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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th42</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: LOPBAN11:8</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>  st <font color="Olive" title="b2">Y</font> is  <a href="lopban_1.html#V3" title="LOPBAN_1:attr.3">complete</a>  holds <br/> for <font color="Olive" title="b3">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <span class="p1">(<span class="default"><a href="lopban10.html#K18" title="LOPBAN10:func.18">R_NormSpace_of_BoundedMultilinearOperators</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span>  st <font color="Olive" title="b3">seq</font> is  <a href="rsspace3.html#NV2" title="RSSPACE3:NV.2">Cauchy_sequence_by_Norm</a>  holds <br/><font color="Olive" title="b3">seq</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a> </div></div>
