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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<a NAME="E1:55"/>
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#V6" title="CLVECT_1:attr.6">convergent</a>
 
<b>by </b><i><a class="ref" href="csspace4.html#T29" target="_self" title="CSSPACE4:th.29">Th29</a></i>;<br/>
<b>hence </b><a NAME="E2:55"/>
 <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>
 <b>by </b><i><a class="ref" href="clopban1.html#D14" title="CLOPBAN1:def.14">CLOPBAN1:def 14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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