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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: RLSUB_2:47</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">W1</font>, <font color="Olive" title="b3">W2</font> being    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">V</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>  st <font color="Olive" title="b1">V</font> <a href="rlsub_2.html#R1" title="RLSUB_2:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b2">W1</font>,<font color="Olive" title="b3">W2</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="rlsub_2.html#K4" title="RLSUB_2:func.4">|--</a> (<font color="Olive" title="b2">W1</font>,<font color="Olive" title="b3">W2</font>)</span>)</span> <a href="domain_1.html#K2" title="DOMAIN_1:func.2">`1</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="rlsub_2.html#K4" title="RLSUB_2:func.4">|--</a> (<font color="Olive" title="b3">W2</font>,<font color="Olive" title="b2">W1</font>)</span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </div></div>
