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

<span class="kw">let </span><font color="Maroon" title="c1">z</font> be   <a href="quaterni.html#V1" title="QUATERNI:attr.1">quaternion</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span><br/>

<a NAME="E1:48"/>
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E2:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E3:48"/>
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E4:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E5:48"/>
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E6:48"/><span class="kw">then </span>
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E7:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E12">A3</font></span>: 
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T73" title="QUATERNI:th.73">QUATERNI:73</a></span>;<br/>
<a NAME="E8:48"/>
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E9:48"/><span class="kw">then </span>
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E10:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A4</font></span>: 
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T73" title="QUATERNI:th.73">QUATERNI:73</a></span>;<br/>
<a NAME="E11:48"/>
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E12:48"/><span class="kw">then </span>
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E13:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A5</font></span>: 
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T73" title="QUATERNI:th.73">QUATERNI:73</a></span>;<br/>
<a NAME="E14:48"/>
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E15:48"/><span class="kw">then </span>
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E16:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A6</font></span>: 
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T73" title="QUATERNI:th.73">QUATERNI:73</a></span>;<br/>
<a NAME="E17:48"/>
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E18:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A7</font></span>: 
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<a NAME="E19:48"/>
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>;<br/>
<a NAME="E20:48"/><span class="kw">then </span>
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T44" title="QUATERNI:th.44">QUATERNI:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:48"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a></span>)</span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E18:48"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E16:48"><span class="lab"><font color="Green" title="E15">A6</font></span></a>, <a class="txt" href="#E10:48"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E7:48"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E13:48"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="quaterni.html#T25" title="QUATERNI:th.25">QUATERNI:25</a></span>; <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>
