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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">G</font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/>







<b>set </b><font color="Maroon">N</font> =  <a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>;<br/>
<b>assume </b><a NAME="E1:33"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font></span>)</span> &amp;  <a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> )
 ;<br/>

<a NAME="E2:33"/><b>then </b><i><font color="Green">E40</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:33"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:33"/><b>then </b><i><font color="Green">E41</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font></span>)</span> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E6:33"/><i><font color="Green">E43</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <span class="p2">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">G</font>,<font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#D9">MATRIX_1:def 9</a></i>;<br/>
<a NAME="E7:33"/><i><font color="Green">E44</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:33"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:33_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <span class="p2">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">k</font></span>)</span> )
 ;<br/><a NAME="E2:33_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:33_1"/><i><font color="Green">E49</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:33_1"/><i><font color="Green">E50</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <font color="Maroon">G</font>,<font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="matrix_1.html#D8">MATRIX_1:def 8</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <span class="p2">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <font color="Maroon">j</font>,<font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="matrix_1.html#D9">MATRIX_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_3.html#K2">Del</a> <span class="p2">(<span class="default"><a href="matrix_1.html#K8">Line</a> <font color="Maroon">G</font>,<font color="Maroon">j</font></span>)</span>,<font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, , , , , , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K8">Line</a> <font color="Maroon">G</font>,<font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, , <a class="ref" href="finseq_3.html#T119">FINSEQ_3:119</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrix_1.html#K9">Col</a> <font color="Maroon">G</font>,<font color="Maroon">k</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , , , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:33"/>
(  <a href="matrix_1.html#K9">Col</a> <span class="p1">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K9">Col</a> <font color="Maroon">G</font>,<font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <span class="p2">(<span class="default"><a href="goboard1.html#K4" target="_self">DelCol</a> <font color="Maroon">G</font>,<font color="Maroon">i</font></span>)</span></span>)</span> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font></span>)</span> )
 <b>by </b><i>, , , , , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>


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