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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">k</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="c4">f</font> be  non <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="goboard5.html#V2" title="GOBOARD5:attr.2">standard</a> <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:53"/><i><font color="Green" title="E36">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:53"/><i><font color="Green" title="E37">A2</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> )
 <b>and </b><br/><a NAME="E3:53"/><i><font color="Green" title="E38">A3</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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="c4">f</font> )
 <b>and </b><br/><a NAME="E4:53"/><i><font color="Green" title="E39">A4</font></i>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K4" title="TOPREAL1:func.4">LSeg</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">k</font>
 <b>and </b><br/><a NAME="E5:53"/><i><font color="Green" title="E40">A5</font></i>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K4" title="TOPREAL1:func.4">LSeg</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 ;<br/>

<a NAME="E6:53"/><i><font color="Green" title="E41">A6</font></i>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard7.html#E3:53"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="goboard7.html#E4:53"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="topreal1.html#D5" title="TOPREAL1:def.5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E7:53"/><b>then </b><i><font color="Green" title="E42">A7</font></i>: 
( ( <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">k</font> &amp; <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) or ( <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">k</font> ) )
 
<b>by </b><i><a class="ref" href="sppol_1.html#T25" title="SPPOL_1:th.25">SPPOL_1:25</a></i>;<br/>
<a NAME="E8:53"/><i><font color="Green" title="E43">A8</font></i>: 
<font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
;<br/>
<a NAME="E9:53"/><b>then </b><i><font color="Green" title="E44">A9</font></i>: 
<font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <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="c4">f</font>
 
<b>by </b><i><a class="txt" href="goboard7.html#E3:53"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E10:53"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E11:53"/><b>then </b><i><font color="Green" title="E45">A10</font></i>: 
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard7.html#E5:53"><i><font color="Green" title="E40">A5</font></i></a>, <a class="txt" href="goboard7.html#E8:53"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="goboard7.html#E9:53"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="topreal1.html#D5" title="TOPREAL1:def.5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E12:53"/><b>then </b><i><font color="Green" title="E46">A11</font></i>: 
( ( <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> ) or ( <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> ) )
 
<b>by </b><i><a class="ref" href="sppol_1.html#T25" title="SPPOL_1:th.25">SPPOL_1:25</a></i>;<br/>
<a NAME="E13:53"/><i><font color="Green" title="E47">A12</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E14:53"/><i><font color="Green" title="E48">A13</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard7.html#E1:53"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E15:53"/><i><font color="Green" title="E49">A14</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard7.html#E2:53"><i><font color="Green" title="E37">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="E16:53"/><i><font color="Green" title="E50">A15</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#K2" title="NAT_1:func.2">+</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/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c1">i</font>,1</span>)</span> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a> 
<b>by </b><i><a class="txt" href="goboard7.html#E1:53"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="goboard7.html#E2:53"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="goboard7.html#E14:53"><i><font color="Green" title="E48">A13</font></i></a>, <a class="txt" href="goboard7.html#E15:53"><i><font color="Green" title="E49">A14</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"><span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</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="goboard7.html#E1:53"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="goboard7.html#E2:53"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="goboard7.html#E13:53"><i><font color="Green" title="E47">A12</font></i></a>, <a class="txt" href="goboard7.html#E14:53"><i><font color="Green" title="E48">A13</font></i></a>, <a class="ref" href="goboard5.html#T3" title="GOBOARD5:th.3">GOBOARD5:3</a></i>
;<br/>
<a NAME="E18:53"/><b>then </b><i><font color="Green" title="E51">A16</font></i>: 
<span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="goboard7.html#E1:53"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="goboard7.html#E2:53"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="goboard7.html#E13:53"><i><font color="Green" title="E47">A12</font></i></a>, <a class="txt" href="goboard7.html#E16:53"><i><font color="Green" title="E50">A15</font></i></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></i>;<br/>
<b>hence </b><a NAME="E19:53"/>
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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>
 <b>by </b><i><a class="txt" href="goboard7.html#E7:53"><i><font color="Green" title="E42">A7</font></i></a>, <a class="txt" href="goboard7.html#E11:53"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="sppol_1.html#T25" title="SPPOL_1:th.25">SPPOL_1:25</a></i>;<br/>

<b>thus </b><a NAME="E20:53"/>
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font>
 <b>by </b><i><a class="txt" href="goboard7.html#E6:53"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="goboard7.html#E12:53"><i><font color="Green" title="E46">A11</font></i></a>, <a class="txt" href="goboard7.html#E18:53"><i><font color="Green" title="E51">A16</font></i></a>, <a class="ref" href="sppol_1.html#T25" title="SPPOL_1:th.25">SPPOL_1:25</a></i>;<br/>

<b>thus </b><a NAME="E21:53"/>
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c4">f</font></span>)</span> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard7.html#E6:53"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="goboard7.html#E12:53"><i><font color="Green" title="E46">A11</font></i></a>, <a class="txt" href="goboard7.html#E18:53"><i><font color="Green" title="E51">A16</font></i></a>, <a class="ref" href="sppol_1.html#T25" title="SPPOL_1:th.25">SPPOL_1:25</a></i>;<br/>


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