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<b>let </b><font color="Maroon" title="c1">T</font> be  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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a> <font color="Maroon" title="c1">T</font> is   <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a></span><br/>

<a NAME="E1:20"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a> <font color="Maroon" title="c1">T</font></span>)</span>  st not <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/> ex <font color="Olive" title="b3">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a> <font color="Maroon" title="c1">T</font></span>)</span> st <br/>( <font color="Olive" title="b3">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; ( ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A</font> &amp; not <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A</font> ) or ( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A</font> &amp; not <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">A</font> ) ) )
 
<b>by </b><i><a class="txt" href="t_0topsp.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:20"/>
 <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a> <font color="Maroon" title="c1">T</font> is   <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a>
 <b>by </b><i><a class="ref" href="t_0topsp.html#D7" target="_self" title="T_0TOPSP:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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