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<b>let </b><font color="Maroon" title="c2">Y0</font> be  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">Y</font>;<br/>

<b>assume </b><a NAME="E1:40_2_1"/><i><font color="Green" title="E13">A2</font></i>: 
( <font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> &amp; not <font color="Maroon" title="c2">Y0</font> is <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a> )
 ;<br/>

<b>assume </b><a NAME="E2:40_2_1"/>
<font color="Maroon" title="c2">Y0</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a>
 ;<br/>

<a NAME="E3:40_2_1"/><b>then </b><i><font color="Green" title="E14">A3</font></i>: 
 <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="tex_2.html#E1:40_2_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="tdlat_3.html#T12" title="TDLAT_3:th.12">TDLAT_3:12</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_2_1_1"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon" title="c3">d0</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">Y0</font>;<br/><b>take </b><font color="Maroon" title="c4">d0</font> = <font color="Maroon" title="c3">d0</font>;<br/><b>thus </b><a NAME="E2:40_2_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">d0</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E3:40_2_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:40_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:40_2_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="tex_1.html#D1" title="TEX_1:def.1">TEX_1:def 1</a></i>;<br/>


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