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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>
<b>take </b>
 <a href="t_0topsp.html#K3" target="_self">T_0-reflex</a> <font color="Maroon">c<sub>1</sub></font>
;<br/>

<a NAME="E2:19_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="t_0topsp.html#K3" target="_self">T_0-reflex</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b<sub>2</sub></font> holds <br/>ex <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="t_0topsp.html#K3" target="_self">T_0-reflex</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>3</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; ( ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>3</sub></font> &amp; not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>3</sub></font> ) or ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>3</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>3</sub></font> ) ) )
 
<b>by </b><i><a class="txt" href="t_0topsp.html#E19"><i><font color="Green">Lemma15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:19_1_1"/>
(  <a href="t_0topsp.html#K3" target="_self">T_0-reflex</a> <font color="Maroon">c<sub>1</sub></font> is <a href="t_0topsp.html#V2" target="_self">discerning</a> &amp; not  <a href="t_0topsp.html#K3" target="_self">T_0-reflex</a> <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i><a class="ref" href="t_0topsp.html#D7" target="_self">Def7</a></i>;<br/>


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