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<b>consider </b><font color="Maroon">A0</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:86_2_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">A0</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E3:86_2_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">A0</font> is <a href="tops_1.html#V1">dense</a> &amp; <font color="Maroon">A0</font> is <a href="pre_topc.html#V3">open</a> )
 <b>by </b><i><a class="ref" href="tex_1.html#T38">TEX_1:38</a></i>;<br/>
<a NAME="E4:86_2_1"/>
not <font color="Maroon">A0</font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i>, <a class="ref" href="tops_3.html#T17">TOPS_3:17</a></i>;<br/>
<b>then consider </b><font color="Maroon">X0</font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V1">strict</a> <a href="tsep_1.html#V1">open</a> <a href="tex_3.html#V1" target="_self">dense</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E6:86_2_1"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">A0</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font>
 <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">X0</font>
;<br/>

<a NAME="E7:86_2_1"/>
<font color="Maroon">A0</font> is <a href="tex_2.html#V1">proper</a>
 
<b>by </b><i>, <a class="ref" href="tex_2.html#T5">TEX_2:5</a></i>;<br/>
<b>hence </b><a NAME="E8:86_2_1"/>
( <font color="Maroon">X0</font> is <a href="tex_3.html#V1" target="_self">dense</a> &amp; <font color="Maroon">X0</font> is <a href="tsep_1.html#V1">open</a> &amp; <font color="Maroon">X0</font> is <a href="tex_2.html#V2">proper</a> &amp; <font color="Maroon">X0</font> is <a href="pre_topc.html#V1">strict</a> &amp; not <font color="Maroon">X0</font> is <a href="struct_0.html#V3">empty</a> )
 <b>by </b><i>, <a class="ref" href="tex_2.html#T13">TEX_2:13</a></i>;<br/>


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