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<b>let </b><font color="Maroon">G</font> be   <a href="goboard1.html#NM1">Go-board</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>, <font color="Maroon">g</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<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>assume </b><b>that </b><br/><a NAME="E1:53"/><i><font color="Green">E38</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E2:53"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E3:53"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">f</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">g</font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">G</font>
 ;<br/>

<a NAME="E4:53"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">g</font></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:53"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E6:53"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="topreal8.html#T7">TOPREAL8:7</a></i>;<br/>
<a NAME="E7:53"/><b>then </b>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E8:53"/>
(  <a href="gobrd13.html#K4">left_cell</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">k</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="gobrd13.html#K4">left_cell</a> <font color="Maroon">f</font>,<font color="Maroon">k</font>,<font color="Maroon">G</font> &amp;  <a href="gobrd13.html#K3">right_cell</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">k</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="gobrd13.html#K3">right_cell</a> <font color="Maroon">f</font>,<font color="Maroon">k</font>,<font color="Maroon">G</font> )
 <b>by </b><i>, , , , <a class="ref" href="gobrd13.html#T32">GOBRD13:32</a></i>;<br/>


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