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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>  st  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Olive" title="b1">y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> holds <br/>(  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Olive" title="b1">y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Olive" title="b1">y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )</span><br/><b>let </b><font color="Maroon" title="c2">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> implies (  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> ) )</span><br/>



<b>assume </b><a NAME="E1:47"/>
 <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )</span><br/>

<a NAME="E2:47"/><b>then </b>
 <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>
 
;<br/>
<b>hence </b><a NAME="E3:47"/>
(  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</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"> verum</span><br/>


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