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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: OPENLATT:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</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">p</font>, <font color="Olive" title="b3">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <font color="Olive" title="b1">T</font></span>)</span><br/>  for <font color="Olive" title="b4">p9</font>, <font color="Olive" title="b5">q9</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="openlatt.html#K1" title="OPENLATT:func.1">Topology_of</a> <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">p9</font> &amp; <font color="Olive" title="b3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">q9</font> holds <br/>( <font color="Olive" title="b2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b3">q</font> iff <font color="Olive" title="b4">p9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">q9</font> )</div></div>
