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<b>let </b><font color="Maroon">V</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">W1</font> be    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>, <font color="Maroon">W2</font> be    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>, <font color="Maroon">W3</font> be    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">W1</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W3</font> &amp; <font color="Maroon">W2</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W3</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>assume </b><a NAME="E1:12_1"/>
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font> <a href="rusub_2.html#K1">+</a> <font color="Maroon">W2</font>
 ;<br/><b>then consider </b><font color="Maroon">v1</font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v2</font> being   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:12_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">v1</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font> &amp; <font color="Maroon">v2</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font> )
 <b>and </b><br/><a NAME="E4:12_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font>
 <b>by </b><i><a class="ref" href="rusub_2.html#T1">RUSUB_2:1</a></i>;<br/><a NAME="E5:12_1"/>
( <font color="Maroon">v1</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W3</font> &amp; <font color="Maroon">v2</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W3</font> )
 <b>by </b><i>, , <a class="ref" href="rusub_1.html#T1">RUSUB_1:1</a></i>;<br/><b>hence </b><a NAME="E6:12_1"/>
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W3</font>
 <b>by </b><i>, <a class="ref" href="rusub_1.html#T14">RUSUB_1:14</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:12"/>
<font color="Maroon">W1</font> <a href="rusub_2.html#K1">+</a> <font color="Maroon">W2</font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">W3</font>
 <b>by </b><i><a class="ref" href="rusub_1.html#T23">RUSUB_1:23</a></i>;<br/>


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