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

<b>assume </b><a NAME="E1:95_2_1"/><i><font color="Green">E41</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> is <a href="tdlat_3.html#V1">discrete</a>
 ;<br/>

<b>assume </b><a NAME="E2:95_2_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V5" target="_self">maximal_discrete</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="tex_2.html#E17"><i><font color="Green">Lemma9</font></i></a></i>;<br/>
<a NAME="E4:95_2_1"/>
<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#E2:95_2_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="tex_2.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E5:95_2_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E6:95_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_2.html#E1:95_2_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tex_2.html#T26" target="_self">Th26</a></i>;<br/>


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