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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>let </b><font color="Maroon">x</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>assume </b><a NAME="E1:67"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:67"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">x</font>,0</span><a href="arytm_0.html#K5">*]</a></span>
 
<b>by </b><i><a class="ref" href="arytm_0.html#D7">ARYTM_0:def 7</a></i>;<br/>
<a NAME="E3:67"/>
<span class="p1"><a href="arytm_0.html#K5">[*</a><span class="default"><font color="Maroon">x</font>,0</span><a href="arytm_0.html#K5">*]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="quaterni.html#K6" target="_self">[*</a><span class="default"><font color="Maroon">x</font>,0,0,0</span><a href="quaterni.html#K6" target="_self">*]</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:67"/>
(  <a href="quaterni.html#K17" target="_self">Rea</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp;  <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 )
 <b>by </b><i>, <a class="txt" href="quaterni.html#E8"><i><font color="Green">Lemma45</font></i></a>, </i>;<br/>


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