<?xml version="1.0"?>
<div class="add">

<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> implies  <a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:43"/>
(  <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">x2</font> = <font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c5">y2</font> = <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c6">z2</font> = <font color="Maroon" title="c3">z</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<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> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<i><font color="Green" title="E31">A1</font></i>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> = 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">y2</font> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <font color="Maroon" title="c6">z2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
;<br/>
<i><font color="Green" title="E32">A2</font></i>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span>)</span> = 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
;<br/>
<i><font color="Green" title="E33">A3</font></i>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span> = 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <span class="p3">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c6">z2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
;<br/>
<a NAME="E6:43"/>
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> holds <br/><span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> implies <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> )</span><br/>

<b>assume </b><a NAME="E1:43_4"/><i><font color="Green" title="E34">A4</font></i>: 
<font color="Maroon" title="c7">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span><br/>

<a NAME="E2:43_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y2</font> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <font color="Maroon" title="c6">z2</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="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/>
<b>then </b><i><font color="Green" title="E35">A5</font></i>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">y2</font> <a href="complsp2.html#K3" title="COMPLSP2:func.3">+</a> <font color="Maroon" title="c6">z2</font></span>)</span> = 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<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>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="matrixc1.html#K8" title="MATRIXC1:func.8">mlt</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c8">a</font> = <font color="Maroon" title="c2">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font>;<br/>
<b>set </b><font color="Maroon" title="c9">b</font> = <font color="Maroon" title="c3">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font>;<br/>
<b>set </b><font color="Maroon" title="c10">d</font> = <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="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font>;<br/>
<b>set </b><font color="Maroon" title="c11">e</font> = <font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font>;<br/>
<a NAME="E4:43_4"/><i><font color="Green" title="E36">A6</font></i>: 
<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="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="#E4:43"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="#E1:43_4"><i><font color="Green" title="E34">A4</font></i></a>, <a class="txt" href="#E3:43_4"><i><font color="Green" title="E35">A5</font></i></a>, <a class="ref" href="complsp2.html#T1" title="COMPLSP2:th.1">COMPLSP2:1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <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="c3">z</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:43_4"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="matrixc1.html#T19" target="_self" title="MATRIXC1:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:43_4"><i><font color="Green" title="E36">A6</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="#E4:43"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="#E1:43_4"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="matrixc1.html#T19" target="_self" title="MATRIXC1:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="#E5:43"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="#E1:43_4"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="matrixc1.html#T19" target="_self" title="MATRIXC1:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="matrix_5.html#K9" title="MATRIX_5:func.9">.</a> <font color="Maroon" title="c7">i</font>
<b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="#E1:43_4"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="complsp2.html#T1" title="COMPLSP2:th.1">COMPLSP2:1</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:43"/>
 <a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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> <span class="p1">(<span class="default"><a href="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<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="matrixc1.html#K5" title="MATRIXC1:func.5">mlt</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:43"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
