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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</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="E1:44"/><i><font color="Green" title="E35">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>
 ;<br/>

<a NAME="E2:44"/><i><font color="Green" title="E36">A2</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="E3:44"/><i><font color="Green" title="E37">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="c1">x</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#T5" target="_self" title="COMPLSP2:th.5">Th5</a></i>;<br/>
<a NAME="E4:44"/><i><font color="Green" title="E38">A4</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="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</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="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="complsp2.html#T6" target="_self" title="COMPLSP2:th.6">Th6</a></i>;<br/>
<a NAME="E5:44"/><i><font color="Green" title="E39">A5</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c1">x</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="c2">y</font></span>)</span></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> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</font></span>)</span>
 
<b>by </b><i><a class="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:44"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="complsp2.html#E3:44"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="complsp2.html#T6" target="_self" title="COMPLSP2:th.6">Th6</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> <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"><span class="p2">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</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="c2">y</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</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="c1">x</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="c2">y</font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:44"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="complsp2.html#E3:44"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="complsp2.html#E4:44"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="complsp2.html#T28" target="_self" title="COMPLSP2:th.28">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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="c1">x</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="c1">x</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="c2">y</font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="complsp2.html#T29" target="_self" title="COMPLSP2:th.29">Th29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p3">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</font></span>)</span></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="c2">y</font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="complsp2.html#E3:44"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="complsp2.html#T28" target="_self" title="COMPLSP2:th.28">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p2">(<span class="default"><a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font></span>)</span></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="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T34" target="_self" title="COMPLSP2:th.34">Th34</a></i>
<br/>.= 
<font color="Maroon" title="c2">y</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> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="complsp2.html#T33" target="_self" title="COMPLSP2:th.33">Th33</a></i>
<br/>.= 
 <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T34" target="_self" title="COMPLSP2:th.34">Th34</a></i>
;<br/>
<b>hence </b><a NAME="E7:44"/>
 <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</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="c2">y</font></span>)</span>
 <b>by </b><i><a class="txt" href="complsp2.html#E1:44"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="complsp2.html#E3:44"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="complsp2.html#E4:44"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="complsp2.html#E5:44"><i><font color="Green" title="E39">A5</font></i></a>, <a class="ref" href="complsp2.html#T32" target="_self" title="COMPLSP2:th.32">Th32</a></i>;<br/>


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