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<div><span class="kw">theorem </span><a NAME="T53"><span class="comment"><font color="firebrick">:: RUSUB_2:53</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><br/>  for <font color="Olive" title="b3">L</font> being    <a href="rusub_2.html#M1" title="RUSUB_2:mode.1">Linear_Compl</a> of <font color="Olive" title="b2">W</font><br/>  for <font color="Olive" title="b4">v</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="rusub_2.html#K4" title="RUSUB_2:func.4">|--</a> (<font color="Olive" title="b2">W</font>,<font color="Olive" title="b3">L</font>)</span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="rusub_2.html#K4" title="RUSUB_2:func.4">|--</a> (<font color="Olive" title="b3">L</font>,<font color="Olive" title="b2">W</font>)</span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_2.html#T35" target="_self" onmouseover="rs('rusub_2/T35')" onmouseout="rh()">Th35</a>, <a class="ref" href="rusub_2.html#T48" target="_self" onmouseover="rs('rusub_2/T48')" onmouseout="rh()">Th48</a></span>;<br/></div></div>
