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

<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">W2</font> be    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">W1</font> be  <a href="rlvect_1.html#V2">strict</a>  <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/>





<b>thus </b><a NAME="E1:19"/>
( <font color="Maroon">W1</font> is    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font> implies <font color="Maroon">W1</font> <a href="rlsub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon">W1</font> is    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font>
 ;<br/>

<a NAME="E2:19_1"/><b>then </b><i><font color="Green">E32</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font>
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D2">RLSUB_1:def 2</a></i>;<br/>
<a NAME="E3:19_1"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="rlsub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:19_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">W1</font> <a href="rlsub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E5:19_1"/>
<font color="Maroon">W1</font> <a href="rlsub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font>
 <b>by </b><i><a class="ref" href="rlsub_1.html#T38">RLSUB_1:38</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:19"/>
( <font color="Maroon">W1</font> <a href="rlsub_2.html#K2" target="_self">/\</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W1</font> implies <font color="Maroon">W1</font> is    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">W2</font> )
 <b>by </b><i/>;<br/>


</div>
