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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: RUSUB_1:51</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">u</font>, <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>  st <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">v</font> <a href="rusub_1.html#K3" title="RUSUB_1:func.3">+</a> <font color="Olive" title="b2">W</font> &amp; <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b4">v</font></span>)</span> <a href="rusub_1.html#K3" title="RUSUB_1:func.3">+</a> <font color="Olive" title="b2">W</font> holds <br/><font color="Olive" title="b4">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">W</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="rusub_1.html#T50" target="_self" onmouseover="rs('rusub_1/T50')" onmouseout="rh()">Th50</a>, <a class="ref" href="rusub_1.html#T49" target="_self" onmouseover="rs('rusub_1/T49')" onmouseout="rh()">Th49</a></span>;<br/></div></div>
