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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E44">LMQ21</font></span>: <a NAME="T64"><span class="comment"><font color="firebrick">:: NORMSP_3:64</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">W</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b3">L</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>  ex <font color="Olive" title="b4">QL</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <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>,<span class="p2">(<span class="default"><a href="normsp_3.html#K5" title="NORMSP_3:func.5">Ker</a> <font color="Olive" title="b3">L</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="normsp_3.html#K7" title="NORMSP_3:func.7">Im</a> <font color="Olive" title="b3">L</font></span>)</span> st <br/>( <font color="Olive" title="b4">QL</font> is  <a href="normsp_3.html#V3" title="NORMSP_3:attr.3">isomorphism</a>  &amp; (  for <font color="Olive" title="b5">z</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <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>,<span class="p2">(<span class="default"><a href="normsp_3.html#K5" title="NORMSP_3:func.5">Ker</a> <font color="Olive" title="b3">L</font></span>)</span>)</span>)</span><br/>  for <font color="Olive" title="b6">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="b5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">v</font> <a href="rlsub_1.html#K3" title="RLSUB_1:func.3">+</a> <span class="p1">(<span class="default"><a href="normsp_3.html#K5" title="NORMSP_3:func.5">Ker</a> <font color="Olive" title="b3">L</font></span>)</span> holds <br/><font color="Olive" title="b4">QL</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">v</font> ) )</div></div>
