ref" href="jgraph_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="graph_2.html#M1">FinSubsequence</a> of  <a href="jgraph_1.html#K4" target="_self">PairF</a> <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="graph_2.html#M1">FinSubsequence</a> of <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> being  <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  <a href="jgraph_1.html#K1" target="_self">PGraph</a> <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="graph_1.html#U1">Vertices</a> of <span class="p1">(<span class="default"><a href="jgraph_1.html#K1" target="_self">PGraph</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E5:15"/><i><font color="Green">E14</font></i>: 
(  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="graph_4.html#R3">is_oriented_vertex_seq_of</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="graph_4.html#T23">GRAPH_4:23</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E7:15"/>
<font color="Maroon">c<sub>8</sub></font> <a href="jgraph_1.html#R1" target="_self">is_Shortcut_of</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jgraph_1.html#E5:15"><i><font color="Green">E14</font></i></a>, <a class="ref" href="jgraph_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E8:15"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="jgraph_1.html#R1" target="_self">is_Shortcut_of</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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