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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">Th34</font></span>: <a NAME="T33"><span class="comment"><font color="firebrick">:: REAL_NS3:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">I</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font><br/>  for <font color="Olive" title="b4">s1</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b3">I</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b3">I</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; <font color="Olive" title="b3">I</font> is  <a href="real_ns3.html#V1" title="REAL_NS3:attr.1">isometric-like</a>  &amp; <font color="Olive" title="b4">s1</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  holds <br/>( <font color="Olive" title="b3">I</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">s1</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  &amp;  <a href="normsp_1.html#K5" title="NORMSP_1:func.5">lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">I</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">I</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="normsp_1.html#K5" title="NORMSP_1:func.5">lim</a> <font color="Olive" title="b4">s1</font></span>)</span> )</div></div>
