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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th25</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: LOPBAN10:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">h</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="lopban10.html#K13" title="LOPBAN10:func.13">R_VectorSpace_of_BoundedMultilinearOperators</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span><br/>  for <font color="Olive" title="b5">a</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( <font color="Olive" title="b4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">f</font> iff  for <font color="Olive" title="b6">x</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Olive" title="b1">X</font></span>)</span> holds  <font color="Olive" title="b4">h</font> <a href="lopban10.html#K14" title="LOPBAN10:func.14">.</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="lopban10.html#K14" title="LOPBAN10:func.14">.</a> <font color="Olive" title="b6">x</font></span>)</span> )</div></div>
