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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="comseq_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font> is <a href="comseq_2.html#V2" target="_self">convergent</a>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T21" target="_self">Th21</a></i>;<br/>
 <a href="comseq_2.html#K2" target="_self">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>3</sub></font></span>)</span> = 
 <a href="comseq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K2">+</a> <span class="p2">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#D10">COMSEQ_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <span class="p2">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="comseq_2.html#E1:36"><i><font color="Green">E22</font></i></a>, <a class="txt" href="comseq_2.html#E2:36"><i><font color="Green">E23</font></i></a>, <a class="ref" href="comseq_2.html#T14" target="_self">Th14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K10">-</a> <span class="p2">(<span class="default"><a href="comseq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="comseq_2.html#E1:36"><i><font color="Green">E22</font></i></a>, <a class="ref" href="comseq_2.html#T22" target="_self">Th22</a></i>
;<br/>
<b>hence </b><a NAME="E4:36"/>
 <a href="comseq_2.html#K2" target="_self">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>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="comseq_2.html#K2" target="_self">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" target="_self">lim</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>


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