<?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"> <font color="Maroon" title="c1">z</font> <a href="quatern3.html#K3" title="QUATERN3:func.3">^3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quatern3.html#K4" title="QUATERN3:func.4">^3</a></span>)</span></span><br/>

<a NAME="E1:96"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c1">z</font> <a href="quatern3.html#K3" title="QUATERN3:func.3">^3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern3.html#K1" title="QUATERN3:func.1">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T16" title="QUATERN2:th.16">QUATERN2:16</a></span>;<br/>
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quatern3.html#K4" title="QUATERN3:func.4">^3</a>  = 
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quatern3.html#K2" title="QUATERN3:func.2">^2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T16" title="QUATERN2:th.16">QUATERN2:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern3.html#K1" title="QUATERN3:func.1">^2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern3.html#T81" target="_self" title="QUATERN3:th.81">Th81</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern3.html#K1" title="QUATERN3:func.1">^2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T19" title="QUATERN2:th.19">QUATERN2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern3.html#K1" title="QUATERN3:func.1">^2</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T16" title="QUATERN2:th.16">QUATERN2:16</a></span>
<br/>.= 
 <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quatern3.html#K3" title="QUATERN3:func.3">^3</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:96"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="quatern2.html#T19" title="QUATERN2:th.19">QUATERN2:19</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:96"/>
<font color="Maroon" title="c1">z</font> <a href="quatern3.html#K3" title="QUATERN3:func.3">^3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="quatern3.html#K4" title="QUATERN3:func.4">^3</a></span>)</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>
