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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="E1:13"/><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>, <font color="Maroon">v1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">v2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E2:13"/>
<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">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span>
 ;<br/>

<a NAME="E3:13"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlsub_2.html#K4">|--</a> <font color="Maroon">W1</font>,<font color="Maroon">W2</font></span>)</span> <a href="domain_1.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlsub_2.html#K4">|--</a> <font color="Maroon">W1</font>,<font color="Maroon">W2</font></span>)</span> <a href="domain_1.html#K3">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<b>hence </b><a NAME="E4:13"/>
<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="rlsub_2.html#D6">RLSUB_2:def 6</a></i>;<br/>


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