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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>;<br/><b>let </b><font color="Maroon" title="c2">i1</font>, <font color="Maroon" title="c3">i2</font>, <font color="Maroon" title="c4">j1</font>, <font color="Maroon" title="c5">j2</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>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green" title="E2">A1</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j1</font>
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green" title="E3">A2</font></i>: 
<font color="Maroon" title="c4">j1</font> <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="c1">G</font>
 <b>and </b><br/><a NAME="E3:1"/><i><font color="Green" title="E4">A3</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">j2</font>
 <b>and </b><br/><a NAME="E4:1"/><i><font color="Green" title="E5">A4</font></i>: 
<font color="Maroon" title="c5">j2</font> <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="c1">G</font>
 <b>and </b><br/><a NAME="E5:1"/><i><font color="Green" title="E6">A5</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">i1</font>
 <b>and </b><br/><a NAME="E6:1"/><i><font color="Green" title="E7">A6</font></i>: 
<font color="Maroon" title="c2">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">i2</font>
 <b>and </b><br/><a NAME="E7:1"/><i><font color="Green" title="E8">A7</font></i>: 
<font color="Maroon" title="c3">i2</font> <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="c1">G</font>
 ;<br/>

<a NAME="E8:1"/><i><font color="Green" title="E9">A8</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i2</font>
 
<b>by </b><i><a class="txt" href="jordan1j.html#E5:1"><i><font color="Green" title="E6">A5</font></i></a>, <a class="txt" href="jordan1j.html#E6:1"><i><font color="Green" title="E7">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j1</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i2</font>,1</span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
<b>by </b><i><a class="txt" href="jordan1j.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="jordan1j.html#E2:1"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="jordan1j.html#E7:1"><i><font color="Green" title="E8">A7</font></i></a>, <a class="ref" href="goboard5.html#T3" title="GOBOARD5:th.3">GOBOARD5:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c5">j2</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
<b>by </b><i><a class="txt" href="jordan1j.html#E3:1"><i><font color="Green" title="E4">A3</font></i></a>, <a class="txt" href="jordan1j.html#E4:1"><i><font color="Green" title="E5">A4</font></i></a>, <a class="txt" href="jordan1j.html#E7:1"><i><font color="Green" title="E8">A7</font></i></a>, <a class="txt" href="jordan1j.html#E8:1"><i><font color="Green" title="E9">A8</font></i></a>, <a class="ref" href="goboard5.html#T3" title="GOBOARD5:th.3">GOBOARD5:3</a></i>
;<br/>
<b>hence </b><a NAME="E10:1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c2">i1</font>,<font color="Maroon" title="c4">j1</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c5">j2</font></span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
 <b>by </b><i><a class="txt" href="jordan1j.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="jordan1j.html#E2:1"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="jordan1j.html#E5:1"><i><font color="Green" title="E6">A5</font></i></a>, <a class="txt" href="jordan1j.html#E6:1"><i><font color="Green" title="E7">A6</font></i></a>, <a class="txt" href="jordan1j.html#E7:1"><i><font color="Green" title="E8">A7</font></i></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></i>;<br/>


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