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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#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Y0</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b2">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="Olive" title="b1">Y0</font> holds <br/>( <font color="Olive" title="b2">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a> iff <font color="Olive" title="b1">Y0</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a> )</span><br/><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">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">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> holds <br/>( <font color="Olive" title="b1">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a> iff <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a> )</span><br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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="c3">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> implies ( <font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a> iff <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a> ) )</span><br/>





<b>assume </b><a NAME="E1:81"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a> iff <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a> )</span><br/>

<div><b>hereby </b> <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#V4" title="TEX_2:attr.4">maximal_discrete</a> implies <font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:81_1"/>
<font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">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="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a></span><br/><a NAME="E2:81_1"/><b>then </b>
for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">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> holds <br/><font color="Olive" title="b1">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a>
 <b>by </b><i><a class="txt" href="#E1:81"><i><font color="Green" title="E34">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:81_1"/>
<font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D8" target="_self" title="TEX_2:def.8">Def8</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>thus </b><a NAME="E3:81"/>
( <font color="Maroon" title="c2">Y0</font> is <a href="tex_2.html#V4" title="TEX_2:attr.4">maximal_discrete</a> implies <font color="Maroon" title="c3">A</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a> )
 <b>by </b><i><a class="txt" href="#E1:81"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="tex_2.html#D8" target="_self" title="TEX_2:def.8">Def8</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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