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<b>let </b><font color="Maroon" title="c1">c1</font>, <font color="Maroon" title="c2">c2</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span><br/>



<span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quaterni.html#T56" title="QUATERNI:th.56">QUATERNI:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T17" target="_self" title="QUATERN2:th.17">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T18" target="_self" title="QUATERN2:th.18">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T18" target="_self" title="QUATERN2:th.18">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T20" target="_self" title="QUATERN2:th.20">Thd3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T21" target="_self" title="QUATERN2:th.21">Thd4a</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T22" target="_self" title="QUATERN2:th.22">Thd5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T2" target="_self" title="QUATERN2:th.2">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span>
<b>by </b><i><a class="ref" href="quatern2.html#T2" target="_self" title="QUATERN2:th.2">Th5</a></i>
;<br/>
<b>hence </b><a NAME="E2:79"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">c2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">c1</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c1">c1</font></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c2</font> <a href="quatern2.html#K18" title="QUATERN2:func.18">.|.</a> <font color="Maroon" title="c2">c2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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