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



<b>assume </b><a NAME="E1:16"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">V</font> <a href="rlsub_2.html#R1">is_the_direct_sum_of</a> <font color="Maroon">W1</font>,<font color="Maroon">W2</font>
 ;<br/>

<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="E2:16"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font>
 ;<br/>

<a NAME="E3:16"/><i><font color="Green">E25</font></i>: 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font>
 
<b>by </b><i><a class="ref" href="rlsub_1.html#T25">RLSUB_1:25</a></i>;<br/>
<a NAME="E4:16"/>
<font color="Maroon">v</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/>
<b>hence </b><a NAME="E5:16"/>
<font color="Maroon">v</font> <a href="rlsub_2.html#K4">|--</a> <font color="Maroon">W1</font>,<font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v</font>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i>, , , </i>;<br/>


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