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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><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="E1:18"/><i><font color="Green">E15</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</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>
 ;<br/>

<a NAME="E2:18"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_1.html#D6">COMSEQ_1:def 6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:18_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E2:18"><i><font color="Green">E16</font></i></a>, <a class="ref" href="cfcont_1.html#T4" target="_self">Th4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cfcont_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E2:18"><i><font color="Green">E16</font></i></a>, <a class="ref" href="cfcont_1.html#T16" target="_self">Th16</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:18_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="cfunct_1.html#T7">CFUNCT_1:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<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>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cfcont_1.html#E1:18"><i><font color="Green">E15</font></i></a>, <a class="ref" href="cfcont_1.html#T16" target="_self">Th16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K4">(#)</a> <span class="p2">(<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>2</sub></font></span>)</span></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="comseq_1.html#D7">COMSEQ_1:def 7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:18"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cfcont_1.html#K1" target="_self">*</a> <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_1.html#K4">(#)</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>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="comseq_1.html#T6">COMSEQ_1:6</a></i>;<br/>


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