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<b>let </b><font color="Maroon" title="c2">Y0</font> be    <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"> ( <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</a> implies  not <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V5" title="TEX_2:attr.5">maximal_discrete</a> )</span><br/>

<b>assume </b><a NAME="E1:96_2_1"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">proper</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="tex_2.html#V5" title="TEX_2:attr.5">maximal_discrete</a></span><br/>

<b>assume </b><a NAME="E2:96_2_1"/><i><font color="Green" title="E43">A4</font></i>: 
<font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V5" title="TEX_2:attr.5">maximal_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>reconsider </b><font color="Maroon" title="c3">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="tex_2.html#E17"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/>
<a NAME="E4:96_2_1"/><i><font color="Green" title="E44">A5</font></i>: 
<font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a>
 
<b>by </b><i><a class="txt" href="tex_2.html#E2:96_2_1"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="tex_2.html#D8" target="_self" title="TEX_2:def.8">Def8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_2_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c4">A</font> = <font color="Maroon" title="c3">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">A</font> <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> &amp; not <font color="Maroon" title="c4">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> )</span><br/><b>thus </b><a NAME="E1:96_2_1_1"/>
<font color="Maroon" title="c4">A</font> <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c4">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a></span><br/><b>thus </b><a NAME="E2:96_2_1_1"/>
not <font color="Maroon" title="c4">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E4:96_2_1"><i><font color="Green" title="E44">A5</font></i></a>, <a class="ref" href="tex_2.html#T49" target="_self" title="TEX_2:th.49">Th49</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="E6:96_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:96_2_1"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="tex_2.html#D3" target="_self" title="TEX_2:def.3">Def3</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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