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<b>let </b><font color="Maroon" title="c1">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">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><a NAME="E1:38"/><i><font color="Green" title="E5">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font> &amp; <font color="Maroon" title="c1">k</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="c2">f</font> )
 ;<br/>

<a NAME="E2:38"/>
<font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</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#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E3:38"/><b>then </b>
<font color="Maroon" title="c1">k</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="c2">f</font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:38"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">i1</font>, <font color="Maroon" title="c4">j1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E6:38"/><i><font color="Green" title="E7">A3</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i1</font>,<font color="Maroon" title="c4">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 <b>and </b><br/><a NAME="E7:38"/><i><font color="Green" title="E8">A4</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c1">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="c2">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i1</font>,<font color="Maroon" title="c4">j1</font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25" title="GOBOARD2:th.25">GOBOARD2:25</a></i>;<br/>
<a NAME="E8:38"/><i><font color="Green" title="E9">A5</font></i>: 
<font color="Maroon" title="c3">i1</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/>
<a NAME="E9:38"/><i><font color="Green" title="E10">A6</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/>
<a NAME="E10:38"/>
<font color="Maroon" title="c3">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E12:38"/><i><font color="Green" title="E11">A7</font></i>: 
<font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<a NAME="E13:38"/>
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i1</font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E12:38"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E14:38"/><b>then </b><i><font color="Green" title="E12">A8</font></i>: 
<font color="Maroon" title="c5">i</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E8:38"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E15:38"/>
<font color="Maroon" title="c4">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c6">j</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E17:38"/><i><font color="Green" title="E13">A9</font></i>: 
<font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">i</font> = <font color="Maroon" title="c5">i</font>, <font color="Maroon" title="c8">j</font> = <font color="Maroon" title="c6">j</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E19:38"/><i><font color="Green" title="E14">A10</font></i>: 
<font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="goboard8.html#E12:38"><i><font color="Green" title="E11">A7</font></i></a></i>;<br/>
<a NAME="E20:38"/><i><font color="Green" title="E15">A11</font></i>: 
<font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="txt" href="goboard8.html#E17:38"><i><font color="Green" title="E13">A9</font></i></a></i>;<br/>
<a NAME="E21:38"/>
<font color="Maroon" title="c8">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j1</font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E17:38"><i><font color="Green" title="E13">A9</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E22:38"/><b>then </b><i><font color="Green" title="E16">A12</font></i>: 
<font color="Maroon" title="c8">j</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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E9:38"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E23:38"/>
<font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</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="E24:38"/><b>then </b><i><font color="Green" title="E17">A13</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c9">i2</font>, <font color="Maroon" title="c10">j2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E26:38"/><i><font color="Green" title="E18">A14</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">i2</font>,<font color="Maroon" title="c10">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 <b>and </b><br/><a NAME="E27:38"/><i><font color="Green" title="E19">A15</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c2">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c9">i2</font>,<font color="Maroon" title="c10">j2</font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25" title="GOBOARD2:th.25">GOBOARD2:25</a></i>;<br/>
<a NAME="E28:38"/><i><font color="Green" title="E20">A16</font></i>: 
<font color="Maroon" title="c9">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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/>
<a NAME="E29:38"/><i><font color="Green" title="E21">A17</font></i>: 
<font color="Maroon" title="c10">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> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">i1'</font> = <font color="Maroon" title="c3">i1</font>, <font color="Maroon" title="c12">i2'</font> = <font color="Maroon" title="c9">i2</font>, <font color="Maroon" title="c13">j1'</font> = <font color="Maroon" title="c4">j1</font>, <font color="Maroon" title="c14">j2'</font> = <font color="Maroon" title="c10">j2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E31:38"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">i1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">i2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">j1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c10">j2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="goboard8.html#E4:38"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="goboard8.html#E7:38"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="goboard8.html#E24:38"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="goboard8.html#E27:38"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="goboard5.html#T13" title="GOBOARD5:th.13">GOBOARD5:13</a></i>;<br/>
<a NAME="E32:38"/><b>then </b><i><font color="Green" title="E22">A18</font></i>: 
( (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">i1'</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c12">i2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> ) or (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">j1'</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c14">j2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> ) )
 
<b>by </b><i><a class="ref" href="goboard1.html#T2" title="GOBOARD1:th.2">GOBOARD1:2</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_1"/>
( ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> &amp; <font color="Maroon" title="c4">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> ) or ( <font color="Maroon" title="c3">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> ) or ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> ) or ( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="goboard8.html#E32:38"><i><font color="Green" title="E22">A18</font></i></a>, <a class="ref" href="goboard1.html#T1" title="GOBOARD1:th.1">GOBOARD1:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1"><b>suppose </b></a><a NAME="E1:38_1_1"/>
( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> &amp; <font color="Maroon" title="c4">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> )
 ;<br/><div class="add"><a NAME="E2:38_1_1"/><b>then </b>
 <a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c3">i1</font>,<font color="Maroon" title="c4">j1</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="goboard8.html#E7:38"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="goboard8.html#E19:38"><i><font color="Green" title="E14">A10</font></i></a>, <a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="goboard8.html#E27:38"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><b>hence </b><a NAME="E3:38_1_1"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E8:38"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="goboard8.html#E9:38"><i><font color="Green" title="E10">A6</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_2"><b>suppose </b></a><a NAME="E1:38_1_2"/>
( <font color="Maroon" title="c3">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> )
 ;<br/><div class="add"><a NAME="E2:38_1_2"/><b>then </b>
 <a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c3">i1</font>,<font color="Maroon" title="c8">j</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="goboard8.html#E7:38"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="goboard8.html#E17:38"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="goboard8.html#E27:38"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><b>hence </b><a NAME="E3:38_1_2"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E8:38"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="goboard8.html#E22:38"><i><font color="Green" title="E16">A12</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_3"><b>suppose </b></a><a NAME="E1:38_1_3"/>
( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> )
 ;<br/><div class="add"><a NAME="E2:38_1_3"/><b>then </b>
 <a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c9">i2</font>,<font color="Maroon" title="c4">j1</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="goboard8.html#E7:38"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="goboard8.html#E20:38"><i><font color="Green" title="E15">A11</font></i></a>, <a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="goboard8.html#E27:38"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><b>hence </b><a NAME="E3:38_1_3"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E9:38"><i><font color="Green" title="E10">A6</font></i></a>, <a class="txt" href="goboard8.html#E28:38"><i><font color="Green" title="E20">A16</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_4"><b>suppose </b></a><a NAME="E1:38_1_4"/>
( <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">i2</font> &amp; <font color="Maroon" title="c4">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">j2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 ;<br/><div class="add"><a NAME="E2:38_1_4"/><b>then </b>
 <a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c2">f</font></span>)</span>,<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c10">j2</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E1:38"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="goboard8.html#E6:38"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="goboard8.html#E7:38"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="goboard8.html#E12:38"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="goboard8.html#E26:38"><i><font color="Green" title="E18">A14</font></i></a>, <a class="txt" href="goboard8.html#E27:38"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><b>hence </b><a NAME="E3:38_1_4"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K4" title="GOBOARD5:func.4">right_cell</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c1">k</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c2">f</font>
 <b>by </b><i><a class="txt" href="goboard8.html#E14:38"><i><font color="Green" title="E12">A8</font></i></a>, <a class="txt" href="goboard8.html#E29:38"><i><font color="Green" title="E21">A17</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
