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<b>let </b><font color="Maroon">Y0</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:98_3_1"/><i><font color="Green">E49</font></i>: 
not <font color="Maroon">Y0</font> is <a href="tex_2.html#V2" target="_self">proper</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i/>;<br/>
<a NAME="E3:98_3_1"/>
not <font color="Maroon">A</font> is <a href="tex_2.html#V1" target="_self">proper</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:98_3_1"/><b>then </b>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font> holds <br/><font color="Olive">A</font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:98_3_1"/>
<font color="Maroon">Y0</font> is <a href="tex_2.html#V5" target="_self">maximal_discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D3" target="_self">Def3</a></i>;<br/>


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