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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E3">Def2</font></span>   defines <a href="fintopo2.html#K2" title="FINTOPO2:func.2">P_2</a> <a onclick="hs(this)" href="javascript:()">FINTOPO2:def 2 : <br/></a><span> for <font color="Olive" title="b1">FT</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">FT</font><br/>  for <font color="Olive" title="b4">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">FT</font> holds <br/> ( ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  implies  <a href="fintopo2.html#K2" title="FINTOPO2:func.2">P_2</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>,<font color="Olive" title="b4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a>  ) &amp; ( (  not <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Olive" title="b2">x</font> or  not <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) implies  <a href="fintopo2.html#K2" title="FINTOPO2:func.2">P_2</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>,<font color="Olive" title="b4">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="margrel1.html#K6" title="MARGREL1:func.6">FALSE</a>  ) );<br/></span></div>
