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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">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp; <font color="Maroon" title="c2">Y0</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> implies ( <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; <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="E1:48_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
( <font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp; <font color="Maroon" title="c2">Y0</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"> ( <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; <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>then consider </b><font color="Maroon" title="c3">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font><b> such that </b><br/><a NAME="E3:48_1_1"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y0</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c3">y</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c3">y</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="tex_2.html#T23" target="_self" title="TEX_2:th.23">Th23</a></i>;<br/>
<a NAME="E4:48_1_1"/>
(  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c3">y</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp;  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c3">y</font> is <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a> )
 
<b>by </b><i><a class="txt" href="tex_2.html#E1:48_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="tex_2.html#E3:48_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="tex_2.html#T12" target="_self" title="TEX_2:th.12">Th12</a></i>;<br/>
<a NAME="E5:48_1_1"/><b>then </b>
(  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c3">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="c3">y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )
 
<b>by </b><i><a class="ref" href="tex_2.html#T24" target="_self" title="TEX_2:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E6:48_1_1"/>
( <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )
 <b>by </b><i><a class="txt" href="tex_2.html#E3:48_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="tex_2.html#T17" target="_self" title="TEX_2:th.17">Th17</a>, <a class="ref" href="tex_2.html#T18" target="_self" title="TEX_2:th.18">Th18</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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