<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>











<b>assume </b><a NAME="E1:10"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> &amp; <font color="Maroon">i2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">j2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">gs1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:10"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> &amp; <font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; ( for <font color="Olive">k</font>, <font color="Olive">k1</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> &amp; <font color="Olive">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> holds <br/><font color="Olive">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> ) &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> holds <br/><font color="Maroon">gs1</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font>,<font color="Maroon">gs1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">gs2</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:10"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">gs2</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font> &amp; <font color="Maroon">gs2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j2</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">j2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; ( for <font color="Olive">k</font>, <font color="Olive">k1</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> &amp; <font color="Olive">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">gs2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> holds <br/><font color="Olive">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> ) &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> holds <br/><font color="Maroon">gs2</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font>,<font color="Maroon">gs2</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 <b>by </b><i>, </i>;<br/>
<b>set </b><font color="Maroon">hs1</font> = <font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">hs2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font>;<br/>
<a NAME="E6:10"/><i><font color="Green">E37</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> )
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E7:10"/><b>then </b><i><font color="Green">E43</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E8:10"/><i><font color="Green">E44</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> )
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E9:10"/><b>then </b><i><font color="Green">E45</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E10:10"/><i><font color="Green">E46</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E11:10"/><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E12:10"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<i><font color="Green">E49</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span>

;<br/>
<i><font color="Green">E50</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</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> <font color="Maroon">gs2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
;<br/>
<div><i><font color="Green">E51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_3_1"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0 or <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_3_1_1"><b>case </b></a><a NAME="E1:10_3_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font>
<b>by </b><i><a class="ref" href="finseq_2.html#T72">FINSEQ_2:72</a></i>
<br/>.= 
<font color="Maroon">gs2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/><b>hence </b><a NAME="E3:10_3_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_3_1_2"><b>case </b></a><a NAME="E1:10_3_1_2"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:10_3_1_2"/><i><font color="Green">E53</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E3:10_3_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i/>;<br/><a NAME="E4:10_3_1_2"/><b>then </b><i><font color="Green">E54</font></i>: 
0 <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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:10_3_1_2"/><b>then </b>
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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E6:10_3_1_2"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E7:10_3_1_2"/><i><font color="Green">E56</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E8:10_3_1_2"/><i><font color="Green">E57</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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</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> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/><a NAME="E9:10_3_1_2"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> )
 <b>by </b><i>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E10:10_3_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs2</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E11:10_3_1_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> )
 <b>by </b><i>, , <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="gobrd10.html#T1" target="_self">Th1</a>, <a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_4"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_4_1"/>
( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0 or <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_4_1_1"><b>case </b></a><a NAME="E1:10_4_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>then </b><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> = 
<font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T72">FINSEQ_2:72</a></i>
<br/>.= 
<font color="Maroon">gs1</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/><b>hence </b><a NAME="E3:10_4_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_4_1_2"><b>case </b></a><a NAME="E1:10_4_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:10_4_1_2"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E3:10_4_1_2"/><i><font color="Green">E61</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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> <font color="Maroon">gs1</font></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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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="E4:10_4_1_2"/><i><font color="Green">E62</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E5:10_4_1_2"/><i><font color="Green">E64</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:10_4_1_2"/><b>then </b><i><font color="Green">E65</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E7:10_4_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="gobrd10.html#T1" target="_self">Th1</a>, </i>;<br/><b>hence </b><a NAME="E8:10_4_1_2"/>
( <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> )
 <b>by </b><i>, , , <a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E17:10"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">j2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E18:10"/><i><font color="Green">E67</font></i>: 
for <font color="Olive">i</font>, <font color="Olive">k1</font>, <font color="Olive">k2</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> &amp; <font color="Olive">k1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Olive">k2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/>( <font color="Olive">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Olive">k2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:10_5"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> &amp; <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 ;<br/>

<a NAME="E2:10_5"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">i</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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:10_5"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/>
<a NAME="E4:10_5"/><b>then </b><i><font color="Green">E70</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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> <font color="Maroon">gs1</font></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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:10_5"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:10_5"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E7:10_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E8:10_5"/><b>then </b><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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> <font color="Maroon">gs1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E9:10_5"/><i><font color="Green">E74</font></i>: 
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> ) or ( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<div><i><font color="Green">E75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_5_1_1"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> ) or ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> ) )
 </span><b>by </b><i><a class="txt" href="gobrd10.html#E3:10"><i><font color="Green">E30</font></i></a>, <a class="ref" href="gobrd10.html#D2" target="_self">Def2</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_5_1_1_1"><b>case </b></a><a NAME="E1:10_5_1_1_1"/><i><font color="Green">E76</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> )
 ;<br/><div class="add"><a NAME="E2:10_5_1_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:10_5_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><b>hence </b><a NAME="E4:10_5_1_1_1"/>
<font color="Maroon">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="gobrd10.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_5_1_1_2"><b>case </b></a><a NAME="E1:10_5_1_1_2"/><i><font color="Green">E77</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:10_5_1_1_2"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E3:10_5_1_1_2"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D3" target="_self">Def3</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:10_5_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D3" target="_self">Def3</a>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:10_5_1_1_2"/><b>then </b><i><font color="Green">E79</font></i>: 
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E1:10"><i><font color="Green">E29</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><a NAME="E6:10_5_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E7:10_5_1_1_2"/><b>then </b><i><font color="Green">E80</font></i>: 
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E8:10_5_1_1_2"/><i><font color="Green">E81</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 <b>by </b><i><a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E9:10_5_1_1_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D3" target="_self">Def3</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E10:10_5_1_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
 ;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">i2</font>
<b>by </b><i><a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, </i>
;<br/><b>hence </b><a NAME="E12:10_5_1_1_2"/>
<font color="Maroon">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E11:10_5"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/>
<a NAME="E12:10_5"/><b>then </b>
 <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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</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> <font color="Maroon">gs2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E13:10_5"/><b>then </b><i><font color="Green">E83</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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E14:10_5"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> ) )
 
<b>by </b><i>, , <a class="ref" href="gobrd10.html#T1" target="_self">Th1</a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E15:10_5"/><b>then </b>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> ) )
 
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E16:10_5"/><b>then </b>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) or ( <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> &amp; <font color="Maroon">i</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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> ) )
 
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E17:10_5"/><b>then </b>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) or ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> &amp; <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> ) )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E18:10_5"/><b>then </b><i><font color="Green">E84</font></i>: 
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) or ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 ) )
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_5_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_5_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_5_2_1"/>
( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></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> <font color="Maroon">gs1</font></span>)</span> ) or ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 ) )
 </span><b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_5_2_1_1"><b>case </b></a><a NAME="E1:10_5_2_1_1"/><i><font color="Green">E85</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></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> <font color="Maroon">gs1</font></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:10_5_2_1_1"/><b>then </b><i><font color="Green">E86</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 ;<br/><a NAME="E3:10_5_2_1_1"/><i><font color="Green">E87</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a></i>;<br/><a NAME="E4:10_5_2_1_1"/><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E5:10_5_2_1_1"/><i><font color="Green">E89</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:10_5_2_1_1"/><i><font color="Green">E90</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i/>;<br/><i><font color="Green">E91</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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="gobrd10.html#D3" target="_self">Def3</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font>

;<br/><a NAME="E8:10_5_2_1_1"/><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E9:10_5_2_1_1"/><i><font color="Green">E93</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E10:10_5_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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">gs2</font></span>)</span>
 <b>by </b><i>, , , , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E11:10_5_2_1_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>

<br/>.= 
<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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="txt" href="gobrd10.html#E7:10"><i><font color="Green">E43</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><a NAME="E13:10_5_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">gs2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E8:10"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><b>hence </b><a NAME="E14:10_5_2_1_1"/>
<font color="Maroon">k2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, , <a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_5_2_1_2"><b>case </b></a><a NAME="E1:10_5_2_1_2"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 ;<br/><div class="add"><a NAME="E2:10_5_2_1_2"/><b>then </b><i><font color="Green">E95</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E3:10_5_2_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E4:10_5_2_1_2"/><b>then </b>
<font color="Maroon">i</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:10_5_2_1_2"/><b>then </b>
<font color="Maroon">i</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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">j1</font>
<b>by </b><i><a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, </i>
;<br/><b>hence </b><a NAME="E7:10_5_2_1_2"/>
<font color="Maroon">k2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E20:10_5"/>
( <font color="Maroon">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">k2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> )
 <b>by </b><i><a class="ref" href="gobrd10.html#T3" target="_self">Th3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E19:10"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font>,<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R2" target="_self">are_adjacent2</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:10_6"/><i><font color="Green">E96</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_6_1_1"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> or <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1"><b>case </b></a><a NAME="E1:10_6_1_1_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>
 ;<br/><div class="add"><a NAME="E2:10_6_1_1_1"/><b>then </b><i><font color="Green">E98</font></i>: 
<font color="Maroon">i</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> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:10_6_1_1_1"/><i><font color="Green">E99</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:10_6_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E5:10_6_1_1_1"/><b>then </b><i><font color="Green">E100</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E6:10_6_1_1_1"/><b>then </b><i><font color="Green">E101</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E7:10_6_1_1_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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E8:10_6_1_1_1"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">i</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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D2" target="_self">Def2</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:10_6_1_1_1"/><i><font color="Green">E103</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T39">FINSEQ_1:39</a></i>;<br/><i><font color="Green">E104</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="gobrd10.html#T3" target="_self">Th3</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">j1</font>
<b>by </b><i><a class="txt" href="gobrd10.html#E3:10"><i><font color="Green">E30</font></i></a>, </i>
;<br/><div><i><font color="Green">E105</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6_1_1_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_6_1_1_1_2_1"/>
( <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 or <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1_2_1_1"><b>case </b></a><a NAME="E1:10_6_1_1_1_2_1_1"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 ;<br/><div class="add"><a NAME="E2:10_6_1_1_1_2_1_1"/><b>then </b><i><font color="Green">E107</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E1:10"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:10_6_1_1_1_2_1_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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E4:10_6_1_1_1_2_1_1"/><b>then </b><i><font color="Green">E114</font></i>: 
<font color="Maroon">i</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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><i><font color="Green">E115</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">j1</font>
<b>by </b><i><a class="txt" href="gobrd10.html#E1:10"><i><font color="Green">E29</font></i></a>, , </i>
;<br/><a NAME="E6:10_6_1_1_1_2_1_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T39">FINSEQ_1:39</a></i>;<br/><b>hence </b><a NAME="E7:10_6_1_1_1_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1_2_1_2"><b>case </b></a><a NAME="E1:10_6_1_1_1_2_1_2"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 ;<br/><div class="add"><a NAME="E2:10_6_1_1_1_2_1_2"/><b>then </b><i><font color="Green">E116</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><i><font color="Green">E117</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>

;<br/><a NAME="E4:10_6_1_1_1_2_1_2"/><b>then </b><i><font color="Green">E118</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, , <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E5:10_6_1_1_1_2_1_2"/>
1 <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">gs2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E6:10_6_1_1_1_2_1_2"/><b>then </b><i><font color="Green">E119</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:10_6_1_1_1_2_1_2"/>
<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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, , </i>;<br/><a NAME="E8:10_6_1_1_1_2_1_2"/><b>then </b><i><font color="Green">E120</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E9:10_6_1_1_1_2_1_2"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><b>then </b> <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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</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> <font color="Maroon">gs2</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><a NAME="E11:10_6_1_1_1_2_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E12:10_6_1_1_1_2_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E13:10_6_1_1_1_2_1_2"/><b>then </b>
<font color="Maroon">i</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E14:10_6_1_1_1_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6_1_1_1_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_6_1_1_1_3_1"/>
( <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 or <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1_3_1_1"><b>case </b></a><a NAME="E1:10_6_1_1_1_3_1_1"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 ;<br/><div class="add"><a NAME="E2:10_6_1_1_1_3_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E3:10_6_1_1_1_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:10_6_1_1_1_3_1_1"/><b>then </b><i><font color="Green">E121</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:10_6_1_1_1_3_1_1"/><i><font color="Green">E122</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:10_6_1_1_1_3_1_1"/><i><font color="Green">E123</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:10_6_1_1_1_3_1_1"/><i><font color="Green">E124</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T39">FINSEQ_1:39</a></i>;<br/><a NAME="E8:10_6_1_1_1_3_1_1"/><i><font color="Green">E125</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, , <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E9:10_6_1_1_1_3_1_1"/><i><font color="Green">E126</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 <b>by </b><i>, <a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><i><font color="Green">E127</font></i>: <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E12:10_6_1_1_1_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a> 
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_1_3_1_2"><b>case </b></a><a NAME="E1:10_6_1_1_1_3_1_2"/>
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 ;<br/><div class="add"><a NAME="E2:10_6_1_1_1_3_1_2"/><i><font color="Green">E128</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:10_6_1_1_1_3_1_2"/><i><font color="Green">E129</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T39">FINSEQ_1:39</a></i>;<br/><a NAME="E4:10_6_1_1_1_3_1_2"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="gobrd10.html#T1" target="_self">Th1</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E5:10_6_1_1_1_3_1_2"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, , <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><i><font color="Green">E132</font></i>: <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, <a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">gs1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E8:10_6_1_1_1_3_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a> 
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="gobrd10.html#T1" target="_self">Th1</a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E13:10_6_1_1_1"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 <b>by </b><i><a class="ref" href="gobrd10.html#T3" target="_self">Th3</a>, <a class="ref" href="gobrd10.html#D3" target="_self">Def3</a>, , <a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_6_1_1_2"><b>case </b></a><a NAME="E1:10_6_1_1_2"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>
 ;<br/><div class="add"><a NAME="E2:10_6_1_1_2"/><b>then </b><i><font color="Green">E134</font></i>: 
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E3:10_6_1_1_2"/><b>then </b><i><font color="Green">E135</font></i>: 
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E4:10_6_1_1_2"/><i><font color="Green">E136</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E5:10_6_1_1_2"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/> <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></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"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i/>
;<br/><a NAME="E7:10_6_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</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> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E8:10_6_1_1_2"/><b>then </b><i><font color="Green">E138</font></i>: 
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><div><i><font color="Green">E139</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:10_6_1_1_2_2"/>
not 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 ;<br/><a NAME="E2:10_6_1_1_2_2"/><b>then </b>
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E3:10_6_1_1_2_2"/><b>then </b>
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:10_6_1_1_2_2"/><b>then </b>
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E5:10_6_1_1_2_2"/><b>then </b><i><font color="Green">E140</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>
 <b>by </b><i><a class="txt" href="gobrd10.html#E1:10"><i><font color="Green">E29</font></i></a></i>;<br/><a NAME="E6:10_6_1_1_2_2"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font>
 <b>by </b><i/>;<br/><a NAME="E7:10_6_1_1_2_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</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">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/><a NAME="E8:10_6_1_1_2_2"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs1</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E9:10_6_1_1_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/></div><b>end;</b></div><a NAME="E10:10_6_1_1_2"/><i><font color="Green">E141</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_6_1_1_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:10_6_1_1_2_3"/><i><font color="Green">E142</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 ;<br/><a NAME="E2:10_6_1_1_2_3"/><b>then </b>
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#T3" target="_self">Th3</a>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:10_6_1_1_2_3"/><b>then </b><i><font color="Green">E143</font></i>: 
<font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">i2</font>
<b>by </b><i><a class="ref" href="gobrd10.html#T3" target="_self">Th3</a>, <a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, </i>
;<br/><b>hence </b><a NAME="E6:10_6_1_1_2_3"/>
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 ;<br/></div><b>end;</b></div><a NAME="E12:10_6_1_1_2"/><b>then </b><i><font color="Green">E144</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 <b>by </b><i><a class="ref" href="gobrd10.html#D2" target="_self">Def2</a>, <a class="ref" href="gobrd10.html#D3" target="_self">Def3</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E13:10_6_1_1_2"/><i><font color="Green">E145</font></i>: 
<font color="Maroon">i</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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E14:10_6_1_1_2"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E15:10_6_1_1_2"/><b>then </b><i><font color="Green">E146</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E16:10_6_1_1_2"/><b>then </b><i><font color="Green">E147</font></i>: 
<font color="Maroon">i</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"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E17:10_6_1_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#T1" target="_self">Th1</a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E18:10_6_1_1_2"/><b>then </b><i><font color="Green">E148</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E19:10_6_1_1_2"/><i><font color="Green">E149</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E20:10_6_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E21:10_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E22:10_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E23:10_6_1_1_2"/><b>then </b><i><font color="Green">E150</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 <b>by </b><i><a class="txt" href="gobrd10.html#E3:10"><i><font color="Green">E30</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E24:10_6_1_1_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E25:10_6_1_1_2"/><b>then </b><i><font color="Green">E151</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E26:10_6_1_1_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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><a NAME="E27:10_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E28:10_6_1_1_2"/><b>then </b><i><font color="Green">E152</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><b>then </b><i><font color="Green">E153</font></i>: <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E7:10"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">i2</font>
<b>by </b><i>, </i>
;<br/><a NAME="E31:10_6_1_1_2"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="gobrd10.html#T2" target="_self">Th2</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E32:10_6_1_1_2"/><b>then </b><i><font color="Green">E154</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span>
 <b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E33:10_6_1_1_2"/><i><font color="Green">E155</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E34:10_6_1_1_2"/><i><font color="Green">E156</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs2</font>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E35:10_6_1_1_2"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">i</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E36:10_6_1_1_2"/><i><font color="Green">E158</font></i>: 
<font color="Maroon">i</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="gobrd10.html#E6:10"><i><font color="Green">E37</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E37:10_6_1_1_2"/>
<font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="gobrd10.html#D1" target="_self">Def1</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E38:10_6_1_1_2"/><b>then </b><i><font color="Green">E159</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font>
 <b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E39:10_6_1_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E40:10_6_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <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">gs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="gobrd10.html#E10:10"><i><font color="Green">E46</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E41:10_6_1_1_2"/><b>then </b><i><font color="Green">E160</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">gs2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1

;<br/><b>then </b><i><font color="Green">E161</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E13:10"><i><font color="Green">E49</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">gs2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E15:10"><i><font color="Green">E51</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">gs2</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E15:10"><i><font color="Green">E51</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="gobrd10.html#T6" target="_self">Th6</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">i</font>

;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="funct_1.html#K1">.</a> <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"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E12:10"><i><font color="Green">E48</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">gs2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E11:10"><i><font color="Green">E47</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">gs2</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="gobrd10.html#E11:10"><i><font color="Green">E47</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>hence </b><a NAME="E46:10_6_1_1_2"/>
( ( <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R1" target="_self">are_adjacent1</a>  ) )
 <b>by </b><i>, <a class="txt" href="gobrd10.html#E5:10"><i><font color="Green">E35</font></i></a>, , <a class="txt" href="gobrd10.html#E8:10"><i><font color="Green">E44</font></i></a>, <a class="txt" href="gobrd10.html#E9:10"><i><font color="Green">E45</font></i></a>, <a class="txt" href="gobrd10.html#E14:10"><i><font color="Green">E50</font></i></a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:10_6"/>
<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">gs1</font> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs2</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">gs1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="gobrd10.html#K1" target="_self">|-&gt;</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">gs2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R2" target="_self">are_adjacent2</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E20:10"/>
 ex <font color="Olive">fs1</font>, <font color="Olive">fs2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( ( for <font color="Olive">i</font>, <font color="Olive">k1</font>, <font color="Olive">k2</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Olive">fs1</font> &amp; <font color="Olive">k1</font> <a href="hidden.html#R1">=</a> <font color="Olive">fs1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Olive">k2</font> <a href="hidden.html#R1">=</a> <font color="Olive">fs2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> holds <br/>( <font color="Olive">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Olive">k2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> ) ) &amp; <font color="Olive">fs1</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> &amp; <font color="Olive">fs1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">fs1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> &amp; <font color="Olive">fs2</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j1</font> &amp; <font color="Olive">fs2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Olive">fs2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">fs1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">fs2</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">fs1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j2</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">j2</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">fs1</font> holds <br/><font color="Olive">fs1</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font>,<font color="Olive">fs2</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">i</font>,<font color="Olive">fs1</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Olive">fs2</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="gobrd10.html#R2" target="_self">are_adjacent2</a>  ) )
 <b>by </b><i>, , , , , </i>;<br/>


</div>
