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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</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>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/>







<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green">E32</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:41"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:41"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="ref" href="jordan8.html#T5">JORDAN8:5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:41"/><i><font color="Green">E36</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>4</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <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>4</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="E7:41"/><i><font color="Green">E37</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</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>4</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <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>4</sub></font> <a href="matrix_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E8:41"/><i><font color="Green">E38</font></i>: 
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 <b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="ref" href="jordan8.html#T6">JORDAN8:6</a></i>;<br/>
<a NAME="E9:41"/><i><font color="Green">E39</font></i>: 
( <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>8</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>8</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> &amp; <font color="Maroon">c<sub>9</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>9</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="gobrd13.html#K4" target="_self">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="gobrd13.html#K4" target="_self">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="gobrd13.html#K3" target="_self">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="gobrd13.html#K3" target="_self">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E10:41"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gobrd13.html#E2:41"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>;<br/>
<a NAME="E11:41"/>
( <font color="Maroon">c<sub>1</sub></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">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="ref" href="goboard2.html#T3">GOBOARD2:3</a></i>;<br/>
<a NAME="E12:41"/><b>then </b><i><font color="Green">E41</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <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>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> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <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>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_5.html#T30">FINSEQ_5:30</a></i>;<br/>
<a NAME="E13:41"/><i><font color="Green">E42</font></i>: 
<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="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E14:41"/>
<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="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <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">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E15:41"/><b>then </b><i><font color="Green">E43</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> &amp; <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="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E10:41"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1"/>
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> ) or ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="gobrd13.html#E8:41"><i><font color="Green">E38</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1"><b>suppose </b></a><a NAME="E1:41_1_1_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b> <a href="gobrd13.html#K4" target="_self">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</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="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
<br/>.= 
 <a href="gobrd13.html#K4" target="_self">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
;<br/><br/><b>thus </b> <a href="gobrd13.html#K3" target="_self">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</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="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="gobrd13.html#K3" target="_self">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_2"><b>suppose </b></a><a NAME="E1:41_1_1_2"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b> <a href="gobrd13.html#K4" target="_self">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</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="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
<br/>.= 
 <a href="gobrd13.html#K4" target="_self">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
;<br/><br/><b>thus </b> <a href="gobrd13.html#K3" target="_self">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</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="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="gobrd13.html#K3" target="_self">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3"><b>suppose </b></a><a NAME="E1:41_1_1_3"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><div class="add"><b>hence </b> <a href="gobrd13.html#K4" target="_self">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
<br/>.= 
 <a href="gobrd13.html#K4" target="_self">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_3"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
;<br/><br/><b>thus </b> <a href="gobrd13.html#K3" target="_self">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_3"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="gobrd13.html#K3" target="_self">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_3"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_4"><b>suppose </b></a><a NAME="E1:41_1_1_4"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><b>hence </b> <a href="gobrd13.html#K4" target="_self">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
<br/>.= 
 <a href="gobrd13.html#K4" target="_self">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D3" target="_self">Def3</a></i>
;<br/><br/><b>thus </b> <a href="gobrd13.html#K3" target="_self">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="goboard5.html#K3">cell</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E3:41"><i><font color="Green">E34</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E12:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="gobrd13.html#E13:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="gobrd13.html#E15:41"><i><font color="Green">E43</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="gobrd13.html#K3" target="_self">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gobrd13.html#E1:41"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gobrd13.html#E4:41"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gobrd13.html#E6:41"><i><font color="Green">E36</font></i></a>, <a class="txt" href="gobrd13.html#E7:41"><i><font color="Green">E37</font></i></a>, <a class="txt" href="gobrd13.html#E9:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="gobrd13.html#E1:41_1_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gobrd13.html#D2" target="_self">Def2</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E17:41"/>
(  <a href="gobrd13.html#K4" target="_self">left_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="gobrd13.html#K4" target="_self">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gobrd13.html#K3" target="_self">right_cell</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="gobrd13.html#K3" target="_self">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 ;<br/>


</div>
