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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">sc</font> being <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a> <a href="graph_2.html#V3" title="GRAPH_2:attr.3">simple</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">sc'</font> being <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">sc'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">sc</font> holds <br/><font color="Olive" title="b2">sc'</font> is <a href="graph_4.html#V1" title="GRAPH_4:attr.1">Simple</a></span><br/><b>let </b><font color="Maroon" title="c2">sc</font> be  <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a> <a href="graph_2.html#V3" title="GRAPH_2:attr.3">simple</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">sc'</font> being <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">sc'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">sc</font> holds <br/><font color="Olive" title="b1">sc'</font> is <a href="graph_4.html#V1" title="GRAPH_4:attr.1">Simple</a></span><br/><b>let </b><font color="Maroon" title="c3">sc'</font> be  <a href="graph_1.html#V7" title="GRAPH_1:attr.7">oriented</a>  <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">sc'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">sc</font> implies <font color="Maroon" title="c3">sc'</font> is <a href="graph_4.html#V1" title="GRAPH_4:attr.1">Simple</a> )</span><br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c3">sc'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">sc</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">sc'</font> is <a href="graph_4.html#V1" title="GRAPH_4:attr.1">Simple</a></span><br/>

<b>consider </b><font color="Maroon" title="c4">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:27"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c4">vs</font> <a href="graph_4.html#R3" title="GRAPH_4:pred.3">is_oriented_vertex_seq_of</a> <font color="Maroon" title="c3">sc'</font>
 <b>by </b><i><a class="ref" href="graph_4.html#T10" target="_self" title="GRAPH_4:th.10">Th10</a></i>;<br/>
<a NAME="E4:27"/>
<font color="Maroon" title="c4">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c2">sc</font>
 
<b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="#E3:27"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="graph_4.html#T5" target="_self" title="GRAPH_4:th.5">Th5</a></i>;<br/>
<a NAME="E5:27"/><b>then </b>
for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b2">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">vs</font> &amp; <font color="Maroon" title="c4">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">m</font> holds <br/>( <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">vs</font> )
 
<b>by </b><i><a class="ref" href="graph_2.html#T51" title="GRAPH_2:th.51">GRAPH_2:51</a></i>;<br/>
<b>hence </b><a NAME="E6:27"/>
<font color="Maroon" title="c3">sc'</font> is <a href="graph_4.html#V1" title="GRAPH_4:attr.1">Simple</a>
 <b>by </b><i><a class="txt" href="#E3:27"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="graph_4.html#D7" target="_self" title="GRAPH_4:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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