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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> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:13"/><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="E2:13"/><i><font color="Green">E13</font></i>: 
<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>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> = 1,<font color="Maroon">c<sub>2</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>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>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E3:13"/><i><font color="Green">E14</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1
 
;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default">1,<font color="Maroon">c<sub>2</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>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="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>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default">1,<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>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <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#E1:13"><i><font color="Green">E12</font></i></a>, <a class="txt" href="graph_2.html#E2:13"><i><font color="Green">E13</font></i></a>, <a class="ref" href="graph_2.html#T8" target="_self">Th8</a></i>
<br/>.= 
1,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="graph_2.html#K1" target="_self">-cut</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="graph_2.html#E2:13"><i><font color="Green">E13</font></i></a>, <a class="txt" href="graph_2.html#E3:13"><i><font color="Green">E14</font></i></a>, <a class="ref" href="graph_2.html#T8" target="_self">Th8</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="graph_2.html#T7" target="_self">Th7</a></i>
;<br/><br/>


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