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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>  st <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b1">G</font></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> holds <br/>(  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Olive" title="b1">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Olive" title="b1">G</font>,<font color="Maroon" title="c3">k</font>) &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Olive" title="b1">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Olive" title="b1">G</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">G</font> be   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font></span>)</span> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> implies (  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>) &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font></span>)</span> ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">N</font> =  <a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>);<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:20"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">and </span><br/><a NAME="E3:20"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E4:20"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font>
 <span class="kw">and </span><br/><a NAME="E5:20"/><span class="lab"><font color="Green" title="E23">A5</font></span>: 
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>) &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font></span>)</span> )</span><br/>

<a NAME="E6:20"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="goboard1.html#T10" target="_self" title="GOBOARD1:th.10">Th26</a></span>;<br/>
<a NAME="E7:20"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="seqm_3.html#T43" title="SEQM_3:th.43">SEQM_3:43</a></span>;<br/>
<a NAME="E8:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A8</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <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="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="goboard1.html#D8" target="_self" title="GOBOARD1:def.8">Def10</a></span>;<br/>
<a NAME="E9:20"/>
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E10:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A9</font></span>: 
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E11:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A10</font></span>: 
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<a NAME="E12:20"/><span class="lab"><font color="Green" title="E29">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <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="c4">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>;<br/>
<a NAME="E13:20"/><span class="lab"><font color="Green" title="E30">A12</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p2">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>;<br/>
<a NAME="E14:20"/><span class="lab"><font color="Green" title="E31">A13</font></span>: 
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E15:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A14</font></span>: 
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j</font> &amp; <font color="Maroon" title="c6">j</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="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p2">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p2">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> )</span><br/><a NAME="E1:20_1"/><span class="lab"><font color="Green" title="E33">A15</font></span>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">G</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/><span class="kw">assume </span><a NAME="E2:20_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">j</font> &amp; <font color="Maroon" title="c6">j</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="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p2">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p2">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font></span><br/><a NAME="E3:20_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A16</font></span>: 
<font color="Maroon" title="c6">j</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> <span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p2">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> = 
<span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c3">k</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> (<span class="p2">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c6">j</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E15:20"><span class="lab"><font color="Green" title="E32">A14</font></span></a>, <a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E3:20_1"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="ref" href="goboard1.html#T12" target="_self" title="GOBOARD1:th.12">Th28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c6">j</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="finseq_3.html#T110" title="FINSEQ_3:th.110">FINSEQ_3:110</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:20"><span class="lab"><font color="Green" title="E28">A10</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="txt" href="#E3:20_1"><span class="lab"><font color="Green" title="E34">A16</font></span></a>, <a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E33">A15</font></span></a>, <a class="ref" href="goboard1.html#T2" target="_self" title="GOBOARD1:th.2">Th17</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E17:20"/>
(  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<span class="p1">(<span class="default"><a href="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span>,<font color="Maroon" title="c3">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c3">k</font>) &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <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="goboard1.html#K3" title="GOBOARD1:func.3">DelCol</a> (<font color="Maroon" title="c4">G</font>,<font color="Maroon" title="c1">i</font>)</span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c4">G</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E27">A9</font></span></a>, <a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E31">A13</font></span></a>, <a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E30">A12</font></span></a>, <a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E29">A11</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E26">A8</font></span></a>, <a class="ref" href="finseq_1.html#T1" title="FINSEQ_1:th.1">FINSEQ_1:1</a>, <a class="ref" href="finseq_1.html#T14" title="FINSEQ_1:th.14">FINSEQ_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
