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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="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E3:16"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="complsp1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K27">addcomplex</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="complsp1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="complsp1.html#E1:16"><i><font color="Green">E18</font></i></a>, <a class="txt" href="complsp1.html#E34"><i><font color="Green">Lemma14</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="complsp1.html#K9" target="_self">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> = 
<a href="binop_2.html#K27">addcomplex</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="complsp1.html#E2:16"><i><font color="Green">E19</font></i></a>, <a class="ref" href="funcop_1.html#T28">FUNCOP_1:28</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K3">+</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="binop_2.html#D3">BINOP_2:def 3</a></i>
;<br/><br/>


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