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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:17"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V4" target="_self">convergent</a>
 ;<br/>

<b>then </b> <a href="seq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_2.html#T22" target="_self">Th22</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

;<br/>
<b>hence </b><a NAME="E3:17"/>
 <a href="seq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><a href="seq_1.html#K17">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#T25">SEQ_1:25</a></i>;<br/>


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