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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>given </b><font color="Maroon" title="c2">X0</font> being  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><a NAME="E1:64"/><i><font color="Green" title="E27">A1</font></i>: 
( <font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a> &amp; <font color="Maroon" title="c2">X0</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a> )
 ;<br/>

<b>assume </b><a NAME="E2:64"/>
<font color="Maroon" title="c1">X</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">X</font> = <font color="Maroon" title="c1">X</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> ;<br/>
<a NAME="E4:64"/>
<font color="Maroon" title="c2">X0</font> is  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X</font>
 
<b>by </b><i><a class="txt" href="tex_3.html#E1:64"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:64"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_3.html#E1:64"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/>


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