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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of  <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> &amp;  <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> )</span><br/>

<a NAME="E1:51"/>
( <font color="Maroon" title="c1">V</font> <a href="rusub_2.html#R1" title="RUSUB_2:pred.1">is_the_direct_sum_of</a>  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font>, <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> &amp; <font color="Maroon" title="c1">V</font> <a href="rusub_2.html#R1" title="RUSUB_2:pred.1">is_the_direct_sum_of</a>  <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font>, <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_2.html#T39" target="_self" title="RUSUB_2:th.39">Th39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:51"/>
(  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of  <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> &amp;  <a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> is    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of  <a href="rusub_1.html#K1" title="RUSUB_1:func.1">(0).</a> <font color="Maroon" title="c1">V</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_2.html#D5" target="_self" title="RUSUB_2:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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