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<b>let </b><font color="Maroon">V</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/>

<a NAME="E1:56"/>
( <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="rusub_2.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bhsp_1.html#G1">UNITSTR</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">V</font>,the <a href="bhsp_1.html#U1">scalar</a> of <font color="Maroon">V</font> #) &amp;  <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font></span>)</span> <a href="rusub_2.html#K2" target="_self">/\</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K2">(Omega).</a> <font color="Maroon">V</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="rusub_2.html#D1" target="_self">Def1</a>, </i>;<br/>
<b>hence </b><a NAME="E2:56"/>
<font color="Maroon">V</font> <a href="rusub_2.html#R1" target="_self">is_the_direct_sum_of</a>  <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font>, <a href="rusub_1.html#K2">(Omega).</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="rusub_2.html#T2" target="_self">Th2</a></i>;<br/>

<b>hence </b><a NAME="E3:56"/>
<font color="Maroon">V</font> <a href="rusub_2.html#R1" target="_self">is_the_direct_sum_of</a>  <a href="rusub_1.html#K2">(Omega).</a> <font color="Maroon">V</font>, <a href="rusub_1.html#K1">(0).</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="txt" href="rusub_2.html#E7"><i><font color="Green">Lemma39</font></i></a></i>;<br/>


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