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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="cc0sp1.html#K7" title="CC0SP1:func.7">C_Normed_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</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="cc0sp1.html#T27" target="_self" onmouseover="rs('cc0sp1/T27')" onmouseout="rh()">Th27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:48_1_1"/>
 <a href="cc0sp1.html#K7" title="CC0SP1:func.7">C_Normed_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font> is  <a href="clopban1.html#V3" title="CLOPBAN1:attr.3">complete</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="clopban1.html#D13" onmouseover="rs('clopban1/D13')" onmouseout="rh()">CLOPBAN1:def 13</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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