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<span class="lab"><font color="Green" title="E18">A1</font></span>:  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span> = 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>
<br/>.= 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T31" title="QUATERNI:th.31">QUATERNI:31</a>, <a class="ref" href="quaterni.html#T71" title="QUATERNI:th.71">QUATERNI:71</a></span>
;<br/>
<span class="lab"><font color="Green" title="E19">A2</font></span>:  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span> = 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T31" title="QUATERNI:th.31">QUATERNI:31</a></span>
;<br/>
<span class="lab"><font color="Green" title="E20">A3</font></span>:  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span> = 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T31" title="QUATERNI:th.31">QUATERNI:31</a></span>
;<br/>
<span class="lab"><font color="Green" title="E21">A4</font></span>:  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1">(<span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T29" title="QUATERN2:th.29">QUATERN2:29</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T31" title="QUATERNI:th.31">QUATERNI:31</a></span>
;<br/>
<span class="lab"><font color="Green" title="E22">A5</font></span>: <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quatern2.html#K8" title="QUATERN2:func.8">"</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="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</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="#E4:79"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="quaterni.html#T24" title="QUATERNI:th.24">QUATERNI:24</a></span>
<br/>.= 
 <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T4" title="QUATERN2:th.4">QUATERN2:4</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E6:79"/>
<a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a>  <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:79"><span class="lab"><font color="Green" title="E22">A5</font></span></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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