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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</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">seq</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> holds <br/> <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K5" title="BHSP_1:func.5">-</a> <font color="Olive" title="b1">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Olive" title="b1">seq</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> implies  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K5" title="BHSP_1:func.5">-</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:18"/>
<font color="Maroon" title="c2">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K5" title="BHSP_1:func.5">-</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span></span><br/>

<a NAME="E2:18"/><b>then </b>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="clvect_2.html#T15" target="_self" title="CLVECT_2:th.15">Th15</a></i>;<br/>
<a NAME="E3:18"/><b>then </b>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K5" title="BHSP_1:func.5">-</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="csspace.html#T77" title="CSSPACE:th.77">CSSPACE:77</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="bhsp_1.html#K5" title="BHSP_1:func.5">-</a> <font color="Maroon" title="c2">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font></span>)</span>
 <b>by </b><i><a class="ref" href="clvect_1.html#T4" title="CLVECT_1:th.4">CLVECT_1:4</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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