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

<b>assume </b><a NAME="E1:103"/><i><font color="Green">E37</font></i>: 
(  <a href="quaterni.html#K18" target="_self">Im1</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="quaterni.html#K19" target="_self">Im2</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="quaterni.html#K20" target="_self">Im3</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<i><font color="Green">E40</font></i>: <font color="Maroon">z</font> = 
<span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font></span>)</span>,0,0,0</span><a href="quaterni.html#K6" target="_self">*]</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font></span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i/>
<br/>.= 
 <a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font>
<b>by </b><i><a class="ref" href="arytm_0.html#D7">ARYTM_0:def 7</a></i>
;<br/>
<font color="Maroon">z</font> <a href="quaterni.html#K31" target="_self">*'</a>  = 
<span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font></span>)</span>,0,0,0</span><a href="quaterni.html#K6" target="_self">*]</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font></span>)</span>,0</span><a href="arytm_0.html#K5">*]</a></span>
<b>by </b><i/>
<br/>.= 
 <a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font>
<b>by </b><i><a class="ref" href="arytm_0.html#D7">ARYTM_0:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E4:103"/>
<font color="Maroon">z</font> <a href="quaterni.html#K31" target="_self">*'</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="quaterni.html#T7" target="_self">Th7</a></i>;<br/>


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