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<b>consider </b><font color="Maroon" title="c2">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="E2:117_1_1"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon" title="c2">M</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#T66" target="_self" title="TEX_2:th.66">Th66</a></i>;<br/>
<a NAME="E3:117_1_1"/>
not <font color="Maroon" title="c2">M</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="tex_2.html#E2:117_1_1"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="tex_2.html#T46" target="_self" title="TEX_2:th.46">Th46</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">X0</font> being  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E5:117_1_1"/><i><font color="Green" title="E55">A2</font></i>: 
<font color="Maroon" title="c3">X0</font> is <a href="tex_2.html#V5" title="TEX_2:attr.5">maximal_discrete</a>
 <b>and </b><br/><a NAME="E6:117_1_1"/>
<font color="Maroon" title="c2">M</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="c3">X0</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E2:117_1_1"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="tex_2.html#T53" target="_self" title="TEX_2:th.53">Th53</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">X0</font>
;<br/>

<b>thus </b><a NAME="E7:117_1_1"/>
( <font color="Maroon" title="c3">X0</font> is <a href="tex_2.html#V5" title="TEX_2:attr.5">maximal_discrete</a> &amp; <font color="Maroon" title="c3">X0</font> is <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> &amp; not <font color="Maroon" title="c3">X0</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> &amp; not <font color="Maroon" title="c3">X0</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> )
 <b>by </b><i><a class="txt" href="tex_2.html#E5:117_1_1"><i><font color="Green" title="E55">A2</font></i></a></i>;<br/>


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