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

<b>let </b><font color="Maroon" title="c2">X0</font> be    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">X0</font> is <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a> implies <font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a> )</span><br/>

<b>assume </b><a NAME="E1:21_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c2">X0</font> is <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a></span><br/>

<b>reconsider </b><font color="Maroon" title="c3">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="tsp_2.html#E19"><i><font color="Green" title="E15">Lm1</font></i></a></i>;<br/>
<a NAME="E3:21_1_1"/>
<font color="Maroon" title="c3">A</font> is <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>
 
<b>by </b><i><a class="txt" href="#E1:21_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="tsp_2.html#T11" target="_self" title="TSP_2:th.11">Th11</a></i>;<br/>
<a NAME="E4:21_1_1"/><b>then </b>
<font color="Maroon" title="c3">A</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a>
 
<b>by </b><i><a class="ref" href="tsp_2.html#T2" target="_self" title="TSP_2:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E5:21_1_1"/>
<font color="Maroon" title="c2">X0</font> is <a href="tex_3.html#V1" title="TEX_3:attr.1">dense</a>
 <b>by </b><i><a class="ref" href="tex_3.html#T9" title="TEX_3:th.9">TEX_3:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
