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

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">Y0</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="t_0topsp.html#V2" title="T_0TOPSP:attr.2">V80</a>  <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<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">Y0</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="E2:22"/>
<font color="Maroon" title="c3">A</font> is <a href="tsp_1.html#V1" title="TSP_1:attr.1">T_0</a>
 
<b>by </b><i><a class="ref" href="tsp_1.html#T15" title="TSP_1:th.15">TSP_1:15</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:22"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">M</font>
 <b>and </b><br/><a NAME="E5:22"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c4">M</font> is <a href="tsp_2.html#V1" title="TSP_2:attr.1">maximal_T_0</a>
 <b>by </b><i><a class="ref" href="tsp_2.html#T9" target="_self" title="TSP_2:th.9">Th9</a></i>;<br/>
<a NAME="E6:22"/>
not <font color="Maroon" title="c4">M</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="tsp_2.html#E5:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="tsp_2.html#T4" target="_self" title="TSP_2:th.4">Th4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">X0</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E8:22"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c5">X0</font> is <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a>
 <b>and </b><br/><a NAME="E9:22"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c4">M</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="c5">X0</font>
 <b>by </b><i><a class="txt" href="tsp_2.html#E5:22"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="tsp_2.html#T12" target="_self" title="TSP_2:th.12">Th12</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">X0</font>
;<br/>

<b>thus </b><a NAME="E10:22"/>
( <font color="Maroon" title="c2">Y0</font> is    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c5">X0</font> &amp; <font color="Maroon" title="c5">X0</font> is <a href="tsp_2.html#V2" title="TSP_2:attr.2">maximal_T_0</a> )
 <b>by </b><i><a class="txt" href="tsp_2.html#E4:22"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="tsp_2.html#E8:22"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="tsp_2.html#E9:22"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="tsep_1.html#T4" title="TSEP_1:th.4">TSEP_1:4</a></i>;<br/>


</div>
