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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">LMQ03</font></span>: <a NAME="T52"><span class="comment"><font color="firebrick">:: NORMSP_3:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b2">Y</font> being    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">v1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="dualsp01.html#K2" title="DUALSP01:func.2">RLSp2RVSp</a> <font color="Olive" title="b1">X</font></span>)</span>  st <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v1</font> holds <br/><font color="Olive" title="b3">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <font color="Olive" title="b2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v1</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <span class="p1">(<span class="default"><a href="normsp_3.html#K9" title="NORMSP_3:func.9">RLSp2RVSp</a> <font color="Olive" title="b2">Y</font></span>)</span></div></div>
