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<b>let </b><font color="Maroon" title="c1">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>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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> ] <b>means </b>( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 &amp; $1 <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> <font color="Maroon" title="c1">f</font> implies  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,$1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font> );<br/>
<a NAME="E1:28"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
;<br/>
<div><i><font color="Green" title="E27">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">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>assume </b><a NAME="E1:28_1"/><i><font color="Green" title="E28">A3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font>]
 ;<br/><b>thus </b><a NAME="E2:28_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:28_1_1"/><i><font color="Green" title="E29">A4</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1"/><i><font color="Green" title="E30">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <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">f</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_1"/>
( <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_1"><b>suppose </b></a><a NAME="E1:28_1_1_1_1"/>
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_1_1_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="ref" href="goboard9.html#D1" target="_self" title="GOBOARD9:def.1">Def1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2"><b>suppose </b></a><a NAME="E1:28_1_1_1_2"/><i><font color="Green" title="E31">A6</font></i>: 
<font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ;<br/><div class="add"><a NAME="E2:28_1_1_1_2"/><i><font color="Green" title="E32">A7</font></i>: 
<font color="Maroon" title="c2">k</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> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:28_1_1_1_2"/><i><font color="Green" title="E33">A8</font></i>: 
<font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">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="E4:28_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E34">A9</font></i>: 
<font color="Maroon" title="c2">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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</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">i0</font>, <font color="Maroon" title="c4">j0</font> being    <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> <b> such that </b><br/><a NAME="E7:28_1_1_1_2"/><i><font color="Green" title="E35">A10</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E8:28_1_1_1_2"/><i><font color="Green" title="E36">A11</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">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="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25" title="GOBOARD2:th.25">GOBOARD2:25</a></i>;<br/><a NAME="E9:28_1_1_1_2"/><i><font color="Green" title="E37">A12</font></i>: 
<font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</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="c5">i1</font>, <font color="Maroon" title="c6">j1</font> being    <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> <b> such that </b><br/><a NAME="E11:28_1_1_1_2"/><i><font color="Green" title="E38">A13</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E12:28_1_1_1_2"/><i><font color="Green" title="E39">A14</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25" title="GOBOARD2:th.25">GOBOARD2:25</a></i>;<br/><a NAME="E13:28_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <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="E14:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E40">A15</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</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="c7">i2</font>, <font color="Maroon" title="c8">j2</font> being    <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> <b> such that </b><br/><a NAME="E16:28_1_1_1_2"/><i><font color="Green" title="E41">A16</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E17:28_1_1_1_2"/><i><font color="Green" title="E42">A17</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">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</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="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="ref" href="goboard2.html#T25" title="GOBOARD2:th.25">GOBOARD2:25</a></i>;<br/><a NAME="E18:28_1_1_1_2"/><i><font color="Green" title="E43">A18</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i0</font> &amp; <font color="Maroon" title="c3">i0</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="c1">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E19:28_1_1_1_2"/><i><font color="Green" title="E44">A19</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c5">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="c1">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E20:28_1_1_1_2"/><i><font color="Green" title="E45">A20</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c7">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="c1">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E21:28_1_1_1_2"/><i><font color="Green" title="E46">A21</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j0</font> &amp; <font color="Maroon" title="c4">j0</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="c1">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E22:28_1_1_1_2"/><i><font color="Green" title="E47">A22</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c6">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="c1">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E23:28_1_1_1_2"/><i><font color="Green" title="E48">A23</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c8">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="c1">f</font></span>)</span> )
 <b>by </b><i><a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E24:28_1_1_1_2"/><i><font color="Green" title="E49">A24</font></i>: 
( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> or <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> )
 <b>by </b><i><a class="txt" href="goboard9.html#E5:28_1_1_1_2"><i><font color="Green" title="E34">A9</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green" title="E37">A12</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="ref" href="goboard2.html#T16" title="GOBOARD2:th.16">GOBOARD2:16</a></i>;<br/><a NAME="E25:28_1_1_1_2"/><i><font color="Green" title="E50">A25</font></i>: 
( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> or <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> )
 <b>by </b><i><a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green" title="E37">A12</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2"><i><font color="Green" title="E40">A15</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="ref" href="goboard2.html#T16" title="GOBOARD2:th.16">GOBOARD2:16</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">i1'</font> = <font color="Maroon" title="c5">i1</font>, <font color="Maroon" title="c10">i0'</font> = <font color="Maroon" title="c3">i0</font>, <font color="Maroon" title="c11">i2'</font> = <font color="Maroon" title="c7">i2</font>, <font color="Maroon" title="c12">j1'</font> = <font color="Maroon" title="c6">j1</font>, <font color="Maroon" title="c13">j0'</font> = <font color="Maroon" title="c4">j0</font>, <font color="Maroon" title="c14">j2'</font> = <font color="Maroon" title="c8">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="E27:28_1_1_1_2"/><i><font color="Green" title="E51">A26</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="goboard1.html#R1" title="GOBOARD1:pred.1">is_sequence_on</a>  <a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="ref" href="goboard5.html#D5" title="GOBOARD5:def.5">GOBOARD5:def 5</a></i>;<br/><a NAME="E28:28_1_1_1_2"/><b>then </b>
<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">i0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c5">i1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</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">j0</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c6">j1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E5:28_1_1_1_2"><i><font color="Green" title="E34">A9</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green" title="E37">A12</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="ref" href="goboard1.html#D11" title="GOBOARD1:def.11">GOBOARD1:def 11</a></i>;<br/><a NAME="E29:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E52">A27</font></i>: 
( (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">i0'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c9">i1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> ) or (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">j0'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">j1'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> ) )
 <b>by </b><i><a class="ref" href="goboard1.html#T2" title="GOBOARD1:th.2">GOBOARD1:2</a></i>;<br/><a NAME="E30:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E53">A28</font></i>: 
( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> or <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> )
 <b>by </b><i><a class="ref" href="goboard1.html#T1" title="GOBOARD1:th.1">GOBOARD1:1</a></i>;<br/><a NAME="E31:28_1_1_1_2"/>
<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="c5">i1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c7">i2</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</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="c6">j1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c8">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="goboard9.html#E9:28_1_1_1_2"><i><font color="Green" title="E37">A12</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2"><i><font color="Green" title="E40">A15</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2"><i><font color="Green" title="E51">A26</font></i></a>, <a class="ref" href="goboard1.html#D11" title="GOBOARD1:def.11">GOBOARD1:def 11</a></i>;<br/><a NAME="E32:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E54">A29</font></i>: 
( (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">i1'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c11">i2'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> ) or (  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">j1'</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</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="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> ) )
 <b>by </b><i><a class="ref" href="goboard1.html#T2" title="GOBOARD1:th.2">GOBOARD1:2</a></i>;<br/><a NAME="E33:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E55">A30</font></i>: 
( <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> or <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> )
 <b>by </b><i><a class="ref" href="goboard1.html#T1" title="GOBOARD1:th.1">GOBOARD1:1</a></i>;<br/><a NAME="E34:28_1_1_1_2"/><i><font color="Green" title="E56">A31</font></i>: 
( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> or <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> )
 <b>by </b><i><a class="txt" href="goboard9.html#E29:28_1_1_1_2"><i><font color="Green" title="E52">A27</font></i></a>, <a class="ref" href="goboard1.html#T1" title="GOBOARD1:th.1">GOBOARD1:1</a></i>;<br/><a NAME="E35:28_1_1_1_2"/><i><font color="Green" title="E57">A32</font></i>: 
( <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> or <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> )
 <b>by </b><i><a class="txt" href="goboard9.html#E32:28_1_1_1_2"><i><font color="Green" title="E54">A29</font></i></a>, <a class="ref" href="goboard1.html#T1" title="GOBOARD1:th.1">GOBOARD1:1</a></i>;<br/><div><i><font color="Green" title="E58">A33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1_2_1"/><i><font color="Green" title="E59">A34</font></i>: 
( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> )
 ;<br/><div><i><font color="Green" title="E60">A35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1_2_1_1"/>
<font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 ;<br/><a NAME="E2:28_1_1_1_2_1_1"/><b>then </b><i><font color="Green" title="E61">A36</font></i>: 
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><b>assume </b><a NAME="E3:28_1_1_1_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 ;<br/><a NAME="E4:28_1_1_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><b>hence </b><a NAME="E5:28_1_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_1_1"><i><font color="Green" title="E61">A36</font></i></a>, <a class="ref" href="goboard7.html#T36" title="GOBOARD7:th.36">GOBOARD7:36</a></i>;<br/></div><b>end;</b></div><a NAME="E3:28_1_1_1_2_1"/><i><font color="Green" title="E61">A37</font></i>: 
<font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_1_2_1_2"/>
( <font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 or <span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <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="c1">f</font> )
 </span><b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_1"><i><font color="Green" title="E60">A35</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_1_2_1"><b>suppose </b></a><a NAME="E1:28_1_1_1_2_1_2_1"/>
<font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_1_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_1"><i><font color="Green" title="E59">A34</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_1"><i><font color="Green" title="E61">A37</font></i></a>, <a class="ref" href="goboard7.html#T39" title="GOBOARD7:th.39">GOBOARD7:39</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_1_2_2"><b>suppose </b></a><a NAME="E1:28_1_1_1_2_1_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <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="c1">f</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_1_1_1_2_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_1"><i><font color="Green" title="E59">A34</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_1"><i><font color="Green" title="E61">A37</font></i></a>, <a class="ref" href="goboard7.html#T38" title="GOBOARD7:th.38">GOBOARD7:38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E37:28_1_1_1_2"/>
<font color="Maroon" title="c5">i1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E38:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E59">A38</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E39:28_1_1_1_2"/>
<font color="Maroon" title="c6">j1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></i>;<br/><a NAME="E40:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E60">A39</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E41:28_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font>
 <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="E42:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E61">A40</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E43:28_1_1_1_2"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="ref" href="goboard7.html#T34" title="GOBOARD7:th.34">GOBOARD7:34</a></i>;<br/><a NAME="E44:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E62">A41</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E45:28_1_1_1_2"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="goboard7.html#T35" title="GOBOARD7:th.35">GOBOARD7:35</a></i>;<br/><a NAME="E46:28_1_1_1_2"/><b>then </b><i><font color="Green" title="E63">A42</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T53" title="BINARITH:th.53">BINARITH:53</a></i>;<br/><a NAME="E47:28_1_1_1_2"/><i><font color="Green" title="E64">A43</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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>
 ;<br/><a NAME="E48:28_1_1_1_2"/><i><font color="Green" title="E65">A44</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">i0</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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i0</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>
 ;<br/><a NAME="E49:28_1_1_1_2"/><i><font color="Green" title="E66">A45</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">i2</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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</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>
 ;<br/><a NAME="E50:28_1_1_1_2"/><i><font color="Green" title="E67">A46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">j0</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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j0</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>
 ;<br/><a NAME="E51:28_1_1_1_2"/><i><font color="Green" title="E68">A47</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">j2</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 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</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>
 ;<br/><a NAME="E52:28_1_1_1_2"/><i><font color="Green" title="E69">A48</font></i>: 
 <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="goboard9.html#D1" target="_self" title="GOBOARD9:def.1">Def1</a></i>;<br/><a NAME="E53:28_1_1_1_2"/><i><font color="Green" title="E70">A49</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard9.html#T22" target="_self" title="GOBOARD9:th.22">Th22</a></i>;<br/><a NAME="E54:28_1_1_1_2"/><i><font color="Green" title="E71">A50</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1_1_1_2_2_1"/>
( ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) or ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 ) or ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) or ( <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span> ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> &amp; <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> &amp; <font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="goboard9.html#E5:28_1_1_1_2"><i><font color="Green" title="E34">A9</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2"><i><font color="Green" title="E37">A12</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2"><i><font color="Green" title="E40">A15</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2"><i><font color="Green" title="E53">A28</font></i></a>, <a class="txt" href="goboard9.html#E33:28_1_1_1_2"><i><font color="Green" title="E55">A30</font></i></a>, <a class="txt" href="goboard9.html#E34:28_1_1_1_2"><i><font color="Green" title="E56">A31</font></i></a>, <a class="txt" href="goboard9.html#E35:28_1_1_1_2"><i><font color="Green" title="E57">A32</font></i></a>, <a class="txt" href="goboard9.html#E36:28_1_1_1_2"><i><font color="Green" title="E58">A33</font></i></a>, <a class="ref" href="goboard7.html#T31" title="GOBOARD7:th.31">GOBOARD7:31</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E72">A51</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E73">A52</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E74">A53</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E75">A54</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E54:28_1_1_1_2"><i><font color="Green" title="E71">A50</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green" title="E72">A51</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_1"><i><font color="Green" title="E74">A53</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_1"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green" title="E72">A51</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green" title="E73">A52</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_1"><i><font color="Green" title="E74">A53</font></i></a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_1"/><b>then </b><i><font color="Green" title="E76">A55</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green" title="E72">A51</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green" title="E73">A52</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_1"><i><font color="Green" title="E74">A53</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E77">A56</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E78">A57</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green" title="E72">A51</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_1"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green" title="E66">A45</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_1"><i><font color="Green" title="E72">A51</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green" title="E73">A52</font></i></a>, <a class="ref" href="goboard8.html#T25" title="GOBOARD8:th.25">GOBOARD8:25</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_1"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_1"/><b>then </b><i><font color="Green" title="E79">A58</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_1"><i><font color="Green" title="E75">A54</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_1"><i><font color="Green" title="E77">A56</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_1"><i><font color="Green" title="E78">A57</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_1"/><i><font color="Green" title="E80">A59</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_1"><i><font color="Green" title="E73">A52</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_1"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E15:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_1"><i><font color="Green" title="E76">A55</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_1"><i><font color="Green" title="E79">A58</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_1"><i><font color="Green" title="E80">A59</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E72">A60</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E73">A61</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E74">A62</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E75">A63</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green" title="E72">A60</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_2"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_2"><i><font color="Green" title="E74">A62</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E76">A64</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green" title="E72">A60</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E77">A65</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green" title="E73">A61</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E78">A66</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E79">A67</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green" title="E72">A60</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_2"><i><font color="Green" title="E76">A64</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_2"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green" title="E66">A45</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green" title="E72">A60</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green" title="E73">A61</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_2"><i><font color="Green" title="E76">A64</font></i></a>, <a class="ref" href="goboard8.html#T11" title="GOBOARD8:th.11">GOBOARD8:11</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_2"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_2"/><b>then </b><i><font color="Green" title="E80">A68</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_2"><i><font color="Green" title="E75">A63</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_2"><i><font color="Green" title="E78">A66</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_2"><i><font color="Green" title="E79">A67</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_2"/><i><font color="Green" title="E81">A69</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green" title="E72">A60</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green" title="E73">A61</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_2"><i><font color="Green" title="E76">A64</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_2"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_2"><i><font color="Green" title="E72">A60</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_2"><i><font color="Green" title="E73">A61</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_2"><i><font color="Green" title="E77">A65</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_2"><i><font color="Green" title="E80">A68</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_2"><i><font color="Green" title="E81">A69</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_3"/><i><font color="Green" title="E72">A70</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_3"/><i><font color="Green" title="E73">A71</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"> <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k</font> = 
 <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_3"><i><font color="Green" title="E72">A70</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_3"><i><font color="Green" title="E73">A71</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>
<br/>.= 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_3"><i><font color="Green" title="E73">A71</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E72">A72</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E73">A73</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E74">A74</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E75">A75</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E76">A76</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green" title="E72">A72</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E77">A77</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E78">A78</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green" title="E72">A72</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green" title="E74">A74</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_4"><i><font color="Green" title="E75">A75</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_4"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="ref" href="goboard8.html#T35" title="GOBOARD8:th.35">GOBOARD8:35</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green" title="E79">A79</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_4"><i><font color="Green" title="E76">A76</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_4"><i><font color="Green" title="E77">A77</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_4"><i><font color="Green" title="E78">A78</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E80">A80</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E81">A81</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green" title="E72">A72</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green" title="E74">A74</font></i></a>, <a class="ref" href="goboard6.html#T93" title="GOBOARD6:th.93">GOBOARD6:93</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_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#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green" title="E82">A82</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_4"><i><font color="Green" title="E79">A79</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_4"><i><font color="Green" title="E80">A80</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_4"><i><font color="Green" title="E81">A81</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E83">A83</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_4"><i><font color="Green" title="E73">A73</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_4"><i><font color="Green" title="E75">A75</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E84">A84</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E85">A85</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green" title="E72">A72</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green" title="E74">A74</font></i></a>, <a class="ref" href="goboard6.html#T93" title="GOBOARD6:th.93">GOBOARD6:93</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_4"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="ref" href="goboard8.html#T27" title="GOBOARD8:th.27">GOBOARD8:27</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_4"/><b>then </b><i><font color="Green" title="E86">A86</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_4"><i><font color="Green" title="E82">A82</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_4"><i><font color="Green" title="E84">A84</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_4"><i><font color="Green" title="E85">A85</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_4"/><i><font color="Green" title="E87">A87</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><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="c1">f</font></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_4"><i><font color="Green" title="E72">A72</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_4"><i><font color="Green" title="E73">A73</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_4"><i><font color="Green" title="E74">A74</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_4"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E25:28_1_1_1_2_2_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_4"><i><font color="Green" title="E83">A83</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_4"><i><font color="Green" title="E86">A86</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_4"><i><font color="Green" title="E87">A87</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_5"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E72">A88</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E73">A89</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E74">A90</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E75">A91</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E76">A92</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green" title="E72">A88</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_5"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_5"><i><font color="Green" title="E74">A90</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green" title="E77">A93</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">i0</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/><a NAME="E8:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E78">A94</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E79">A95</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green" title="E72">A88</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_5"><i><font color="Green" title="E75">A91</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green" title="E77">A93</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_5"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,2</span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green" title="E66">A45</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green" title="E72">A88</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green" title="E73">A89</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_5"><i><font color="Green" title="E75">A91</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green" title="E77">A93</font></i></a>, <a class="ref" href="goboard8.html#T8" title="GOBOARD8:th.8">GOBOARD8:8</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green" title="E80">A96</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_5"><i><font color="Green" title="E76">A92</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_5"><i><font color="Green" title="E78">A94</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_5"><i><font color="Green" title="E79">A95</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E81">A97</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E82">A98</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green" title="E72">A88</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green" title="E77">A93</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_5"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green" title="E83">A99</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_5"><i><font color="Green" title="E80">A96</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_5"><i><font color="Green" title="E81">A97</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_5"><i><font color="Green" title="E82">A98</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E84">A100</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green" title="E73">A89</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_5"><i><font color="Green" title="E75">A91</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E85">A101</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E86">A102</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green" title="E72">A88</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green" title="E73">A89</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green" title="E77">A93</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_5"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_5"><i><font color="Green" title="E72">A88</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green" title="E73">A89</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_5"><i><font color="Green" title="E77">A93</font></i></a>, <a class="ref" href="goboard8.html#T25" title="GOBOARD8:th.25">GOBOARD8:25</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_5"/><b>then </b><i><font color="Green" title="E87">A103</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_5"><i><font color="Green" title="E83">A99</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_5"><i><font color="Green" title="E85">A101</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_5"><i><font color="Green" title="E86">A102</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_5"/><i><font color="Green" title="E88">A104</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_5"><i><font color="Green" title="E73">A89</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_5"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_5"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E27:28_1_1_1_2_2_1_5"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_5"><i><font color="Green" title="E84">A100</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_5"><i><font color="Green" title="E87">A103</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_5"><i><font color="Green" title="E88">A104</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_6"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E72">A105</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E73">A106</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E74">A107</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E75">A108</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E76">A109</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_6"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_6"><i><font color="Green" title="E75">A108</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green" title="E77">A110</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E78">A111</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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>
 <b>by </b><i><a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E79">A112</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E80">A113</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green" title="E74">A107</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_6"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green" title="E77">A110</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_6"><i><font color="Green" title="E78">A111</font></i></a>, <a class="ref" href="goboard8.html#T34" title="GOBOARD8:th.34">GOBOARD8:34</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green" title="E81">A114</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_6"><i><font color="Green" title="E76">A109</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_6"><i><font color="Green" title="E79">A112</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_6"><i><font color="Green" title="E80">A113</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E82">A115</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E42:28_1_1_1_2"><i><font color="Green" title="E61">A40</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_6"/>
<font color="Maroon" title="c6">j1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_6"><i><font color="Green" title="E75">A108</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_6"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green" title="E83">A116</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green" title="E74">A107</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_6"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E42:28_1_1_1_2"><i><font color="Green" title="E61">A40</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green" title="E84">A117</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_6"><i><font color="Green" title="E81">A114</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_6"><i><font color="Green" title="E82">A115</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_6"><i><font color="Green" title="E83">A116</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E85">A118</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green" title="E73">A106</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E86">A119</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E87">A120</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green" title="E74">A107</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green" title="E77">A110</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E88">A121</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green" title="E73">A106</font></i></a>, <a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_6"><i><font color="Green" title="E72">A105</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green" title="E73">A106</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_6"><i><font color="Green" title="E74">A107</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green" title="E77">A110</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_6"><i><font color="Green" title="E78">A111</font></i></a>, <a class="ref" href="goboard8.html#T19" title="GOBOARD8:th.19">GOBOARD8:19</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_6"/><b>then </b><i><font color="Green" title="E89">A122</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_6"><i><font color="Green" title="E84">A117</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_6"><i><font color="Green" title="E86">A119</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_6"><i><font color="Green" title="E87">A120</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_6"/><i><font color="Green" title="E90">A123</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_6"><i><font color="Green" title="E73">A106</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_6"><i><font color="Green" title="E77">A110</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_6"><i><font color="Green" title="E88">A121</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_6"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_6"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E31:28_1_1_1_2_2_1_6"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_6"><i><font color="Green" title="E85">A118</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_6"><i><font color="Green" title="E89">A122</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_6"><i><font color="Green" title="E90">A123</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_7"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E72">A124</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E73">A125</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E74">A126</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E75">A127</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E76">A128</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_7"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_7"><i><font color="Green" title="E75">A127</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green" title="E77">A129</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_7"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_7"><i><font color="Green" title="E74">A126</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green" title="E78">A130</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">i0</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/><a NAME="E10:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E79">A131</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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>
 <b>by </b><i><a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E80">A132</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E81">A133</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green" title="E78">A130</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_7"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green" title="E66">A45</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green" title="E73">A125</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green" title="E77">A129</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green" title="E78">A130</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_7"><i><font color="Green" title="E79">A131</font></i></a>, <a class="ref" href="goboard8.html#T5" title="GOBOARD8:th.5">GOBOARD8:5</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green" title="E82">A134</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_7"><i><font color="Green" title="E76">A128</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_7"><i><font color="Green" title="E80">A132</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_7"><i><font color="Green" title="E81">A133</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E83">A135</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E42:28_1_1_1_2"><i><font color="Green" title="E61">A40</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_7"/>
<font color="Maroon" title="c6">j1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_7"><i><font color="Green" title="E75">A127</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_7"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green" title="E84">A136</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green" title="E78">A130</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_7"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E42:28_1_1_1_2"><i><font color="Green" title="E61">A40</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green" title="E85">A137</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_7"><i><font color="Green" title="E82">A134</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_7"><i><font color="Green" title="E83">A135</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_7"><i><font color="Green" title="E84">A136</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E86">A138</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green" title="E73">A125</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E87">A139</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E88">A140</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green" title="E77">A129</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_7"><i><font color="Green" title="E78">A130</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_7"/>
<font color="Maroon" title="c5">i1</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_7"><i><font color="Green" title="E74">A126</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_7"/><b>then </b>
<font color="Maroon" title="c5">i1</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="c1">f</font></span>)</span>
 <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="E28:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E49:28_1_1_1_2"><i><font color="Green" title="E66">A45</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_7"><i><font color="Green" title="E72">A124</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green" title="E73">A125</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green" title="E77">A129</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_7"><i><font color="Green" title="E79">A131</font></i></a>, <a class="ref" href="goboard8.html#T13" title="GOBOARD8:th.13">GOBOARD8:13</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_7"/><b>then </b><i><font color="Green" title="E89">A141</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_7"><i><font color="Green" title="E85">A137</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_7"><i><font color="Green" title="E87">A139</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_7"><i><font color="Green" title="E88">A140</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_7"/><i><font color="Green" title="E90">A142</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green" title="E73">A125</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_7"><i><font color="Green" title="E77">A129</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_7"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E33:28_1_1_1_2_2_1_7"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E34:28_1_1_1_2_2_1_7"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_7"><i><font color="Green" title="E73">A125</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_7"><i><font color="Green" title="E86">A138</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2_2_1_7"><i><font color="Green" title="E89">A141</font></i></a>, <a class="txt" href="goboard9.html#E31:28_1_1_1_2_2_1_7"><i><font color="Green" title="E90">A142</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_8"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E72">A143</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E73">A144</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E74">A145</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E75">A146</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E44:28_1_1_1_2"><i><font color="Green" title="E62">A41</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green" title="E72">A143</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green" title="E74">A145</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E76">A147</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E44:28_1_1_1_2"><i><font color="Green" title="E62">A41</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green" title="E72">A143</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green" title="E73">A144</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green" title="E74">A145</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E77">A148</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E78">A149</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green" title="E72">A143</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green" title="E73">A144</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_8"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green" title="E72">A143</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green" title="E73">A144</font></i></a>, <a class="ref" href="goboard8.html#T34" title="GOBOARD8:th.34">GOBOARD8:34</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_8"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_8"/><b>then </b><i><font color="Green" title="E79">A150</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_8"><i><font color="Green" title="E75">A146</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_8"><i><font color="Green" title="E77">A148</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_8"><i><font color="Green" title="E78">A149</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_8"/><i><font color="Green" title="E80">A151</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green" title="E72">A143</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_8"><i><font color="Green" title="E73">A144</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green" title="E74">A145</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_8"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_8"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E14:28_1_1_1_2_2_1_8"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_8"><i><font color="Green" title="E72">A143</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_8"><i><font color="Green" title="E74">A145</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_8"><i><font color="Green" title="E76">A147</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_8"><i><font color="Green" title="E79">A150</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_8"><i><font color="Green" title="E80">A151</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_9"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E72">A152</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E73">A153</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E74">A154</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E75">A155</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green" title="E72">A152</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_9"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_9"><i><font color="Green" title="E74">A154</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_9"/><b>then </b><i><font color="Green" title="E76">A156</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">i0</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/><a NAME="E7:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E77">A157</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green" title="E73">A153</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E78">A158</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E79">A159</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green" title="E72">A152</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green" title="E73">A153</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_9"><i><font color="Green" title="E76">A156</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_9"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green" title="E72">A152</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green" title="E73">A153</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_9"><i><font color="Green" title="E76">A156</font></i></a>, <a class="ref" href="goboard8.html#T4" title="GOBOARD8:th.4">GOBOARD8:4</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_9"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_9"/><b>then </b><i><font color="Green" title="E80">A160</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_9"><i><font color="Green" title="E75">A155</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_9"><i><font color="Green" title="E78">A158</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_9"><i><font color="Green" title="E79">A159</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_9"/><i><font color="Green" title="E81">A161</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_9"><i><font color="Green" title="E72">A152</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_9"><i><font color="Green" title="E73">A153</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_9"><i><font color="Green" title="E76">A156</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_9"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_9"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_9"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_9"><i><font color="Green" title="E77">A157</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_9"><i><font color="Green" title="E80">A160</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_9"><i><font color="Green" title="E81">A161</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_10"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E72">A162</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E73">A163</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E74">A164</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E75">A165</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E76">A166</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green" title="E72">A162</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E77">A167</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E78">A168</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green" title="E72">A162</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green" title="E75">A165</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_10"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E44:28_1_1_1_2"><i><font color="Green" title="E62">A41</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green" title="E72">A162</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green" title="E74">A164</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green" title="E75">A165</font></i></a>, <a class="ref" href="goboard8.html#T30" title="GOBOARD8:th.30">GOBOARD8:30</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_10"/><b>then </b><i><font color="Green" title="E79">A169</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_10"><i><font color="Green" title="E76">A166</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_10"><i><font color="Green" title="E77">A167</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_10"><i><font color="Green" title="E78">A168</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E80">A170</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E81">A171</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green" title="E72">A162</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green" title="E74">A164</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green" title="E75">A165</font></i></a>, <a class="ref" href="goboard6.html#T91" title="GOBOARD6:th.91">GOBOARD6:91</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_10"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_10"/><b>then </b><i><font color="Green" title="E82">A172</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_10"><i><font color="Green" title="E79">A169</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_10"><i><font color="Green" title="E80">A170</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_10"><i><font color="Green" title="E81">A171</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E83">A173</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_10"><i><font color="Green" title="E73">A163</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E84">A174</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E85">A175</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green" title="E72">A162</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green" title="E74">A164</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green" title="E75">A165</font></i></a>, <a class="ref" href="goboard6.html#T91" title="GOBOARD6:th.91">GOBOARD6:91</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_10"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green" title="E63">A42</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_10"><i><font color="Green" title="E72">A162</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_10"><i><font color="Green" title="E73">A163</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green" title="E74">A164</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_10"><i><font color="Green" title="E75">A165</font></i></a>, <a class="ref" href="goboard8.html#T36" title="GOBOARD8:th.36">GOBOARD8:36</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_10"/><b>then </b><i><font color="Green" title="E86">A176</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_10"><i><font color="Green" title="E82">A172</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_10"><i><font color="Green" title="E84">A174</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_10"><i><font color="Green" title="E85">A175</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_10"/><i><font color="Green" title="E87">A177</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_10"><i><font color="Green" title="E73">A163</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_10"><i><font color="Green" title="E74">A164</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_10"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_10"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E25:28_1_1_1_2_2_1_10"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_10"><i><font color="Green" title="E83">A173</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_10"><i><font color="Green" title="E86">A176</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_10"><i><font color="Green" title="E87">A177</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_11"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E72">A178</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E73">A179</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E74">A180</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E75">A181</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E76">A182</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_11"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_11"><i><font color="Green" title="E74">A180</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green" title="E77">A183</font></i>: 
<font color="Maroon" title="c5">i1</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="c1">f</font></span>)</span>
 <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="E8:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E78">A184</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E79">A185</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green" title="E75">A181</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_11"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green" title="E75">A181</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green" title="E77">A183</font></i></a>, <a class="ref" href="goboard8.html#T28" title="GOBOARD8:th.28">GOBOARD8:28</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green" title="E80">A186</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_11"><i><font color="Green" title="E76">A182</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_11"><i><font color="Green" title="E78">A184</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_11"><i><font color="Green" title="E79">A185</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E81">A187</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E82">A188</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green" title="E75">A181</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green" title="E77">A183</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_11"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green" title="E83">A189</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_11"><i><font color="Green" title="E80">A186</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_11"><i><font color="Green" title="E81">A187</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_11"><i><font color="Green" title="E82">A188</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E84">A190</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green" title="E73">A179</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E85">A191</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E86">A192</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green" title="E75">A181</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green" title="E77">A183</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_11"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green" title="E63">A42</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green" title="E65">A44</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green" title="E73">A179</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green" title="E75">A181</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green" title="E77">A183</font></i></a>, <a class="ref" href="goboard8.html#T10" title="GOBOARD8:th.10">GOBOARD8:10</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_11"/><b>then </b><i><font color="Green" title="E87">A193</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_11"><i><font color="Green" title="E83">A189</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_11"><i><font color="Green" title="E85">A191</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_11"><i><font color="Green" title="E86">A192</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_11"/><i><font color="Green" title="E88">A194</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_11"><i><font color="Green" title="E72">A178</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_11"><i><font color="Green" title="E73">A179</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_11"><i><font color="Green" title="E75">A181</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_11"><i><font color="Green" title="E77">A183</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_11"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_11"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E27:28_1_1_1_2_2_1_11"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_11"><i><font color="Green" title="E84">A190</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_11"><i><font color="Green" title="E87">A193</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_11"><i><font color="Green" title="E88">A194</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_12"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E72">A195</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E73">A196</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E74">A197</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E75">A198</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E76">A199</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green" title="E72">A195</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_12"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_12"><i><font color="Green" title="E75">A198</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green" title="E77">A200</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">j0</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/><a NAME="E8:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E78">A201</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E79">A202</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green" title="E72">A195</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green" title="E77">A200</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_12"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E44:28_1_1_1_2"><i><font color="Green" title="E62">A41</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green" title="E68">A47</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green" title="E72">A195</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green" title="E73">A196</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green" title="E74">A197</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green" title="E77">A200</font></i></a>, <a class="ref" href="goboard8.html#T20" title="GOBOARD8:th.20">GOBOARD8:20</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green" title="E80">A203</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_12"><i><font color="Green" title="E76">A199</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_12"><i><font color="Green" title="E78">A201</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_12"><i><font color="Green" title="E79">A202</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E81">A204</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E82">A205</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green" title="E72">A195</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green" title="E74">A197</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green" title="E77">A200</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_12"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green" title="E83">A206</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_12"><i><font color="Green" title="E80">A203</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_12"><i><font color="Green" title="E81">A204</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_12"><i><font color="Green" title="E82">A205</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E84">A207</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green" title="E73">A196</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E85">A208</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E86">A209</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green" title="E72">A195</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green" title="E74">A197</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green" title="E77">A200</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_12"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green" title="E68">A47</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_12"><i><font color="Green" title="E72">A195</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green" title="E73">A196</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_12"><i><font color="Green" title="E77">A200</font></i></a>, <a class="ref" href="goboard8.html#T34" title="GOBOARD8:th.34">GOBOARD8:34</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_12"/><b>then </b><i><font color="Green" title="E87">A210</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_12"><i><font color="Green" title="E83">A206</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_12"><i><font color="Green" title="E85">A208</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_12"><i><font color="Green" title="E86">A209</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_12"/><i><font color="Green" title="E88">A211</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_12"><i><font color="Green" title="E73">A196</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_12"><i><font color="Green" title="E74">A197</font></i></a>, <a class="ref" href="goboard6.html#T89" title="GOBOARD6:th.89">GOBOARD6:89</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_12"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_12"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E27:28_1_1_1_2_2_1_12"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_12"><i><font color="Green" title="E84">A207</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_12"><i><font color="Green" title="E87">A210</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_12"><i><font color="Green" title="E88">A211</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_13"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E72">A212</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E73">A213</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E74">A214</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E75">A215</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E76">A216</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_13"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_13"><i><font color="Green" title="E74">A214</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green" title="E77">A217</font></i>: 
<font color="Maroon" title="c5">i1</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="c1">f</font></span>)</span>
 <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="E8:28_1_1_1_2_2_1_13"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_13"><i><font color="Green" title="E75">A215</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green" title="E78">A218</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">j0</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/><a NAME="E10:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E79">A219</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E80">A220</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green" title="E78">A218</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_13"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green" title="E65">A44</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green" title="E68">A47</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green" title="E77">A217</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green" title="E78">A218</font></i></a>, <a class="ref" href="goboard8.html#T16" title="GOBOARD8:th.16">GOBOARD8:16</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green" title="E81">A221</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_13"><i><font color="Green" title="E76">A216</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_13"><i><font color="Green" title="E79">A219</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_13"><i><font color="Green" title="E80">A220</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E82">A222</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E83">A223</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green" title="E77">A217</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green" title="E78">A218</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_13"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green" title="E84">A224</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_13"><i><font color="Green" title="E81">A221</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_13"><i><font color="Green" title="E82">A222</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_13"><i><font color="Green" title="E83">A223</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E85">A225</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E86">A226</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E87">A227</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green" title="E77">A217</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green" title="E78">A218</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_13"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green" title="E65">A44</font></i></a>, <a class="txt" href="goboard9.html#E51:28_1_1_1_2"><i><font color="Green" title="E68">A47</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green" title="E77">A217</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_13"><i><font color="Green" title="E78">A218</font></i></a>, <a class="ref" href="goboard8.html#T6" title="GOBOARD8:th.6">GOBOARD8:6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_13"/><b>then </b><i><font color="Green" title="E88">A228</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_13"><i><font color="Green" title="E84">A224</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_13"><i><font color="Green" title="E86">A226</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_13"><i><font color="Green" title="E87">A227</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_13"/><i><font color="Green" title="E89">A229</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c8">j2</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c8">j2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_13"><i><font color="Green" title="E72">A212</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_13"><i><font color="Green" title="E73">A213</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_13"><i><font color="Green" title="E77">A217</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_13"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_13"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E29:28_1_1_1_2_2_1_13"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_13"><i><font color="Green" title="E85">A225</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_13"><i><font color="Green" title="E88">A228</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_13"><i><font color="Green" title="E89">A229</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_14"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_14"/><i><font color="Green" title="E72">A230</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_14"/><i><font color="Green" title="E73">A231</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><div class="add"> <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k</font> = 
 <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="c1">f</font></span>)</span>,<font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c4">j0</font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_14"><i><font color="Green" title="E72">A230</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_14"><i><font color="Green" title="E73">A231</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>
<br/>.= 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_14"><i><font color="Green" title="E72">A230</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_14"><i><font color="Green" title="E73">A231</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_14"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_15"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E72">A232</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E73">A233</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E74">A234</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E75">A235</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E76">A236</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green" title="E72">A232</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E77">A237</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_15"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green" title="E78">A238</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E79">A239</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green" title="E75">A235</font></i></a>, <a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E80">A240</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green" title="E74">A234</font></i></a>, <a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_15"/>
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green" title="E81">A241</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E82">A242</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green" title="E72">A232</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green" title="E75">A235</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_15"><i><font color="Green" title="E79">A239</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_15"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green" title="E72">A232</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green" title="E74">A234</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green" title="E75">A235</font></i></a>, <a class="ref" href="goboard8.html#T26" title="GOBOARD8:th.26">GOBOARD8:26</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green" title="E83">A243</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_15"><i><font color="Green" title="E76">A236</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_15"><i><font color="Green" title="E77">A237</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_15"><i><font color="Green" title="E82">A242</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E84">A244</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_15"><i><font color="Green" title="E78">A238</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_15"><i><font color="Green" title="E81">A241</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E85">A245</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green" title="E72">A232</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green" title="E74">A234</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green" title="E75">A235</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_15"><i><font color="Green" title="E79">A239</font></i></a>, <a class="ref" href="goboard6.html#T90" title="GOBOARD6:th.90">GOBOARD6:90</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_15"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_15"><i><font color="Green" title="E78">A238</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_15"><i><font color="Green" title="E81">A241</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green" title="E86">A246</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_15"><i><font color="Green" title="E72">A232</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_15"><i><font color="Green" title="E83">A243</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_15"><i><font color="Green" title="E84">A244</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_15"><i><font color="Green" title="E85">A245</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E87">A247</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_15"><i><font color="Green" title="E73">A233</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E88">A248</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E89">A249</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green" title="E74">A234</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green" title="E75">A235</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_15"><i><font color="Green" title="E79">A239</font></i></a>, <a class="ref" href="goboard6.html#T90" title="GOBOARD6:th.90">GOBOARD6:90</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_15"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_15"><i><font color="Green" title="E73">A233</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green" title="E74">A234</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_15"><i><font color="Green" title="E75">A235</font></i></a>, <a class="ref" href="goboard8.html#T32" title="GOBOARD8:th.32">GOBOARD8:32</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_15"/><b>then </b><i><font color="Green" title="E90">A250</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_15"><i><font color="Green" title="E86">A246</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_15"><i><font color="Green" title="E88">A248</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_15"><i><font color="Green" title="E89">A249</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_15"/><i><font color="Green" title="E91">A251</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_15"><i><font color="Green" title="E73">A233</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_15"><i><font color="Green" title="E74">A234</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_15"><i><font color="Green" title="E80">A240</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_15"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_15"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E31:28_1_1_1_2_2_1_15"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_15"><i><font color="Green" title="E87">A247</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_15"><i><font color="Green" title="E90">A250</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_15"><i><font color="Green" title="E91">A251</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_16"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E72">A252</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E73">A253</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E74">A254</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E75">A255</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E76">A256</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green" title="E72">A252</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_16"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_16"><i><font color="Green" title="E74">A254</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green" title="E77">A257</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E78">A258</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green" title="E72">A252</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E79">A259</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_16"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green" title="E80">A260</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E81">A261</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_16"><i><font color="Green" title="E75">A255</font></i></a>, <a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_16"/>
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green" title="E82">A262</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E83">A263</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green" title="E72">A252</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_16"><i><font color="Green" title="E81">A261</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_16"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green" title="E77">A257</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_16"><i><font color="Green" title="E78">A258</font></i></a>, <a class="ref" href="goboard8.html#T25" title="GOBOARD8:th.25">GOBOARD8:25</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green" title="E84">A264</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_16"><i><font color="Green" title="E76">A256</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_16"><i><font color="Green" title="E79">A259</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_16"><i><font color="Green" title="E83">A263</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E85">A265</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_16"><i><font color="Green" title="E80">A260</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_16"><i><font color="Green" title="E82">A262</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E86">A266</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green" title="E72">A252</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green" title="E77">A257</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_16"><i><font color="Green" title="E81">A261</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_16"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_16"><i><font color="Green" title="E80">A260</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_16"><i><font color="Green" title="E82">A262</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green" title="E87">A267</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_16"><i><font color="Green" title="E72">A252</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_16"><i><font color="Green" title="E84">A264</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_16"><i><font color="Green" title="E85">A265</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_16"><i><font color="Green" title="E86">A266</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E88">A268</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_16"><i><font color="Green" title="E73">A253</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E89">A269</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,2</span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E90">A270</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green" title="E77">A257</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_16"><i><font color="Green" title="E81">A261</font></i></a>, <a class="ref" href="goboard6.html#T87" title="GOBOARD6:th.87">GOBOARD6:87</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_16"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,2</span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_16"><i><font color="Green" title="E73">A253</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_16"><i><font color="Green" title="E75">A255</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green" title="E77">A257</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_16"><i><font color="Green" title="E78">A258</font></i></a>, <a class="ref" href="goboard8.html#T7" title="GOBOARD8:th.7">GOBOARD8:7</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_16"/><b>then </b><i><font color="Green" title="E91">A271</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,2</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_16"><i><font color="Green" title="E87">A267</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_16"><i><font color="Green" title="E89">A269</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_16"><i><font color="Green" title="E90">A270</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_16"/><i><font color="Green" title="E92">A272</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,1</span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,1</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_16"><i><font color="Green" title="E73">A253</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_16"><i><font color="Green" title="E75">A255</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_16"><i><font color="Green" title="E77">A257</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_16"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_16"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E33:28_1_1_1_2_2_1_16"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_16"><i><font color="Green" title="E88">A268</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2_2_1_16"><i><font color="Green" title="E91">A271</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2_2_1_16"><i><font color="Green" title="E92">A272</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_17"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E72">A273</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E73">A274</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E74">A275</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E75">A276</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E76">A277</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_17"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_17"><i><font color="Green" title="E75">A276</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E77">A278</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E78">A279</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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> <font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green" title="E73">A274</font></i></a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E79">A280</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E80">A281</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_17"><i><font color="Green" title="E74">A275</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green" title="E77">A278</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_17"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green" title="E73">A274</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_17"><i><font color="Green" title="E74">A275</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green" title="E77">A278</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_17"><i><font color="Green" title="E78">A279</font></i></a>, <a class="ref" href="goboard8.html#T17" title="GOBOARD8:th.17">GOBOARD8:17</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E81">A282</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_17"><i><font color="Green" title="E76">A277</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_17"><i><font color="Green" title="E79">A280</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_17"><i><font color="Green" title="E80">A281</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_17"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E82">A283</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E83">A284</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_17"><i><font color="Green" title="E74">A275</font></i></a>, <a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_17"/>
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E84">A285</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E85">A286</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_17"><i><font color="Green" title="E82">A283</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E86">A287</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green" title="E77">A278</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_17"><i><font color="Green" title="E83">A284</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_17"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_17"><i><font color="Green" title="E82">A283</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_17"><i><font color="Green" title="E84">A285</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E87">A288</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_17"><i><font color="Green" title="E81">A282</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_17"><i><font color="Green" title="E85">A286</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_17"><i><font color="Green" title="E86">A287</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E88">A289</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green" title="E73">A274</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E89">A290</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E90">A291</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green" title="E77">A278</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_17"><i><font color="Green" title="E83">A284</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_17"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_17"><i><font color="Green" title="E72">A273</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green" title="E73">A274</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_17"><i><font color="Green" title="E77">A278</font></i></a>, <a class="ref" href="goboard8.html#T31" title="GOBOARD8:th.31">GOBOARD8:31</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_17"/><b>then </b><i><font color="Green" title="E91">A292</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_17"><i><font color="Green" title="E87">A288</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_17"><i><font color="Green" title="E89">A290</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_17"><i><font color="Green" title="E90">A291</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_17"/><i><font color="Green" title="E92">A293</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_17"><i><font color="Green" title="E73">A274</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_17"><i><font color="Green" title="E83">A284</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_17"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_17"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E33:28_1_1_1_2_2_1_17"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_17"><i><font color="Green" title="E88">A289</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2_2_1_17"><i><font color="Green" title="E91">A292</font></i></a>, <a class="txt" href="goboard9.html#E30:28_1_1_1_2_2_1_17"><i><font color="Green" title="E92">A293</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_18"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E72">A294</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E73">A295</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E74">A296</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E75">A297</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E76">A298</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="ref" href="goboard5.html#T30" title="GOBOARD5:th.30">GOBOARD5:30</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_18"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_18"><i><font color="Green" title="E75">A297</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E77">A299</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_18"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_18"><i><font color="Green" title="E74">A296</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E78">A300</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E79">A301</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E80">A302</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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> <font color="Maroon" title="c8">j2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green" title="E73">A295</font></i></a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E81">A303</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E82">A304</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green" title="E77">A299</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_18"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green" title="E73">A295</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green" title="E77">A299</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green" title="E78">A300</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_18"><i><font color="Green" title="E79">A301</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_18"><i><font color="Green" title="E80">A302</font></i></a>, <a class="ref" href="goboard8.html#T12" title="GOBOARD8:th.12">GOBOARD8:12</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E83">A305</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_18"><i><font color="Green" title="E76">A298</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_18"><i><font color="Green" title="E81">A303</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_18"><i><font color="Green" title="E82">A304</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_18"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E84">A306</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_18"/>
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E85">A307</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E86">A308</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_18"><i><font color="Green" title="E84">A306</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E87">A309</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green" title="E77">A299</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green" title="E78">A300</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_18"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_18"><i><font color="Green" title="E84">A306</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_18"><i><font color="Green" title="E85">A307</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E88">A310</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_18"><i><font color="Green" title="E83">A305</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_18"><i><font color="Green" title="E86">A308</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_18"><i><font color="Green" title="E87">A309</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E89">A311</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green" title="E73">A295</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E90">A312</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E91">A313</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_18"><i><font color="Green" title="E72">A294</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green" title="E77">A299</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green" title="E78">A300</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_18"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green" title="E73">A295</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_18"><i><font color="Green" title="E77">A299</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green" title="E78">A300</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_18"><i><font color="Green" title="E79">A301</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_18"><i><font color="Green" title="E80">A302</font></i></a>, <a class="ref" href="goboard8.html#T2" title="GOBOARD8:th.2">GOBOARD8:2</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_18"/><b>then </b><i><font color="Green" title="E92">A314</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_18"><i><font color="Green" title="E88">A310</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_18"><i><font color="Green" title="E90">A312</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_18"><i><font color="Green" title="E91">A313</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E32:28_1_1_1_2_2_1_18"/><i><font color="Green" title="E93">A315</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_18"><i><font color="Green" title="E73">A295</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_18"><i><font color="Green" title="E78">A300</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E33:28_1_1_1_2_2_1_18"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E34:28_1_1_1_2_2_1_18"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E35:28_1_1_1_2_2_1_18"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_18"><i><font color="Green" title="E89">A311</font></i></a>, <a class="txt" href="goboard9.html#E31:28_1_1_1_2_2_1_18"><i><font color="Green" title="E92">A314</font></i></a>, <a class="txt" href="goboard9.html#E32:28_1_1_1_2_2_1_18"><i><font color="Green" title="E93">A315</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_19"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_19"/><i><font color="Green" title="E72">A316</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_19"/><i><font color="Green" title="E73">A317</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 ;<br/><div class="add"> <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k</font> = 
 <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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_19"><i><font color="Green" title="E72">A316</font></i></a>, <a class="ref" href="goboard5.html#T31" title="GOBOARD5:th.31">GOBOARD5:31</a></i>
<br/>.= 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_19"><i><font color="Green" title="E72">A316</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_19"><i><font color="Green" title="E73">A317</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_19"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_20"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E72">A318</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E73">A319</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E74">A320</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E75">A321</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green" title="E63">A42</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green" title="E72">A318</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_20"><i><font color="Green" title="E74">A320</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E76">A322</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E46:28_1_1_1_2"><i><font color="Green" title="E63">A42</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green" title="E72">A318</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_20"><i><font color="Green" title="E73">A319</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_20"><i><font color="Green" title="E74">A320</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E77">A323</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E78">A324</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green" title="E72">A318</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_20"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green" title="E65">A44</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_20"><i><font color="Green" title="E72">A318</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_20"><i><font color="Green" title="E73">A319</font></i></a>, <a class="ref" href="goboard8.html#T28" title="GOBOARD8:th.28">GOBOARD8:28</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_20"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_20"/><b>then </b><i><font color="Green" title="E79">A325</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_20"><i><font color="Green" title="E75">A321</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_20"><i><font color="Green" title="E77">A323</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_20"><i><font color="Green" title="E78">A324</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_20"/><i><font color="Green" title="E80">A326</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p0">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<span class="p2">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_20"><i><font color="Green" title="E73">A319</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_20"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_20"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E14:28_1_1_1_2_2_1_20"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_20"><i><font color="Green" title="E76">A322</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_20"><i><font color="Green" title="E79">A325</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_20"><i><font color="Green" title="E80">A326</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_21"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E72">A327</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E73">A328</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E74">A329</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E75">A330</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green" title="E72">A327</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_21"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_21"><i><font color="Green" title="E74">A329</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_21"/><b>then </b><i><font color="Green" title="E76">A331</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">j0</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/><a NAME="E7:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E77">A332</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_21"><i><font color="Green" title="E73">A328</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E78">A333</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E79">A334</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green" title="E72">A327</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_21"><i><font color="Green" title="E76">A331</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_21"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E48:28_1_1_1_2"><i><font color="Green" title="E65">A44</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green" title="E72">A327</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_21"><i><font color="Green" title="E73">A328</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_21"><i><font color="Green" title="E76">A331</font></i></a>, <a class="ref" href="goboard8.html#T14" title="GOBOARD8:th.14">GOBOARD8:14</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_21"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_21"/><b>then </b><i><font color="Green" title="E80">A335</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_21"><i><font color="Green" title="E75">A330</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_21"><i><font color="Green" title="E78">A333</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_21"><i><font color="Green" title="E79">A334</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_21"/><i><font color="Green" title="E81">A336</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_21"><i><font color="Green" title="E72">A327</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_21"><i><font color="Green" title="E73">A328</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_21"><i><font color="Green" title="E76">A331</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_21"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_21"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_21"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_21"><i><font color="Green" title="E77">A332</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_21"><i><font color="Green" title="E80">A335</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_21"><i><font color="Green" title="E81">A336</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_22"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_22"/><i><font color="Green" title="E72">A337</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_22"/><i><font color="Green" title="E73">A338</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 ;<br/><div class="add"> <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">k</font> = 
 <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="c1">f</font></span>)</span>,<font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E40:28_1_1_1_2"><i><font color="Green" title="E60">A39</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_22"><i><font color="Green" title="E72">A337</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>
<br/>.= 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_22"><i><font color="Green" title="E72">A337</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_22"><i><font color="Green" title="E73">A338</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>
;<br/><b>hence </b><a NAME="E4:28_1_1_1_2_2_1_22"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_23"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E72">A339</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E73">A340</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E74">A341</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E75">A342</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E76">A343</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E77">A344</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_23"><i><font color="Green" title="E74">A341</font></i></a>, <a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E78">A345</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E79">A346</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E80">A347</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_23"><i><font color="Green" title="E77">A344</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_23"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green" title="E75">A342</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_23"><i><font color="Green" title="E78">A345</font></i></a>, <a class="ref" href="goboard8.html#T33" title="GOBOARD8:th.33">GOBOARD8:33</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green" title="E81">A348</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_23"><i><font color="Green" title="E76">A343</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_23"><i><font color="Green" title="E79">A346</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_23"><i><font color="Green" title="E80">A347</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_23"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green" title="E82">A349</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green" title="E83">A350</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E84">A351</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green" title="E75">A342</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_23"><i><font color="Green" title="E77">A344</font></i></a>, <a class="ref" href="goboard6.html#T92" title="GOBOARD6:th.92">GOBOARD6:92</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_23"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_23"><i><font color="Green" title="E82">A349</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green" title="E85">A352</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_23"><i><font color="Green" title="E81">A348</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_23"><i><font color="Green" title="E83">A350</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_23"><i><font color="Green" title="E84">A351</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E86">A353</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_23"><i><font color="Green" title="E73">A340</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E87">A354</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E88">A355</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green" title="E75">A342</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_23"><i><font color="Green" title="E77">A344</font></i></a>, <a class="ref" href="goboard6.html#T92" title="GOBOARD6:th.92">GOBOARD6:92</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_23"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green" title="E75">A342</font></i></a>, <a class="ref" href="goboard8.html#T29" title="GOBOARD8:th.29">GOBOARD8:29</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_23"/><b>then </b><i><font color="Green" title="E89">A356</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_23"><i><font color="Green" title="E85">A352</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_23"><i><font color="Green" title="E87">A354</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_23"><i><font color="Green" title="E88">A355</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_23"/><i><font color="Green" title="E90">A357</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"><span class="p3">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_23"><i><font color="Green" title="E72">A339</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_23"><i><font color="Green" title="E73">A340</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_23"><i><font color="Green" title="E74">A341</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_23"><i><font color="Green" title="E75">A342</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_23"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_23"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E29:28_1_1_1_2_2_1_23"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_23"><i><font color="Green" title="E86">A353</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_23"><i><font color="Green" title="E89">A356</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_23"><i><font color="Green" title="E90">A357</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_24"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E72">A358</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E73">A359</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E74">A360</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E75">A361</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E76">A362</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_24"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_24"><i><font color="Green" title="E74">A360</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green" title="E77">A363</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E78">A364</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E79">A365</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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> <font color="Maroon" title="c7">i2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_24"><i><font color="Green" title="E73">A359</font></i></a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E80">A366</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E81">A367</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green" title="E77">A363</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_24"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green" title="E75">A361</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green" title="E77">A363</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_24"><i><font color="Green" title="E78">A364</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_24"><i><font color="Green" title="E79">A365</font></i></a>, <a class="ref" href="goboard8.html#T9" title="GOBOARD8:th.9">GOBOARD8:9</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green" title="E82">A368</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_24"><i><font color="Green" title="E76">A362</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_24"><i><font color="Green" title="E80">A366</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_24"><i><font color="Green" title="E81">A367</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_24"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green" title="E83">A369</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green" title="E84">A370</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E85">A371</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green" title="E75">A361</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green" title="E77">A363</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_24"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_24"><i><font color="Green" title="E83">A369</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green" title="E86">A372</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E14:28_1_1_1_2_2_1_24"><i><font color="Green" title="E82">A368</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_24"><i><font color="Green" title="E84">A370</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_24"><i><font color="Green" title="E85">A371</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E87">A373</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_24"><i><font color="Green" title="E73">A359</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E88">A374</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E89">A375</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green" title="E75">A361</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green" title="E77">A363</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_24"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_24"><i><font color="Green" title="E72">A358</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green" title="E75">A361</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_24"><i><font color="Green" title="E77">A363</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_24"><i><font color="Green" title="E79">A365</font></i></a>, <a class="ref" href="goboard8.html#T28" title="GOBOARD8:th.28">GOBOARD8:28</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_24"/><b>then </b><i><font color="Green" title="E90">A376</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_24"><i><font color="Green" title="E86">A372</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_24"><i><font color="Green" title="E88">A374</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_24"><i><font color="Green" title="E89">A375</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_24"/><i><font color="Green" title="E91">A377</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_24"><i><font color="Green" title="E73">A359</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_24"><i><font color="Green" title="E75">A361</font></i></a>, <a class="ref" href="goboard6.html#T86" title="GOBOARD6:th.86">GOBOARD6:86</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_24"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_24"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E31:28_1_1_1_2_2_1_24"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_24"><i><font color="Green" title="E87">A373</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_24"><i><font color="Green" title="E90">A376</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_24"><i><font color="Green" title="E91">A377</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_25"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E72">A378</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E73">A379</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E74">A380</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E75">A381</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E76">A382</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_25"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_25"><i><font color="Green" title="E75">A381</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green" title="E77">A383</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c6">j1</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/><a NAME="E8:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E78">A384</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green" title="E74">A380</font></i></a>, <a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E79">A385</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E80">A386</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green" title="E74">A380</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_25"><i><font color="Green" title="E78">A384</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_25"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green" title="E67">A46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green" title="E74">A380</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green" title="E77">A383</font></i></a>, <a class="ref" href="goboard8.html#T31" title="GOBOARD8:th.31">GOBOARD8:31</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green" title="E81">A387</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_25"><i><font color="Green" title="E76">A382</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_25"><i><font color="Green" title="E79">A385</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_25"><i><font color="Green" title="E80">A386</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_25"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green" title="E82">A388</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green" title="E83">A389</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E84">A390</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green" title="E74">A380</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green" title="E77">A383</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_25"><i><font color="Green" title="E78">A384</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_25"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_25"><i><font color="Green" title="E82">A388</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green" title="E85">A391</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_25"><i><font color="Green" title="E81">A387</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2_2_1_25"><i><font color="Green" title="E83">A389</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_25"><i><font color="Green" title="E84">A390</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E86">A392</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_25"><i><font color="Green" title="E73">A379</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E87">A393</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E88">A394</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green" title="E74">A380</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green" title="E77">A383</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_25"><i><font color="Green" title="E78">A384</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_25"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_25"><i><font color="Green" title="E73">A379</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_25"><i><font color="Green" title="E74">A380</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green" title="E77">A383</font></i></a>, <a class="ref" href="goboard8.html#T18" title="GOBOARD8:th.18">GOBOARD8:18</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_25"/><b>then </b><i><font color="Green" title="E89">A395</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2_2_1_25"><i><font color="Green" title="E85">A391</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_25"><i><font color="Green" title="E87">A393</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_25"><i><font color="Green" title="E88">A394</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_25"/><i><font color="Green" title="E90">A396</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_25"><i><font color="Green" title="E72">A378</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_25"><i><font color="Green" title="E73">A379</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_25"><i><font color="Green" title="E77">A383</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_25"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_25"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E30:28_1_1_1_2_2_1_25"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2_2_1_25"><i><font color="Green" title="E86">A392</font></i></a>, <a class="txt" href="goboard9.html#E26:28_1_1_1_2_2_1_25"><i><font color="Green" title="E89">A395</font></i></a>, <a class="txt" href="goboard9.html#E27:28_1_1_1_2_2_1_25"><i><font color="Green" title="E90">A396</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_26"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E72">A397</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E73">A398</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">i2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E74">A399</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E4:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E75">A400</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="c1">f</font></span>)</span>
 ;<br/><div class="add"><a NAME="E5:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E76">A401</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_26"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_26"><i><font color="Green" title="E74">A399</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E77">A402</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_26"/>
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_26"><i><font color="Green" title="E75">A400</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E78">A403</font></i>: 
 <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="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c6">j1</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/><a NAME="E10:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E79">A404</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <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> <font color="Maroon" title="c7">i2</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_26"><i><font color="Green" title="E73">A398</font></i></a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E80">A405</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E81">A406</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green" title="E77">A402</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_26"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green" title="E67">A46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green" title="E77">A402</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green" title="E78">A403</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_26"><i><font color="Green" title="E79">A404</font></i></a>, <a class="ref" href="goboard8.html#T3" title="GOBOARD8:th.3">GOBOARD8:3</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E82">A407</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_26"><i><font color="Green" title="E76">A401</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_26"><i><font color="Green" title="E80">A405</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_26"><i><font color="Green" title="E81">A406</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E16:28_1_1_1_2_2_1_26"/>
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">i1</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52" title="BINARITH:th.52">BINARITH:52</a></i>;<br/><a NAME="E17:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E83">A408</font></i>: 
<font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E18:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E84">A409</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="ref" href="goboard9.html#T21" target="_self" title="GOBOARD9:th.21">Th21</a></i>;<br/><a NAME="E19:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E85">A410</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green" title="E77">A402</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green" title="E78">A403</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E20:28_1_1_1_2_2_1_26"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2_2_1_26"><i><font color="Green" title="E83">A408</font></i></a>, <a class="ref" href="goboard7.html#T14" title="GOBOARD7:th.14">GOBOARD7:14</a></i>;<br/><a NAME="E21:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E22:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E86">A411</font></i>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E15:28_1_1_1_2_2_1_26"><i><font color="Green" title="E82">A407</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2_2_1_26"><i><font color="Green" title="E84">A409</font></i></a>, <a class="txt" href="goboard9.html#E19:28_1_1_1_2_2_1_26"><i><font color="Green" title="E85">A410</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E23:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E87">A412</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_26"><i><font color="Green" title="E73">A398</font></i></a>, <a class="ref" href="goboard5.html#T29" title="GOBOARD5:th.29">GOBOARD5:29</a></i>;<br/><a NAME="E24:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E88">A413</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E25:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E89">A414</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green" title="E77">A402</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green" title="E78">A403</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E26:28_1_1_1_2_2_1_26"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green" title="E67">A46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_26"><i><font color="Green" title="E72">A397</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_26"><i><font color="Green" title="E77">A402</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green" title="E78">A403</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_26"><i><font color="Green" title="E79">A404</font></i></a>, <a class="ref" href="goboard8.html#T15" title="GOBOARD8:th.15">GOBOARD8:15</a></i>;<br/><a NAME="E27:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E28:28_1_1_1_2_2_1_26"/><b>then </b><i><font color="Green" title="E90">A415</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2_2_1_26"><i><font color="Green" title="E86">A411</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2_2_1_26"><i><font color="Green" title="E88">A413</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2_2_1_26"><i><font color="Green" title="E89">A414</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/><a NAME="E29:28_1_1_1_2_2_1_26"/><i><font color="Green" title="E91">A416</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c7">i2</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<font color="Maroon" title="c5">i1</font>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E20:28_1_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_26"><i><font color="Green" title="E73">A398</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_26"><i><font color="Green" title="E78">A403</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E30:28_1_1_1_2_2_1_26"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E31:28_1_1_1_2_2_1_26"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E32:28_1_1_1_2_2_1_26"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2_2_1_26"><i><font color="Green" title="E87">A412</font></i></a>, <a class="txt" href="goboard9.html#E28:28_1_1_1_2_2_1_26"><i><font color="Green" title="E90">A415</font></i></a>, <a class="txt" href="goboard9.html#E29:28_1_1_1_2_2_1_26"><i><font color="Green" title="E91">A416</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_27"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E72">A417</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E73">A418</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E74">A419</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E75">A420</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E54:28_1_1_1_2"><i><font color="Green" title="E71">A50</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green" title="E72">A417</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_27"><i><font color="Green" title="E74">A419</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E76">A421</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E54:28_1_1_1_2"><i><font color="Green" title="E71">A50</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green" title="E72">A417</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_27"><i><font color="Green" title="E73">A418</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_27"><i><font color="Green" title="E74">A419</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E77">A422</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E78">A423</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c4">j0</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green" title="E72">A417</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_27"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green" title="E67">A46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_27"><i><font color="Green" title="E72">A417</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_27"><i><font color="Green" title="E73">A418</font></i></a>, <a class="ref" href="goboard8.html#T31" title="GOBOARD8:th.31">GOBOARD8:31</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_27"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_27"/><b>then </b><i><font color="Green" title="E79">A424</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_27"><i><font color="Green" title="E75">A420</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_27"><i><font color="Green" title="E77">A422</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_27"><i><font color="Green" title="E78">A423</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_27"/><i><font color="Green" title="E80">A425</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K20" title="EUCLID:func.20">-</a> <span class="p2"><a href="euclid.html#K23" title="EUCLID:func.23">|[</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="euclid.html#K23" title="EUCLID:func.23">]|</a></span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_27"><i><font color="Green" title="E73">A418</font></i></a>, <a class="ref" href="goboard6.html#T88" title="GOBOARD6:th.88">GOBOARD6:88</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_27"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_27"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E14:28_1_1_1_2_2_1_27"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E5:28_1_1_1_2_2_1_27"><i><font color="Green" title="E76">A421</font></i></a>, <a class="txt" href="goboard9.html#E10:28_1_1_1_2_2_1_27"><i><font color="Green" title="E79">A424</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2_2_1_27"><i><font color="Green" title="E80">A425</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1_1_2_2_1_28"><b>suppose </b></a><b>that </b><a NAME="E1:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E72">A426</font></i>: 
<font color="Maroon" title="c4">j0</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">j1</font>
 <b>and </b><br/><a NAME="E2:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E73">A427</font></i>: 
<font color="Maroon" title="c6">j1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">j2</font>
 <b>and </b><br/><a NAME="E3:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E74">A428</font></i>: 
<font color="Maroon" title="c3">i0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><div class="add"><a NAME="E4:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E75">A429</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2"><i><font color="Green" title="E35">A10</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green" title="E72">A426</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E5:28_1_1_1_2_2_1_28"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">i0</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E3:28_1_1_1_2_2_1_28"><i><font color="Green" title="E74">A428</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E6:28_1_1_1_2_2_1_28"/><b>then </b><i><font color="Green" title="E76">A430</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green" title="E72">A426</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E7:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E77">A431</font></i>: 
 <a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">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>  <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="c1">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E11:28_1_1_1_2"><i><font color="Green" title="E38">A13</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E16:28_1_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_28"><i><font color="Green" title="E73">A427</font></i></a>, <a class="ref" href="goboard5.html#T28" title="GOBOARD5:th.28">GOBOARD5:28</a></i>;<br/><a NAME="E8:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E78">A432</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="goboard9.html#T8" target="_self" title="GOBOARD9:th.8">Th8</a></i>;<br/><a NAME="E9:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E79">A433</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E19:28_1_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green" title="E72">A426</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_28"><i><font color="Green" title="E76">A430</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E10:28_1_1_1_2_2_1_28"/>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2"><i><font color="Green" title="E36">A11</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="txt" href="goboard9.html#E17:28_1_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E21:28_1_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E25:28_1_1_1_2"><i><font color="Green" title="E50">A25</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E47:28_1_1_1_2"><i><font color="Green" title="E64">A43</font></i></a>, <a class="txt" href="goboard9.html#E50:28_1_1_1_2"><i><font color="Green" title="E67">A46</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green" title="E72">A426</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_28"><i><font color="Green" title="E73">A427</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_28"><i><font color="Green" title="E76">A430</font></i></a>, <a class="ref" href="goboard8.html#T1" title="GOBOARD8:th.1">GOBOARD8:1</a></i>;<br/><a NAME="E11:28_1_1_1_2_2_1_28"/><b>then </b>
 <a href="topreal1.html#K3" title="TOPREAL1:func.3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><a NAME="E12:28_1_1_1_2_2_1_28"/><b>then </b><i><font color="Green" title="E80">A434</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E4:28_1_1_1_2_2_1_28"><i><font color="Green" title="E75">A429</font></i></a>, <a class="txt" href="goboard9.html#E8:28_1_1_1_2_2_1_28"><i><font color="Green" title="E78">A432</font></i></a>, <a class="txt" href="goboard9.html#E9:28_1_1_1_2_2_1_28"><i><font color="Green" title="E79">A433</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E13:28_1_1_1_2_2_1_28"/><i><font color="Green" title="E81">A435</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">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c4">j0</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c6">j1</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> 2</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c3">i0</font>,<font color="Maroon" title="c8">j2</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p2">(<span class="default"><a href="goboard2.html#K3" title="GOBOARD2:func.3">GoB</a> <font color="Maroon" title="c1">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">i0</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>,<font color="Maroon" title="c6">j1</font></span>)</span>
 <b>by </b><i><a class="txt" href="goboard9.html#E18:28_1_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="goboard9.html#E22:28_1_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="goboard9.html#E23:28_1_1_1_2"><i><font color="Green" title="E48">A23</font></i></a>, <a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E38:28_1_1_1_2"><i><font color="Green" title="E59">A38</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green" title="E72">A426</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1_1_2_2_1_28"><i><font color="Green" title="E73">A427</font></i></a>, <a class="txt" href="goboard9.html#E6:28_1_1_1_2_2_1_28"><i><font color="Green" title="E76">A430</font></i></a>, <a class="ref" href="goboard6.html#T85" title="GOBOARD6:th.85">GOBOARD6:85</a></i>;<br/><a NAME="E14:28_1_1_1_2_2_1_28"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E1:28_1_1"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="goboard9.html#E2:28_1_1"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="goboard8.html#T37" title="GOBOARD8:th.37">GOBOARD8:37</a></i>;<br/><a NAME="E15:28_1_1_1_2_2_1_28"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T43" title="SUBSET_1:th.43">SUBSET_1:43</a></i>;<br/><b>hence </b><a NAME="E16:28_1_1_1_2_2_1_28"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="goboard9.html#E24:28_1_1_1_2"><i><font color="Green" title="E49">A24</font></i></a>, <a class="txt" href="goboard9.html#E52:28_1_1_1_2"><i><font color="Green" title="E69">A48</font></i></a>, <a class="txt" href="goboard9.html#E53:28_1_1_1_2"><i><font color="Green" title="E70">A49</font></i></a>, <a class="txt" href="goboard9.html#E1:28_1_1_1_2_2_1_28"><i><font color="Green" title="E72">A426</font></i></a>, <a class="txt" href="goboard9.html#E7:28_1_1_1_2_2_1_28"><i><font color="Green" title="E77">A431</font></i></a>, <a class="txt" href="goboard9.html#E12:28_1_1_1_2_2_1_28"><i><font color="Green" title="E80">A434</font></i></a>, <a class="txt" href="goboard9.html#E13:28_1_1_1_2_2_1_28"><i><font color="Green" title="E81">A435</font></i></a>, <a class="ref" href="goboard9.html#T6" target="_self" title="GOBOARD9:th.6">Th6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E56:28_1_1_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#K5" title="GOBOARD5:func.5">left_cell</a> <font color="Maroon" title="c1">f</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard9.html#K2" title="GOBOARD9:func.2">LeftComp</a> <font color="Maroon" title="c1">f</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div>
<b>thus </b><a NAME="E3:28"/>
for <font color="Olive" title="b1">k</font> being   <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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 <b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="goboard9.html#E1:28"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="goboard9.html#E2:28"><i><font color="Green" title="E27">A2</font></i></a>);</i><br/>


</div>
