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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th11</font></span>: <a NAME="T11"><span class="comment"><font color="firebrick">:: RUSUB_2:11</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">W</font> being    <a href="rusub_1.html#M1" title="RUSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <span class="p1">(<span class="default"><a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Olive" title="b1">V</font></span>)</span> <a href="rusub_2.html#K1" title="RUSUB_2:func.1">+</a> <font color="Olive" title="b2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_1.html#G1" title="BHSP_1:aggr.1">UNITSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">V</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">U7</a> of <font color="Olive" title="b1">V</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">V</font>, the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <font color="Olive" title="b1">V</font> #) &amp; <font color="Olive" title="b2">W</font> <a href="rusub_2.html#K1" title="RUSUB_2:func.1">+</a> <span class="p1">(<span class="default"><a href="rusub_1.html#K2" title="RUSUB_1:func.2">(Omega).</a> <font color="Olive" title="b1">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_1.html#G1" title="BHSP_1:aggr.1">UNITSTR</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>, the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">ZeroF</a> of <font color="Olive" title="b1">V</font>, the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">U7</a> of <font color="Olive" title="b1">V</font>, the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Olive" title="b1">V</font>, the <a href="bhsp_1.html#U1" title="BHSP_1:sel.1">scalar</a> of <font color="Olive" title="b1">V</font> #) )</div></div>
