<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">g1</font>, <font color="Maroon" title="c3">g2</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c4">seq1</font>, <font color="Maroon" title="c5">seq2</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c4">seq1</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green" title="E29">A2</font></i>: 
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c4">seq1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g1</font>
 <b>and </b><br/><a NAME="E3:41"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c5">seq2</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 <b>and </b><br/><a NAME="E4:41"/><i><font color="Green" title="E31">A4</font></i>: 
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c5">seq2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g2</font>
 ;<br/>

<a NAME="E5:41"/><i><font color="Green" title="E32">A5</font></i>: 
<font color="Maroon" title="c4">seq1</font> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <font color="Maroon" title="c5">seq2</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 
<b>by </b><i><a class="txt" href="clvect_2.html#E1:41"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="clvect_2.html#E3:41"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="clvect_2.html#T3" target="_self" title="CLVECT_2:th.3">Th3</a></i>;<br/>
<a NAME="E6:41"/>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1</font> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <font color="Maroon" title="c5">seq2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">g2</font>
 
<b>by </b><i><a class="txt" href="clvect_2.html#E1:41"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="clvect_2.html#E2:41"><i><font color="Green" title="E29">A2</font></i></a>, <a class="txt" href="clvect_2.html#E3:41"><i><font color="Green" title="E30">A3</font></i></a>, <a class="txt" href="clvect_2.html#E4:41"><i><font color="Green" title="E31">A4</font></i></a>, <a class="ref" href="clvect_2.html#T13" target="_self" title="CLVECT_2:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E7:41"/>
(  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq1</font> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <font color="Maroon" title="c5">seq2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">g2</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">seq1</font> <a href="csspace.html#K16" title="CSSPACE:func.16">+</a> <font color="Maroon" title="c5">seq2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">g2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 <b>by </b><i><a class="txt" href="clvect_2.html#E5:41"><i><font color="Green" title="E32">A5</font></i></a>, <a class="ref" href="clvect_2.html#T24" target="_self" title="CLVECT_2:th.24">Th24</a></i>;<br/>


</div>
