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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">G</font> be   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E22">A1</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">G</font>
 <b>and </b><br/><a NAME="E3:22"/><i><font color="Green" title="E24">A3</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font>
 <b>and </b><br/><a NAME="E4:22"/><i><font color="Green" title="E25">A4</font></i>: 
<font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">G</font>
 ;<br/>

<a NAME="E5:22"/><i><font color="Green" title="E26">A5</font></i>: 
( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E6:22"/><i><font color="Green" title="E27">A6</font></i>: 
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">G</font>
 
<b>by </b><i><a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E7:22"/><i><font color="Green" title="E28">A7</font></i>: 
<font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c3">G</font>
 
<b>by </b><i><a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E8:22"/><b>then </b><i><font color="Green" title="E29">A8</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></i>;<br/>
<a NAME="E9:22"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E6:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="goboard5.html#T5" title="GOBOARD5:th.5">GOBOARD5:5</a></i>;<br/>
<b>hence </b><a NAME="E10:22"/>
<font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <font color="Maroon" title="c3">G</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E8:22"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="jordan9.html#T19" target="_self" title="JORDAN9:th.19">Th19</a></i>;<br/>

<a NAME="E11:22"/><i><font color="Green" title="E30">A9</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="jordan9.html#T18" target="_self" title="JORDAN9:th.18">Th18</a></i>;<br/>
<a NAME="E12:22"/><b>then </b><i><font color="Green" title="E31">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E7:22"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></i>;<br/>
<a NAME="E13:22"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E6:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="goboard5.html#T5" title="GOBOARD5:th.5">GOBOARD5:5</a></i>;<br/>
<b>hence </b><a NAME="E14:22"/>
<font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <font color="Maroon" title="c3">G</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E11:22"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="jordan9.html#E12:22"><i><font color="Green" title="E31">A10</font></i></a>, <a class="ref" href="jordan9.html#T19" target="_self" title="JORDAN9:th.19">Th19</a></i>;<br/>

<a NAME="E15:22"/><i><font color="Green" title="E32">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="jordan9.html#T18" target="_self" title="JORDAN9:th.18">Th18</a></i>;<br/>
<a NAME="E16:22"/><b>then </b><i><font color="Green" title="E33">A12</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E7:22"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></i>;<br/>
<a NAME="E17:22"/><i><font color="Green" title="E34">A13</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="jordan9.html#T18" target="_self" title="JORDAN9:th.18">Th18</a></i>;<br/>
<a NAME="E18:22"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E6:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="goboard5.html#T5" title="GOBOARD5:th.5">GOBOARD5:5</a></i>;<br/>
<b>hence </b><a NAME="E19:22"/>
<font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <font color="Maroon" title="c3">G</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E15:22"><i><font color="Green" title="E32">A11</font></i></a>, <a class="txt" href="jordan9.html#E16:22"><i><font color="Green" title="E33">A12</font></i></a>, <a class="txt" href="jordan9.html#E17:22"><i><font color="Green" title="E34">A13</font></i></a>, <a class="ref" href="jordan9.html#T19" target="_self" title="JORDAN9:th.19">Th19</a></i>;<br/>

<a NAME="E20:22"/><i><font color="Green" title="E35">A14</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E7:22"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></i>;<br/>
<a NAME="E21:22"/><i><font color="Green" title="E36">A15</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="jordan9.html#T18" target="_self" title="JORDAN9:th.18">Th18</a></i>;<br/>
<a NAME="E22:22"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E5:22"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="jordan9.html#E6:22"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="goboard5.html#T5" title="GOBOARD5:th.5">GOBOARD5:5</a></i>;<br/>
<b>hence </b><a NAME="E23:22"/>
<font color="Maroon" title="c3">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <font color="Maroon" title="c3">G</font>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>
 <b>by </b><i><a class="txt" href="jordan9.html#E1:22"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="jordan9.html#E2:22"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="jordan9.html#E3:22"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="jordan9.html#E4:22"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="jordan9.html#E20:22"><i><font color="Green" title="E35">A14</font></i></a>, <a class="txt" href="jordan9.html#E21:22"><i><font color="Green" title="E36">A15</font></i></a>, <a class="ref" href="jordan9.html#T19" target="_self" title="JORDAN9:th.19">Th19</a></i>;<br/>


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