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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="tdlat_3.html#V3" title="TDLAT_3:attr.3">almost_discrete</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">  ex <font color="Olive" title="b1">M</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <font color="Olive" title="b1">M</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a></span><br/>

<b>set </b><font color="Maroon" title="c2">A</font> =  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">X</font>;<br/>
<a NAME="E1:100"/>
 <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">X</font> is <a href="tex_2.html#V2" title="TEX_2:attr.2">discrete</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T35" target="_self" title="TEX_2:th.35">Th35</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:100"/>
 <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">M</font>
 <b>and </b><br/><a NAME="E4:100"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c3">M</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#T65" target="_self" title="TEX_2:th.65">Th65</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">M</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">M</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a></span><br/>

<b>thus </b><a NAME="E5:100"/>
<font color="Maroon" title="c3">M</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">maximal_discrete</a>
 <b>by </b><i><a class="txt" href="#E4:100"><i><font color="Green" title="E46">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/>


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