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<div><span class="kw">theorem </span><a NAME="T32"><span class="comment"><font color="firebrick">:: CONNSP_3:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">GX</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">GX</font><br/>  for <font color="Olive" title="b3">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b2">B</font></span>)</span>  st <font color="Olive" title="b3">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font> holds <br/> <a href="connsp_3.html#K4" title="CONNSP_3:func.4">Down</a> (<span class="p1">(<span class="default"><a href="connsp_3.html#K5" title="CONNSP_3:func.5">Up</a> <font color="Olive" title="b3">V</font></span>)</span>,<font color="Olive" title="b2">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">V</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" onmouseover="rs('xboole_1/T28')" onmouseout="rh()">XBOOLE_1:28</a></span>;<br/></div></div>
