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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="lopban_1.html#NM2">RealBanachSpace</a>;<br/>



<a NAME="E1:85"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="normsp_1.html#NM2">sequence</a> of <span class="p1">(<span class="default"><a href="lopban_1.html#K16" target="_self">R_NormSpace_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> st <font color="Olive">b<sub>1</sub></font> is <a href="rsspace3.html#V1">CCauchy</a> holds <br/><font color="Olive">b<sub>1</sub></font> is <a href="normsp_1.html#V4">convergent</a>
 
<b>by </b><i><a class="ref" href="lopban_1.html#T48" target="_self">Th48</a></i>;<br/>
<b>hence </b><a NAME="E2:85"/>
 <a href="lopban_1.html#K16" target="_self">R_NormSpace_of_BoundedLinearOperators</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is   <a href="lopban_1.html#NM2">RealBanachSpace</a>
 <b>by </b><i><a class="ref" href="lopban_1.html#D16" target="_self">Def16</a></i>;<br/>


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