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

<b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">X</font>;<br/>

<b>reconsider </b><font color="Maroon">A0</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E2:47_1_1"/>
<font color="Maroon">X</font> is    <a href="tsp_1.html#M2" target="_self">SubSpace</a> of <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T2">TSEP_1:2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>assume </b><a NAME="E4:47_1_1"/>
not <font color="Maroon">X0</font> is <a href="tex_2.html#V2">proper</a>
 ;<br/>

<a NAME="E5:47_1_1"/><b>then </b>
not <font color="Maroon">A0</font> is <a href="tex_2.html#V1">proper</a>
 
<b>by </b><i><a class="ref" href="tex_2.html#T13">TEX_2:13</a></i>;<br/>
<a NAME="E6:47_1_1"/><b>then </b>
<font color="Maroon">A0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="tex_2.html#T5">TEX_2:5</a></i>;<br/>
<a NAME="E7:47_1_1"/><b>then </b>
not <font color="Maroon">A0</font> is <a href="tsp_1.html#V1" target="_self">T_0</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:47_1_1"/>
not <font color="Maroon">X0</font> is <a href="t_0topsp.html#V2">T_0</a>
 <b>by </b><i/>;<br/>


</div>
