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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">W</font> be    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">L</font> be    <a href="rusub_2.html#M1" target="_self">Linear_Compl</a> of <font color="Maroon">W</font>;<br/>





<a NAME="E1:69"/>
<font color="Maroon">V</font> <a href="rusub_2.html#R1" target="_self">is_the_direct_sum_of</a> <font color="Maroon">W</font>,<font color="Maroon">L</font>
 
<b>by </b><i><a class="txt" href="rusub_2.html#E8"><i><font color="Green">Lemma40</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:69"/>
for <font color="Olive">v</font> being  <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">v</font> <a href="rusub_2.html#K4" target="_self">|--</a> <font color="Maroon">W</font>,<font color="Maroon">L</font></span>)</span> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">v</font> <a href="rusub_2.html#K4" target="_self">|--</a> <font color="Maroon">W</font>,<font color="Maroon">L</font></span>)</span> <a href="domain_1.html#K3">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">v</font>
 <b>by </b><i/>;<br/>


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