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<b>let </b><font color="Maroon" title="c1">seq</font>, <font color="Maroon" title="c2">seq1</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green" title="E36">A2</font></i>: 
<font color="Maroon" title="c2">seq1</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 ;<br/>

<a NAME="E3:52"/><i><font color="Green" title="E37">A3</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T48" target="_self" title="CFCONT_1:th.48">Th48</a></i>;<br/>
<b>hence </b> <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c2">seq1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="comseq_2.html#T14" title="COMSEQ_2:th.14">COMSEQ_2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self" title="CFCONT_1:th.49">Th49</a></i>
;<br/><br/>

<b>thus </b> <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c2">seq1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="cfcont_1.html#E3:52"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="comseq_2.html#T26" title="COMSEQ_2:th.26">COMSEQ_2:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self" title="CFCONT_1:th.49">Th49</a></i>
;<br/>

<b>thus </b> <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">seq1</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c1">seq</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="cfcont_1.html#E3:52"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="comseq_2.html#T26" title="COMSEQ_2:th.26">COMSEQ_2:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self" title="CFCONT_1:th.49">Th49</a></i>
;<br/>

<b>thus </b> <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <font color="Maroon" title="c2">seq1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="cfcont_1.html#E3:52"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="comseq_2.html#T30" title="COMSEQ_2:th.30">COMSEQ_2:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="comseq_1.html#K1" title="COMSEQ_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq1</font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self" title="CFCONT_1:th.49">Th49</a></i>
;<br/>


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