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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Y</font> being  <a href="clopban1.html#NM2" title="CLOPBAN1:NM.2">ComplexBanachSpace</a> holds   <a href="csspace4.html#K9" title="CSSPACE4:func.9">C_NormSpace_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">Y</font> is   <a href="clopban1.html#NM2" title="CLOPBAN1:NM.2">ComplexBanachSpace</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y</font> be   <a href="clopban1.html#NM2" title="CLOPBAN1:NM.2">ComplexBanachSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="csspace4.html#K9" title="CSSPACE4:func.9">C_NormSpace_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> is   <a href="clopban1.html#NM2" title="CLOPBAN1:NM.2">ComplexBanachSpace</a></span><br/>



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for <font color="Olive" title="b1">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="csspace4.html#K9" title="CSSPACE4:func.9">C_NormSpace_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span>)</span>  st <font color="Olive" title="b1">seq</font> is  <a href="csspace3.html#V1" title="CSSPACE3:attr.1">CCauchy</a>  holds <br/><font color="Olive" title="b1">seq</font> is  <a href="clvect_1.html#V9" title="CLVECT_1:attr.9">convergent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="csspace4.html#T29" target="_self" title="CSSPACE4:th.29">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:57"/>
 <a href="csspace4.html#K9" title="CSSPACE4:func.9">C_NormSpace_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> is   <a href="clopban1.html#NM2" title="CLOPBAN1:NM.2">ComplexBanachSpace</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="clopban1.html#D14" title="CLOPBAN1:def.14">CLOPBAN1:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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