<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:94"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:94_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a>
 ;<br/><a NAME="E2:94_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:94"><i><font color="Green">E41</font></i></a></i>;<br/><b>hence </b><a NAME="E3:94_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V5" target="_self">maximal_discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D8" target="_self">Def8</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E3:94"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V5" target="_self">maximal_discrete</a> implies <font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a> )
 <b>by </b><i><a class="txt" href="tex_2.html#E1:94"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tex_2.html#D8" target="_self">Def8</a></i>;<br/>


</div>
