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<span class="kw">set </span><font color="Maroon" title="c1">T</font> =  the   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/>
<span class="kw">take </span>
 <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a>  the   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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a>  the   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> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a>  &amp;  not  <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a>  the   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> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )</span><br/>

<a NAME="E1:18_1_1"/>
 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>  the   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></span>)</span>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> holds <br/> ex <font color="Olive" title="b3">V</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>  the   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></span>)</span> st <br/>( <font color="Olive" title="b3">V</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="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">V</font> &amp;  not <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">V</font> ) or ( <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">V</font> &amp;  not <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">V</font> ) ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="t_0topsp.html#E15"><span class="lab"><font color="Green" title="E10">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:18_1_1"/>
(  <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a>  the   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> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a>  &amp;  not  <a href="t_0topsp.html#K3" title="T_0TOPSP:func.3">T_0-reflex</a>  the   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> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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