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<b>let </b><font color="Maroon">z1</font> be  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">z2</font> be  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">z3</font> be  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">z4</font> be  <a href="quaterni.html#V1" target="_self">quaternion</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<a NAME="E1:66"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z2</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z3</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z4</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="quaterni.html#K6" target="_self">[*</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"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z4</font></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"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z4</font></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"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z4</font></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"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z4</font></span>)</span></span>)</span></span><a href="quaterni.html#K6" target="_self">*]</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:66"/>
(  <a href="quaterni.html#K17" target="_self">Rea</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z2</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z3</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z4</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z4</font></span>)</span> &amp;  <a href="quaterni.html#K18" target="_self">Im1</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z2</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z3</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z4</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z4</font></span>)</span> &amp;  <a href="quaterni.html#K19" target="_self">Im2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z2</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z3</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z4</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z4</font></span>)</span> &amp;  <a href="quaterni.html#K20" target="_self">Im3</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z1</font> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z2</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z3</font></span>)</span> <a href="quaterni.html#K7" target="_self">+</a> <font color="Maroon">z4</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z3</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z4</font></span>)</span> )
 <b>by </b><i/>;<br/>


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