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

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A0</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c2">A0</font> is <a href="tops_3.html#V1" title="TOPS_3:attr.1">everywhere_dense</a>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">X0</font> being  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:23"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c2">A0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">X0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T10" title="TSEP_1:th.10">TSEP_1:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">Y0</font> = <font color="Maroon" title="c3">X0</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a> <a href="tex_3.html#V2" title="TEX_3:attr.2">everywhere_dense</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="tex_3.html#E1:23"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="tex_3.html#E3:23"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="tex_3.html#T16" target="_self" title="TEX_3:th.16">Th16</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">Y0</font>
;<br/>

<b>thus </b><a NAME="E5:23"/>
<font color="Maroon" title="c2">A0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">Y0</font>
 <b>by </b><i><a class="txt" href="tex_3.html#E3:23"><i><font color="Green" title="E15">A2</font></i></a></i>;<br/>


</div>
