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<b>let </b><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">s'</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c2">s</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> &amp; <font color="Maroon" title="c3">s'</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green" title="E23">A2</font></i>: 
 <a href="comseq_1.html#K5" title="COMSEQ_1:func.5">-</a> <font color="Maroon" title="c3">s'</font> is <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>
 
<b>by </b><i><a class="ref" href="comseq_2.html#T21" target="_self" title="COMSEQ_2:th.21">Th21</a></i>;<br/>
 <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c3">s'</font></span>)</span> = 
 <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <span class="p2">(<span class="default"><a href="comseq_1.html#K5" title="COMSEQ_1:func.5">-</a> <font color="Maroon" title="c3">s'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comseq_1.html#D10" title="COMSEQ_1:def.10">COMSEQ_1:def 10</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">s</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> <span class="p2">(<span class="default"><a href="comseq_1.html#K5" title="COMSEQ_1:func.5">-</a> <font color="Maroon" title="c3">s'</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="comseq_2.html#E1:36"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="comseq_2.html#E2:36"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="comseq_2.html#T14" target="_self" title="COMSEQ_2:th.14">Th14</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">s</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p2">(<span class="default"><a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">s'</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="comseq_2.html#E1:36"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="comseq_2.html#T22" target="_self" title="COMSEQ_2:th.22">Th22</a></i>
;<br/>
<b>hence </b><a NAME="E4:36"/>
 <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c3">s'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">s</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="c3">s'</font></span>)</span>
 ;<br/>


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