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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#NM1" title="PRE_TOPC:NM.1">TopSpace</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="c1">Y</font> is <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</a> implies ( not <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; not <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> ) )</span><br/>

<b>assume </b><a NAME="E1:51_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
not <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</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="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; not <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> )</span><br/>

<div><i><font color="Green" title="E22">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_1_1_1"/>
<font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">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="c2">Y</font> = <font color="Maroon" title="c1">Y</font> as  <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="E3:51_1_1_1"/>
<font color="Maroon" title="c2">Y</font> is <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</a>
 ;<br/><b>hence </b><a NAME="E4:51_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_1.html#E1:51_1_1"><i><font color="Green" title="E21">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/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_1_1_2"/>
<font color="Maroon" title="c1">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"> contradiction</span><br/><b>then reconsider </b><font color="Maroon" title="c2">Y</font> = <font color="Maroon" title="c1">Y</font> as  <a href="tdlat_3.html#V2" title="TDLAT_3:attr.2">anti-discrete</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> ;<br/><a NAME="E3:51_1_1_2"/>
<font color="Maroon" title="c2">Y</font> is <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</a>
 ;<br/><b>hence </b><a NAME="E4:51_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_1.html#E1:51_1_1"><i><font color="Green" title="E21">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/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:51_1_1"/>
( not <font color="Maroon" title="c1">Y</font> is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp; not <font color="Maroon" title="c1">Y</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_1.html#E2:51_1_1"><i><font color="Green" title="E22">A2</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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