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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>;<br/><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> , <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><b>that </b><br/><a NAME="E1:32"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f</font> <a href="goboard1.html#R1">is_sequence_on</a> <font color="Maroon">G</font> &amp; <font color="Maroon">f</font> is <a href="topreal1.html#V1">special</a> )
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <font color="Maroon">G</font> )
 ;<br/>

<a NAME="E3:32"/><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="subset_1.html#T32">SUBSET_1:32</a></i>;<br/>
<a NAME="E4:32"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E5:32"/><i><font color="Green">E45</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i>, <a class="ref" href="goboard9.html#T21">GOBOARD9:21</a></i>;<br/>
<a NAME="E6:32"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , <a class="ref" href="jordan9.html#T16">JORDAN9:16</a></i>;<br/>
<a NAME="E7:32"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E8:32"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/>
<a NAME="E9:32"/><b>then </b><i><font color="Green">E54</font></i>: 
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E10:32"/>
<span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="gobrd11.html#T35">GOBRD11:35</a></i>;<br/>
<b>hence </b><a NAME="E11:32"/>
<span class="p1">(<span class="default"><a href="goboard5.html#K3">cell</a> <font color="Maroon">G</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <font color="Maroon">f</font></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i>, , <a class="ref" href="connsp_1.html#T19">CONNSP_1:19</a></i>;<br/>


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