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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E2">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: GOBRD14:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">G</font> being   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</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> <font color="Olive" title="b3">G</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <font color="Olive" title="b3">G</font> holds <br/> <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<font color="Olive" title="b3">G</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default">(1,2) <a href="funct_4.html#K7" title="FUNCT_4:func.7">--&gt;</a> (<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b3">G</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Olive" title="b1">i</font>,1)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b3">G</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p5">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,1)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a></span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>,<span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b3">G</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,<font color="Olive" title="b2">j</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b3">G</font> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,<span class="p5">(<span class="default"><font color="Olive" title="b2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a></span>)</span></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>)</span>)</span></div></div>
