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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:11"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:11"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:11"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><a NAME="E1:11_1"/><i><font color="Green">E15</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="graph_2.html#E1:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="graph_2.html#E2:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="graph_2.html#E3:11"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E2:11_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>;<br/><a NAME="E3:11_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E4:11_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E5:11_1"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E6:11_1"/><i><font color="Green">E18</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="txt" href="graph_2.html#E2:11"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E7:11_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="graph_2.html#E3:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>;<br/><a NAME="E8:11_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E9:11_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E10:11_1"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E11:11_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="graph_2.html#E1:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="graph_2.html#E2:11"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E12:11_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><a NAME="E13:11_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><i><font color="Green">E21</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="graph_2.html#E4:11_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="graph_2.html#E10:11_1"><i><font color="Green">E19</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>

;<br/><a NAME="E15:11_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="graph_2.html#E1:11_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="graph_2.html#E6:11_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E16:11_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="graph_2.html#E3:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="graph_2.html#E1:11_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>;<br/><a NAME="E17:11_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E18:11_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>hence </b><a NAME="E19:11_1"/><i><font color="Green">E23</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E14:11_1"><i><font color="Green">E21</font></i></a></i>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E20:11_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E21:11_1"/><b>then </b><i><font color="Green">E24</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>10</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="graph_2.html#E1:11"><i><font color="Green">E12</font></i></a>, <a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_1_2"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> or <font color="Maroon">c<sub>12</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2_1"><b>suppose </b></a><a NAME="E1:11_1_2_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/><div class="add"><a NAME="E2:11_1_2_1"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1
 ;<br/><b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:11_1_2_1"/><i><font color="Green">E26</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="txt" href="graph_2.html#E21:11_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="graph_2.html#E1:11_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="graph_2.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E5:11_1_2_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="graph_2.html#E2:11"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E6:11_1_2_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E18:11_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="graph_2.html#E4:11_1_2_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E7:11_1_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E5:11_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="graph_2.html#E21:11_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="graph_2.html#E1:11_1_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="graph_2.html#E1:11_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="graph_2.html#E5:11_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="graph_2.html#E4:11_1_2_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="graph_2.html#E3:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="graph_2.html#E1:11_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="graph_2.html#E12:11_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="graph_2.html#E4:11_1_2_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="graph_2.html#E6:11_1_2_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2_2"><b>suppose </b></a><a NAME="E1:11_1_2_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:11_1_2_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="txt" href="graph_2.html#E21:11_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="graph_2.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>12</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="graph_2.html#E3:11_1_2_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/><a NAME="E6:11_1_2_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E3:11_1_2_2"><i><font color="Green">E25</font></i></a></i>;<br/><a NAME="E7:11_1_2_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><a NAME="E8:11_1_2_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E9:11_1_2_2"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="graph_2.html#E5:11_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="graph_2.html#E3:11_1_2_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E10:11_1_2_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>15</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E11:11_1_2_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E12:11_1_2_2"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="graph_2.html#E5:11_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="graph_2.html#E6:11_1_2_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="graph_2.html#E11:11_1_2_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="graph_2.html#E3:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="graph_2.html#E6:11_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="graph_2.html#E9:11_1_2_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="graph_2.html#E3:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="graph_2.html#E1:11_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="graph_2.html#E12:11_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="graph_2.html#E19:11_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="graph_2.html#E3:11_1_2_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="graph_2.html#E12:11_1_2_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="graph_2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:11"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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