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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green">E5</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:37"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <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="E3:37"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:37"/><b>then </b><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:37"/><i><font color="Green">E7</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E7:37"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25">GOBOARD2:25</a></i>;<br/>
<a NAME="E8:37"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<a NAME="E9:37"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<a NAME="E10:37"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E12:37"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<a NAME="E13:37"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E12:37"><i><font color="Green">E11</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E14:37"/><b>then </b><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E8:37"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E15:37"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E17:37"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<a NAME="E18:37"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E17:37"><i><font color="Green">E13</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E19:37"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E9:37"><i><font color="Green">E10</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E20:37"/>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E21:37"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E23:37"/><i><font color="Green">E16</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E24:37"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25">GOBOARD2:25</a></i>;<br/>
<a NAME="E25:37"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<a NAME="E26:37"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<a NAME="E27:37"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="goboard8.html#E4:37"><i><font color="Green">E6</font></i></a>, <a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="txt" href="goboard8.html#E7:37"><i><font color="Green">E8</font></i></a>, <a class="txt" href="goboard8.html#E21:37"><i><font color="Green">E15</font></i></a>, <a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="goboard8.html#E24:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="goboard5.html#T13">GOBOARD5:13</a></i>;<br/>
<a NAME="E28:37"/><b>then </b><i><font color="Green">E20</font></i>: 
( (  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> ) or (  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) )
 
<b>by </b><i><a class="ref" href="goboard1.html#T2">GOBOARD1:2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_1"/>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="goboard8.html#E28:37"><i><font color="Green">E20</font></i></a>, <a class="ref" href="goboard1.html#T1">GOBOARD1:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1"><b>suppose </b></a><a NAME="E1:37_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><div class="add"><a NAME="E2:37_1_1"/><b>then </b>
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="txt" href="goboard8.html#E7:37"><i><font color="Green">E8</font></i></a>, <a class="txt" href="goboard8.html#E12:37"><i><font color="Green">E11</font></i></a>, <a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="goboard8.html#E24:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="goboard5.html#T28">GOBOARD5:28</a></i>;<br/><b>hence </b><a NAME="E3:37_1_1"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E9:37"><i><font color="Green">E10</font></i></a>, <a class="txt" href="goboard8.html#E14:37"><i><font color="Green">E12</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_2"><b>suppose </b></a><a NAME="E1:37_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><div class="add"><a NAME="E2:37_1_2"/><b>then </b>
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="txt" href="goboard8.html#E7:37"><i><font color="Green">E8</font></i></a>, <a class="txt" href="goboard8.html#E17:37"><i><font color="Green">E13</font></i></a>, <a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="goboard8.html#E24:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="goboard5.html#T29">GOBOARD5:29</a></i>;<br/><b>hence </b><a NAME="E3:37_1_2"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E8:37"><i><font color="Green">E9</font></i></a>, <a class="txt" href="goboard8.html#E9:37"><i><font color="Green">E10</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_3"><b>suppose </b></a><a NAME="E1:37_1_3"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/><div class="add"><a NAME="E2:37_1_3"/><b>then </b>
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="txt" href="goboard8.html#E7:37"><i><font color="Green">E8</font></i></a>, <a class="txt" href="goboard8.html#E17:37"><i><font color="Green">E13</font></i></a>, <a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="goboard8.html#E24:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="goboard5.html#T30">GOBOARD5:30</a></i>;<br/><b>hence </b><a NAME="E3:37_1_3"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E19:37"><i><font color="Green">E14</font></i></a>, <a class="txt" href="goboard8.html#E25:37"><i><font color="Green">E18</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_4"><b>suppose </b></a><a NAME="E1:37_1_4"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><a NAME="E2:37_1_4"/><b>then </b>
 <a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3">GoB</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:37"><i><font color="Green">E5</font></i></a>, <a class="txt" href="goboard8.html#E6:37"><i><font color="Green">E7</font></i></a>, <a class="txt" href="goboard8.html#E7:37"><i><font color="Green">E8</font></i></a>, <a class="txt" href="goboard8.html#E12:37"><i><font color="Green">E11</font></i></a>, <a class="txt" href="goboard8.html#E23:37"><i><font color="Green">E16</font></i></a>, <a class="txt" href="goboard8.html#E24:37"><i><font color="Green">E17</font></i></a>, <a class="ref" href="goboard5.html#T31">GOBOARD5:31</a></i>;<br/><b>hence </b><a NAME="E3:37_1_4"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5">left_cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="goboard8.html#E8:37"><i><font color="Green">E9</font></i></a>, <a class="txt" href="goboard8.html#E26:37"><i><font color="Green">E19</font></i></a>, <a class="ref" href="goboard7.html#T14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
