<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th51</font></span>: <a NAME="T51"><span class="comment"><font color="firebrick">:: SPPOL_2:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="b2">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>  st <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font> <a href="sppol_2.html#R1" title="SPPOL_2:pred.1">split</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b4">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b4">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">p1</font> holds <br/><font color="Olive" title="b2">p1</font>,<font color="Olive" title="b4">q</font> <a href="sppol_2.html#R1" title="SPPOL_2:pred.1">split</a> <font color="Olive" title="b1">P</font></div></div>
