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

<span class="lab"><font color="Green" title="E19">A1</font></span>:  <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a>  = 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T91" title="QUATERNI:th.91">QUATERNI:91</a></span>
;<br/>
<a NAME="E2:90"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A2</font></span>: 
(  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E3:90"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
(  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:90"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> <a href="quatern3.html#K2" title="QUATERN3:func.2">^2</a>  = 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span></span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern3.html#T78" target="_self" title="QUATERN3:th.78">Th78</a></span>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:90"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E3:90"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="quaterni.html#T91" title="QUATERNI:th.91">QUATERNI:91</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="arytm_0.html#D5" title="ARYTM_0:def.5">ARYTM_0:def 5</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:90"/>
<a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> <a href="quatern3.html#K4" title="QUATERN3:func.4">^3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
