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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: HAHNBAN:9</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">V1</font>, <font color="Olive" title="b3">V2</font>, <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><br/>  for <font color="Olive" title="b5">W1</font>, <font color="Olive" title="b6">W2</font> being    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b4">W</font>  st <font color="Olive" title="b5">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">V1</font> &amp; <font color="Olive" title="b6">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">V2</font> holds <br/><font color="Olive" title="b5">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Olive" title="b6">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">V1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Olive" title="b3">V2</font></div></div>
