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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E36">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">z</font> )
 ;<br/>

<a NAME="E2:45"/><b>then </b><i><font color="Green" title="E37">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T6" target="_self" title="COMPLSP2:th.6">Th6</a></i>;<br/>
<a NAME="E3:45"/><i><font color="Green" title="E38">A3</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T5" target="_self" title="COMPLSP2:th.5">Th5</a></i>;<br/>
<a NAME="E4:45"/><i><font color="Green" title="E39">A4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">z</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T5" target="_self" title="COMPLSP2:th.5">Th5</a></i>;<br/>
<a NAME="E5:45"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font>
 
<b>by </b><i><a class="ref" href="complsp2.html#T7" target="_self" title="COMPLSP2:th.7">Th7</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green" title="E36">A1</font></i></a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c3">z</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T31" target="_self" title="COMPLSP2:th.31">Th31</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green" title="E36">A1</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p2">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c3">z</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T31" target="_self" title="COMPLSP2:th.31">Th31</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green" title="E36">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p2">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T28" target="_self" title="COMPLSP2:th.28">Th28</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="complsp2.html#E3:45"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="complsp2.html#E4:45"><i><font color="Green" title="E39">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T35" target="_self" title="COMPLSP2:th.35">Th35</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green" title="E36">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T31" target="_self" title="COMPLSP2:th.31">Th31</a>, <a class="txt" href="complsp2.html#E1:45"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:45"><i><font color="Green" title="E37">A2</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E7:45"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font></span>)</span>
 ;<br/>


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