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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th19</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: WAYBEL14:19</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">V</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b1">T</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">V</font> is  <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</a>  iff  for <font color="Olive" title="b3">X</font>, <font color="Olive" title="b4">Y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Olive" title="b1">T</font></span>)</span>  holds <br/>(  not <font color="Olive" title="b3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> or <font color="Olive" title="b3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> or <font color="Olive" title="b4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> ) )</div></div>
