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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">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#V5" title="TEX_2:attr.5">maximal_discrete</a> implies <font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> )</span><br/>

<b>assume </b><a NAME="E1:97_1_1"/><i><font color="Green" title="E42">A1</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"> <font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a></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  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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="E3:97_1_1"/>
<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#E1:97_1_1"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="tex_2.html#D8" target="_self" title="TEX_2:def.8">Def8</a></i>;<br/>
<a NAME="E4:97_1_1"/><b>then </b>
<font color="Maroon" title="c3">A</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T50" target="_self" title="TEX_2:th.50">Th50</a></i>;<br/>
<b>hence </b><a NAME="E5:97_1_1"/>
<font color="Maroon" title="c2">Y0</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D9" title="STRUCT_0:def.9">STRUCT_0:def 9</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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