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<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font> &amp;  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font></span>)</span> &amp;  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font></span>)</span> &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font></span>)</span> )</span><br/>

<a NAME="E1:97"/>
<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> <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>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font></span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="quaterni.html#E76"><span class="lab"><font color="Green" title="E48">Lm20</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:97"/>
(  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font> &amp;  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font></span>)</span> &amp;  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font></span>)</span> &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T23" target="_self" title="QUATERNI:th.23">Th23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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