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<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   <a href="goboard1.html#NM1">Go-board</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:12"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:12"/><i><font color="Green">E14</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:12"/><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="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:12"/><i><font color="Green">E16</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</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> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E6:12"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E7:12"/><i><font color="Green">E18</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E8:12"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</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> <font color="Maroon">c<sub>2</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E9:12"/><i><font color="Green">E20</font></i>: 
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <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>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <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 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="ref" href="jordan8.html#T6">JORDAN8:6</a></i>;<br/>
<a NAME="E10:12"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E11:12"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<a NAME="E12:12"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>6</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> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="ref" href="goboard5.html#T1">GOBOARD5:1</a></i>;<br/>
<a NAME="E13:12"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</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> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan9.html#E11:12"><i><font color="Green">E22</font></i></a>, <a class="ref" href="jordan3.html#T7">JORDAN3:7</a></i>;<br/>
<a NAME="E14:12"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</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> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan9.html#E12:12"><i><font color="Green">E23</font></i></a>, <a class="ref" href="jordan3.html#T7">JORDAN3:7</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:12_1"/>
( ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <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>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <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 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="jordan9.html#E9:12"><i><font color="Green">E20</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1"><b>suppose </b></a><a NAME="E1:12_1_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:12_1_1"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="ref" href="gobrd13.html#D2">GOBRD13:def 2</a></i>;<br/><a NAME="E3:12_1_1"/>
 <a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="txt" href="jordan9.html#E1:12_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="gobrd13.html#D3">GOBRD13:def 3</a></i>;<br/><b>hence </b><a NAME="E4:12_1_1"/>
(  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> &amp;  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> )
 <b>by </b><i><a class="txt" href="jordan9.html#E11:12"><i><font color="Green">E22</font></i></a>, <a class="txt" href="jordan9.html#E13:12"><i><font color="Green">E24</font></i></a>, <a class="txt" href="jordan9.html#E2:12_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="goboard9.html#T21">GOBOARD9:21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_2"><b>suppose </b></a><a NAME="E1:12_1_2"/><i><font color="Green">E26</font></i>: 
( <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>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:12_1_2"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="ref" href="gobrd13.html#D2">GOBRD13:def 2</a></i>;<br/><a NAME="E3:12_1_2"/>
 <a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="txt" href="jordan9.html#E1:12_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="gobrd13.html#D3">GOBRD13:def 3</a></i>;<br/><b>hence </b><a NAME="E4:12_1_2"/>
(  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> &amp;  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> )
 <b>by </b><i><a class="txt" href="jordan9.html#E11:12"><i><font color="Green">E22</font></i></a>, <a class="txt" href="jordan9.html#E13:12"><i><font color="Green">E24</font></i></a>, <a class="txt" href="jordan9.html#E2:12_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="goboard9.html#T21">GOBOARD9:21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_3"><b>suppose </b></a><a NAME="E1:12_1_3"/><i><font color="Green">E26</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 &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><div class="add"><a NAME="E2:12_1_3"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="ref" href="gobrd13.html#D2">GOBRD13:def 2</a></i>;<br/><a NAME="E3:12_1_3"/>
 <a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="txt" href="jordan9.html#E1:12_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="gobrd13.html#D3">GOBRD13:def 3</a></i>;<br/><b>hence </b><a NAME="E4:12_1_3"/>
(  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> &amp;  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> )
 <b>by </b><i><a class="txt" href="jordan9.html#E12:12"><i><font color="Green">E23</font></i></a>, <a class="txt" href="jordan9.html#E14:12"><i><font color="Green">E25</font></i></a>, <a class="txt" href="jordan9.html#E2:12_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="goboard9.html#T21">GOBOARD9:21</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_4"><b>suppose </b></a><a NAME="E1:12_1_4"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><a NAME="E2:12_1_4"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="ref" href="gobrd13.html#D2">GOBRD13:def 2</a></i>;<br/><a NAME="E3:12_1_4"/>
 <a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="jordan9.html#E2:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="jordan9.html#E3:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="jordan9.html#E5:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="jordan9.html#E6:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="jordan9.html#E7:12"><i><font color="Green">E18</font></i></a>, <a class="txt" href="jordan9.html#E8:12"><i><font color="Green">E19</font></i></a>, <a class="txt" href="jordan9.html#E10:12"><i><font color="Green">E21</font></i></a>, <a class="txt" href="jordan9.html#E1:12_1_4"><i><font color="Green">E26</font></i></a>, <a class="ref" href="gobrd13.html#D3">GOBRD13:def 3</a></i>;<br/><b>hence </b><a NAME="E4:12_1_4"/>
(  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> &amp;  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="connsp_1.html#V2">connected</a> )
 <b>by </b><i><a class="txt" href="jordan9.html#E11:12"><i><font color="Green">E22</font></i></a>, <a class="txt" href="jordan9.html#E12:12"><i><font color="Green">E23</font></i></a>, <a class="txt" href="jordan9.html#E13:12"><i><font color="Green">E24</font></i></a>, <a class="txt" href="jordan9.html#E2:12_1_4"><i><font color="Green">E27</font></i></a>, <a class="ref" href="goboard9.html#T21">GOBOARD9:21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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