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<b>let </b><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> ;<br/>

<b>assume </b><a NAME="E1:103"/><i><font color="Green" title="E54">A1</font></i>: 
(  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp;  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 ;<br/>

<i><font color="Green" title="E55">A2</font></i>: <font color="Maroon" title="c1">z</font> = 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,0,0,0</span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="quaterni.html#E1:103"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="quaterni.html#T24" target="_self" title="QUATERNI:th.24">Th24</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#D6" target="_self" title="QUATERNI:def.6">Def6</a></i>
<br/>.= 
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font>
<b>by </b><i><a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>
;<br/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</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="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,0,0,0</span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="quaterni.html#E1:103"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="quaterni.html#T43" target="_self" title="QUATERNI:th.43">Th43</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,0</span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#D6" target="_self" title="QUATERNI:def.6">Def6</a></i>
<br/>.= 
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font>
<b>by </b><i><a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E4:103"/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font>
 <b>by </b><i><a class="txt" href="quaterni.html#E2:103"><i><font color="Green" title="E55">A2</font></i></a></i>;<br/>


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