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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">LMQ20</font></span>: <a NAME="T63"><span class="comment"><font color="firebrick">:: NORMSP_3:63</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">W</font> being    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font>  ex <font color="Olive" title="b3">QL</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">V</font>,<span class="p1">(<span class="default"><a href="normsp_3.html#K10" title="NORMSP_3:func.10">VectQuot</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>)</span>)</span> st <br/>( <font color="Olive" title="b3">QL</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; (  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> holds  <font color="Olive" title="b3">QL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b2">W</font> ) )</div></div>
