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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th54</font></span>: <a NAME="T54"><span class="comment"><font color="firebrick">:: RLSUB_1:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">u</font>, <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">W</font> being    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">u</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font> iff <font color="Olive" title="b2">u</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b4">W</font> )</div></div>
