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<span class="kw">let </span><font color="Maroon" title="c1">z1</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="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><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">2 <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> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">z</font> =  <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> ;<br/>
<a NAME="E1:25"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><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">z1</font></span>)</span></span>)</span>,<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">z1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></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="quatern2.html#T1" title="QUATERN2:th.1">QUATERN2:1</a>, <a class="ref" href="quaterni.html#T31" title="QUATERNI:th.31">QUATERNI:31</a></span>;<br/>
<a NAME="E2:25"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
(  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font> &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E3:25"/><span class="lab"><font color="Green" title="E8">A3</font></span>: 
<font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><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">z1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span>,<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">z1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></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="quatern2.html#T1" title="QUATERN2:th.1">QUATERN2:1</a>, <a class="ref" href="quaterni.html#T31" title="QUATERNI:th.31">QUATERNI:31</a></span>;<br/>
<a NAME="E4:25"/><span class="lab"><font color="Green" title="E9">A4</font></span>: 
(  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</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> <font color="Maroon" title="c1">z1</font></span>)</span> &amp;  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E5:25"/><span class="lab"><font color="Green" title="E10">A5</font></span>: 
(  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</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> <font color="Maroon" title="c1">z1</font></span>)</span> &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E6:25"/><span class="lab"><font color="Green" title="E11">A6</font></span>: 
(  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></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> <font color="Maroon" title="c1">z1</font></span>)</span> &amp;  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></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> <font color="Maroon" title="c1">z1</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E7:25"/><span class="lab"><font color="Green" title="E12">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p0">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:25"><span class="lab"><font color="Green" title="E11">A6</font></span></a>, <a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E9">A4</font></span></a>, <a class="txt" href="#E5:25"><span class="lab"><font color="Green" title="E10">A5</font></span></a>, <a class="ref" href="quaterni.html#D22" title="QUATERNI:def.22">QUATERNI:def 22</a></span>;<br/>
<span class="kw">thus </span><a NAME="E8:25"/>
<span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><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">2 <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> <font color="Maroon" title="c1">z1</font></span>)</span></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<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"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></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="txt" href="#E7:25"><span class="lab"><font color="Green" title="E12">A7</font></span></a>, <a class="ref" href="quatern2.html#T1" title="QUATERN2:th.1">QUATERN2:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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