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<a NAME="E1:40"/><i><font color="Green" title="E21">A1</font></i>: 
 <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&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">0,1,0,0</span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 
<b>by </b><i><a class="ref" href="quaterni.html#D6" target="_self" title="QUATERNI:def.6">Def6</a></i>;<br/>
<b>then </b><i><font color="Green" title="E22">A2</font></i>: <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a>  <a href="quaterni.html#K10" title="QUATERNI:func.10">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</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">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#D10" target="_self" title="QUATERNI:def.10">Def10</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default">0,0,0,1</span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>

;<br/>
<i><font color="Green" title="E23">A3</font></i>: <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a>  <a href="quaterni.html#K10" title="QUATERNI:func.10">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</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">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default">0 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0</span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="quaterni.html#E1:40"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="quaterni.html#D10" target="_self" title="QUATERNI:def.10">Def10</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default">0,0,0,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>

;<br/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a>  <a href="quaterni.html#K10" title="QUATERNI:func.10">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span> <a href="quaterni.html#K7" title="QUATERNI:func.7">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a>  <a href="quaterni.html#K10" title="QUATERNI:func.10">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span> = 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><span class="p2">(<span class="default">0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0</span>)</span>,<span class="p2">(<span class="default">0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0</span>)</span>,<span class="p2">(<span class="default">0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0</span>)</span>,<span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="quaterni.html#E2:40"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="quaterni.html#E3:40"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="quaterni.html#D7" target="_self" title="QUATERNI:def.7">Def7</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="quaterni.html#E24"><i><font color="Green" title="E18">Lm5</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E5:40"/>
<a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a>  <a href="quaterni.html#K10" title="QUATERNI:func.10">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K8" title="QUATERNI:func.8">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a>  <a href="quaterni.html#K10" title="QUATERNI:func.10">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span>
 <b>by </b><i><a class="ref" href="quaterni.html#D8" target="_self" title="QUATERNI:def.8">Def8</a></i>;<br/>


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