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

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="tsp_1.html#M2">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:21_2_1"/><i><font color="Green">E17</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> is <a href="tex_3.html#V1">dense</a>
 ;<br/>

<b>assume </b><a NAME="E2:21_2_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tsp_2.html#V2" target="_self">maximal_T_0</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="tsp_2.html#E19"><i><font color="Green">Lemma15</font></i></a></i>;<br/>
<a NAME="E4:21_2_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="tsp_2.html#V1" target="_self">maximal_T_0</a>
 
<b>by </b><i><a class="txt" href="tsp_2.html#E2:21_2_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="tsp_2.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E5:21_2_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is <a href="tops_1.html#V1">dense</a>
 
<b>by </b><i><a class="ref" href="tsp_2.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E6:21_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tsp_2.html#E1:21_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="tex_3.html#T9">TEX_3:9</a></i>;<br/>


</div>
