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

<b>let </b><font color="Maroon">Y</font> be    <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">Y0</font> be    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:27_1"/>
<font color="Maroon">A</font> is <a href="tex_2.html#V1" target="_self">proper</a>
 ;<br/><a NAME="E2:27_1"/><b>then </b>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">Y</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y0</font> holds <br/><font color="Olive">A</font> is <a href="tex_2.html#V1" target="_self">proper</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:27_1"/>
<font color="Maroon">Y0</font> is <a href="tex_2.html#V2" target="_self">proper</a>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E3:27"/>
( <font color="Maroon">Y0</font> is <a href="tex_2.html#V2" target="_self">proper</a> implies <font color="Maroon">A</font> is <a href="tex_2.html#V1" target="_self">proper</a> )
 <b>by </b><i>, </i>;<br/>


</div>
