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<span class="kw">let </span><font color="Maroon" title="c1">z</font>, <font color="Maroon" title="c2">z1</font>, <font color="Maroon" title="c3">z2</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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">z</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c3">z2</font></span><br/>





<span class="lab"><font color="Green" title="E14">A1</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c3">z2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <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> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> </span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c2">z1</font></span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c3">z2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T19" title="QUATERN2:th.19">QUATERN2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <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> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> </span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c2">z1</font></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> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> </span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T19" title="QUATERN2:th.19">QUATERN2:19</a></span>
;<br/>
<span class="lab"><font color="Green" title="E15">A2</font></span>:  <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> </span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <font color="Maroon" title="c3">z2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T19" title="QUATERN2:th.19">QUATERN2:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> </span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c2">z1</font></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> <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a> </span>)</span> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T17" title="QUATERN2:th.17">QUATERN2:17</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E3:56"/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <font color="Maroon" title="c3">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z1</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c3">z2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="quatern2.html#T2" title="QUATERN2:th.2">QUATERN2:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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