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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>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K2">COMPLEX</a> , <a href="numbers.html#K2">COMPLEX</a> ;<br/>





<b>assume </b><a NAME="E1:25"/><i><font color="Green">E21</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> is    <a href="comseq_3.html#M1">subsequence</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being  <a href="seqm_3.html#V1">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="comseq_3.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="comseq_3.html#D9">COMSEQ_3:def 9</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="comseq_3.html#D9">COMSEQ_3:def 9</a><br/>

<b>thus </b><a NAME="E4:25"/>
<font color="Maroon">c<sub>3</sub></font> <a href="cfcont_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cfcont_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_3.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E1:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="cfcont_1.html#E3:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="cfcont_1.html#T25" target="_self">Th25</a></i>;<br/>


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