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<b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:59_2_1"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">X0</font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<b>assume </b><a NAME="E2:59_2_1"/>
<font color="Maroon">X0</font> is <a href="tdlat_3.html#V1">discrete</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Y0</font> = <font color="Maroon">X0</font> as  non <a href="struct_0.html#V3">empty</a> <a href="tdlat_3.html#V1">discrete</a> <a href="tdlat_3.html#V2">anti-discrete</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font> ;<br/>
<a NAME="E4:59_2_1"/>
<font color="Maroon">Y0</font> is <a href="realset2.html#V3">trivial</a>
 
;<br/>
<b>hence </b><a NAME="E5:59_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:59_2_1"><i><font color="Green">E17</font></i></a></i>;<br/>


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