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<div><span class="kw">theorem </span><a NAME="T63"><span class="comment"><font color="firebrick">:: RUSUB_2:63</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">v</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b4">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">v</font> <a href="rusub_1.html#K3" title="RUSUB_1:func.3">+</a> <font color="Olive" title="b2">W</font> iff  ex <font color="Olive" title="b5">u</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b5">u</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b2">W</font> &amp; <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b5">u</font> ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="rusub_2.html#E62"><span class="lab"><font color="Green" title="E40">Lm16</font></span></a></span>;<br/></div></div>
