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<b>let </b><font color="Maroon" title="c2">Y0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> implies  not <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )</span><br/>

<b>assume </b><a NAME="E1:55_2_1"/><i><font color="Green" title="E17">A1</font></i>: 
not <font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a></span><br/>

<b>assume </b><a NAME="E2:55_2_1"/>
<font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then reconsider </b><font color="Maroon" title="c3">Y0</font> = <font color="Maroon" title="c2">Y0</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E4:55_2_1"/>
<font color="Maroon" title="c3">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 
;<br/>
<b>hence </b><a NAME="E5:55_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:55_2_1"><i><font color="Green" title="E17">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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