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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green">E36</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:45"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T6" target="_self">Th6</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a></i>;<br/>
<a NAME="E3:45"/><i><font color="Green">E38</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E4:45"/><i><font color="Green">E39</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E5:45"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T7" target="_self">Th7</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complsp1.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complsp1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T31" target="_self">Th31</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a>, <a class="txt" href="complsp2.html#E5:45"><i><font color="Green">E40</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <span class="p2">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="complsp1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T31" target="_self">Th31</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complsp1.html#K3">+</a> <span class="p2">(<span class="default"><a href="complsp1.html#K5">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T28" target="_self">Th28</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a>, <a class="txt" href="complsp2.html#E3:45"><i><font color="Green">E38</font></i></a>, <a class="txt" href="complsp2.html#E4:45"><i><font color="Green">E39</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T35" target="_self">Th35</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T31" target="_self">Th31</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green">E36</font></i></a>, <a class="txt" href="complsp2.html#E2:45"><i><font color="Green">E37</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E7:45"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complsp1.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="complsp1.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>


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