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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/>







<a NAME="E1:17"/><i><font color="Green">E13</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="group_5.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E2:17"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E3:17"/><i><font color="Green">E15</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="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="group_4.html#D4">GROUP_4:def 4</a></i>;<br/>
<i><font color="Green">E16</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="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_5.html#D1" target="_self">Def1</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="group_4.html#D4">GROUP_4:def 4</a></i>
;<br/>
<a NAME="E5:17"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="group_4.html#D4">GROUP_4:def 4</a></i>;<br/>
<a NAME="E6:17"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:17_2"/>
<font color="Maroon">c<sub>5</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> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><a NAME="E2:17_2"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:17_2"/><b>then </b><i><font color="Green">E19</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="group_5.html#E2:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="group_5.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_4.html#K2">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="group_5.html#E2:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="group_5.html#E2:17_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="group_4.html#D4">GROUP_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_3.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_4.html#K2">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="group_5.html#E2:17_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="group_5.html#E3:17_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="group_5.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_1.html#K6">|^</a> <span class="p2">(<span class="default"><a href="group_4.html#K2">@</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="group_3.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="group_3.html#T34">GROUP_3:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_3.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="group_5.html#E2:17_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="group_5.html#E3:17_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="group_4.html#D4">GROUP_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="group_5.html#E6:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="group_5.html#E2:17_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="group_5.html#D1" target="_self">Def1</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:17"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_4.html#K4">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_5.html#K1" target="_self">|^</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="group_5.html#E1:17"><i><font color="Green">E13</font></i></a>, <a class="txt" href="group_5.html#E3:17"><i><font color="Green">E15</font></i></a>, <a class="txt" href="group_5.html#E4:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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