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<b>let </b><font color="Maroon">X0</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>

<b>reconsider </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E2:60_2_1"/>
<font color="Maroon">X0</font> is <a href="tex_2.html#V2">proper</a>
 ;<br/>

<a NAME="E3:60_2_1"/><b>then </b>
<font color="Maroon">A</font> is <a href="tex_2.html#V1">proper</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T13">TEX_2:13</a></i>;<br/>
<a NAME="E4:60_2_1"/><b>then </b>
<font color="Maroon">A</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>by </b><i><a class="ref" href="tex_2.html#T5">TEX_2:5</a></i>;<br/>
<a NAME="E5:60_2_1"/><b>then </b>
not <font color="Maroon">A</font> is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i><a class="ref" href="tex_1.html#T35">TEX_1:35</a></i>;<br/>
<b>hence </b><a NAME="E6:60_2_1"/>
not <font color="Maroon">X0</font> is <a href="tex_3.html#V1" target="_self">dense</a>
 <b>by </b><i/>;<br/>


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