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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="comseq_2.html#V2">convergent</a>
 ;<br/>

<a NAME="E3:52"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="comseq_2.html#V2">convergent</a>
 
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cfcont_1.html#T48" target="_self">Th48</a></i>;<br/>
<b>hence </b> <a href="comseq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green">E36</font></i></a>, <a class="ref" href="comseq_2.html#T14">COMSEQ_2:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self">Th49</a></i>
;<br/><br/>

<b>thus </b> <a href="comseq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green">E36</font></i></a>, <a class="txt" href="cfcont_1.html#E3:52"><i><font color="Green">E37</font></i></a>, <a class="ref" href="comseq_2.html#T26">COMSEQ_2:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self">Th49</a></i>
;<br/>

<b>thus </b> <a href="comseq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green">E36</font></i></a>, <a class="txt" href="cfcont_1.html#E3:52"><i><font color="Green">E37</font></i></a>, <a class="ref" href="comseq_2.html#T26">COMSEQ_2:26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self">Th49</a></i>
;<br/>

<b>thus </b> <a href="comseq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:52"><i><font color="Green">E36</font></i></a>, <a class="txt" href="cfcont_1.html#E3:52"><i><font color="Green">E37</font></i></a>, <a class="ref" href="comseq_2.html#T30">COMSEQ_2:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> 0</span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:52"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cfcont_1.html#T49" target="_self">Th49</a></i>
;<br/>


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