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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be    <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> ;<br/><b>let </b><font color="Maroon" title="c3">G</font> be   <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</a>;<br/><b>let </b><font color="Maroon" title="c4">vs</font>, <font color="Maroon" title="c5">vs1</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c3">G</font>;<br/><b>let </b><font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">c1</font> be    <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c3">G</font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:61"/><i><font color="Green" title="E54">A1</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font>
 <b>and </b><br/><a NAME="E2:61"/><i><font color="Green" title="E55">A2</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font>
 <b>and </b><br/><a NAME="E3:61"/><i><font color="Green" title="E56">A3</font></i>: 
<font color="Maroon" title="c2">n</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="c6">c</font>
 ;<br/>

<b>assume </b><a NAME="E4:61"/><i><font color="Green" title="E57">A4</font></i>: 
<font color="Maroon" title="c7">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c6">c</font>
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E5:61"/><i><font color="Green" title="E58">A5</font></i>: 
<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="c6">c</font>
 <b>and </b><br/><a NAME="E6:61"/><i><font color="Green" title="E59">A6</font></i>: 
<font color="Maroon" title="c5">vs1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">vs</font>
 ;<br/>

<a NAME="E7:61"/><i><font color="Green" title="E60">A7</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">vs</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">c</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="graph_2.html#E5:61"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="graph_2.html#D7" target="_self" title="GRAPH_2:def.7">Def7</a></i>;<br/>
<a NAME="E8:61"/><b>then </b><i><font color="Green" title="E61">A8</font></i>: 
( <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E2:61"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="graph_2.html#E3:61"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/>
<a NAME="E9:61"/><i><font color="Green" title="E62">A9</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="graph_2.html#E1:61"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="graph_2.html#E3:61"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="graph_2.html#E4:61"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="graph_2.html#E8:61"><i><font color="Green" title="E61">A8</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green" title="E8">Lm2</font></i></a></i>;<br/>
<a NAME="E10:61"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="graph_2.html#E1:61"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="graph_2.html#E6:61"><i><font color="Green" title="E59">A6</font></i></a>, <a class="txt" href="graph_2.html#E8:61"><i><font color="Green" title="E61">A8</font></i></a>, <a class="ref" href="graph_2.html#D1" target="_self" title="GRAPH_2:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E11:61"/><i><font color="Green" title="E63">A10</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="graph_2.html#E9:61"><i><font color="Green" title="E62">A9</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="graph_2.html#D7" target="_self" title="GRAPH_2:def.7">GRAPH_2:def 7</a><br/>

<b>let </b><font color="Maroon" title="c8">k</font> be    <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> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E12:61"/><i><font color="Green" title="E64">A11</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 <b>and </b><br/><a NAME="E13:61"/><i><font color="Green" title="E65">A12</font></i>: 
<font color="Maroon" title="c8">k</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="c7">c1</font>
 ;<br/>

<a NAME="E14:61"/>
0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<b>by </b><i><a class="txt" href="graph_2.html#E12:61"><i><font color="Green" title="E64">A11</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">j</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> <b> such that </b><br/><a NAME="E16:61"/><i><font color="Green" title="E66">A13</font></i>: 
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">j</font> &amp; <font color="Maroon" title="c9">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font> &amp; <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="txt" href="graph_2.html#E13:61"><i><font color="Green" title="E65">A12</font></i></a>, <a class="ref" href="graph_2.html#T1" target="_self" title="GRAPH_2:th.1">Th1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">i</font> = <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font>;<br/>
<b>set </b><font color="Maroon" title="c11">v1</font> = <font color="Maroon" title="c4">vs</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">v2</font> = <font color="Maroon" title="c4">vs</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E17:61"/>
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="txt" href="graph_2.html#E13:61"><i><font color="Green" title="E65">A12</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E18:61"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<b>by </b><i><a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/>
<a NAME="E19:61"/><b>then </b><i><font color="Green" title="E67">A14</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font> &amp; <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</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="c6">c</font> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E1:61"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="graph_2.html#E3:61"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="graph_2.html#E9:61"><i><font color="Green" title="E62">A9</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/>
<a NAME="E20:61"/><b>then </b><i><font color="Green" title="E68">A15</font></i>: 
<font color="Maroon" title="c6">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c4">vs</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span>,<font color="Maroon" title="c4">vs</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="graph_2.html#E5:61"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="graph_2.html#D7" target="_self" title="GRAPH_2:def.7">Def7</a></i>;<br/>
<a NAME="E21:61"/>
<font color="Maroon" title="c9">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs1</font>
 
<b>by </b><i><a class="txt" href="graph_2.html#E11:61"><i><font color="Green" title="E63">A10</font></i></a>, <a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E22:61"/><b>then </b><i><font color="Green" title="E69">A16</font></i>: 
<font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span>
 
<b>by </b><i><a class="txt" href="graph_2.html#E1:61"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="graph_2.html#E6:61"><i><font color="Green" title="E59">A6</font></i></a>, <a class="txt" href="graph_2.html#E8:61"><i><font color="Green" title="E61">A8</font></i></a>, <a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="graph_2.html#D1" target="_self" title="GRAPH_2:def.1">Def1</a></i>;<br/>
<a NAME="E23:61"/><i><font color="Green" title="E70">A17</font></i>: 
<font color="Maroon" title="c9">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs1</font>
 
<b>by </b><i><a class="txt" href="graph_2.html#E11:61"><i><font color="Green" title="E63">A10</font></i></a>, <a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E24:61"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E25:61"/><b>then </b><i><font color="Green" title="E71">A18</font></i>: 
<font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="graph_2.html#E1:61"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="graph_2.html#E6:61"><i><font color="Green" title="E59">A6</font></i></a>, <a class="txt" href="graph_2.html#E8:61"><i><font color="Green" title="E61">A8</font></i></a>, <a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="txt" href="graph_2.html#E23:61"><i><font color="Green" title="E70">A17</font></i></a>, <a class="ref" href="graph_2.html#D1" target="_self" title="GRAPH_2:def.1">Def1</a></i>;<br/>
<a NAME="E26:61"/>
( <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</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; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E7:61"><i><font color="Green" title="E60">A7</font></i></a>, <a class="txt" href="graph_2.html#E19:61"><i><font color="Green" title="E67">A14</font></i></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E27:61"/><b>then </b><i><font color="Green" title="E72">A19</font></i>: 
( <font color="Maroon" title="c4">vs</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> &amp; <font color="Maroon" title="c4">vs</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E19:61"><i><font color="Green" title="E67">A14</font></i></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E28:61"/>
0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
;<br/>
<a NAME="E29:61"/><b>then </b><i><font color="Green" title="E73">A20</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c8">k</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="c7">c1</font> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E30:61"/><b>then </b>
( <font color="Maroon" title="c8">k</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="c5">vs1</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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="c5">vs1</font> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E11:61"><i><font color="Green" title="E63">A10</font></i></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E31:61"/><b>then </b>
( <font color="Maroon" title="c5">vs1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c5">vs1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="graph_2.html#E29:61"><i><font color="Green" title="E73">A20</font></i></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a></i>;<br/>
<b>hence </b><a NAME="E32:61"/>
<font color="Maroon" title="c7">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c5">vs1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c5">vs1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E1:61"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="graph_2.html#E3:61"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="graph_2.html#E4:61"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="graph_2.html#E8:61"><i><font color="Green" title="E61">A8</font></i></a>, <a class="txt" href="graph_2.html#E16:61"><i><font color="Green" title="E66">A13</font></i></a>, <a class="txt" href="graph_2.html#E20:61"><i><font color="Green" title="E68">A15</font></i></a>, <a class="txt" href="graph_2.html#E22:61"><i><font color="Green" title="E69">A16</font></i></a>, <a class="txt" href="graph_2.html#E25:61"><i><font color="Green" title="E71">A18</font></i></a>, <a class="txt" href="graph_2.html#E27:61"><i><font color="Green" title="E72">A19</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green" title="E8">Lm2</font></i></a></i>;<br/>


</div>
