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<div><span class="kw">theorem </span><a NAME="T48"><span class="comment"><font color="firebrick">:: JORDAN1J:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a><br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">k</font> &amp; <font color="Olive" title="b4">k</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="b2">f</font> &amp; <font color="Olive" title="b2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">g</font> <a href="goboard1.html#R1" title="GOBOARD1:pred.1">is_sequence_on</a> <font color="Olive" title="b1">G</font> holds <br/>(  <a href="gobrd13.html#K2" title="GOBRD13:func.2">left_cell</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">g</font></span>)</span>,<font color="Olive" title="b4">k</font>,<font color="Olive" title="b1">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gobrd13.html#K2" title="GOBRD13:func.2">left_cell</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b4">k</font>,<font color="Olive" title="b1">G</font>) &amp;  <a href="gobrd13.html#K1" title="GOBRD13:func.1">right_cell</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">g</font></span>)</span>,<font color="Olive" title="b4">k</font>,<font color="Olive" title="b1">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gobrd13.html#K1" title="GOBRD13:func.1">right_cell</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b4">k</font>,<font color="Olive" title="b1">G</font>) )</div></div>
