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<b>let </b><font color="Maroon" title="c1">c</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"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span></span><br/>

<i><font color="Green" title="E29">A1</font></i>:  <a href="quatern2.html#K2" title="QUATERN2:func.2">1q</a>  = 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#D6" title="QUATERNI:def.6">QUATERNI:def 6</a></i>
;<br/>
<b>consider </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">x3</font>, <font color="Maroon" title="c5">x4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E3:45"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c1">c</font> <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"><font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">x3</font>,<font color="Maroon" title="c5">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 <b>by </b><i><a class="txt" href="quatern2.html#E1"><i><font color="Green" title="E1">QUA7</font></i></a></i>;<br/>
<a NAME="E4:45"/><i><font color="Green" title="E31">A3</font></i>: 
 <a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font> <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="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x3</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">x4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 
<b>by </b><i><a class="txt" href="#E3:45"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="quatern2.html#T4" target="_self" title="QUATERN2:th.4">Thc1</a></i>;<br/>
<a NAME="E5:45"/><i><font color="Green" title="E32">A4</font></i>: 
<span class="p1"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span>
 
<b>by </b><i><a class="ref" href="quaterni.html#T72" title="QUATERNI:th.72">QUATERNI:72</a></i>;<br/>
<i><font color="Green" title="E33">A6</font></i>: <font color="Maroon" title="c1">c</font> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E3:45"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="quatern2.html#D1" target="_self" title="QUATERN2:def.1">Def1</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</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"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</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"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>

;<br/>
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">x4</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">x4</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">x4</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x3</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">x4</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span></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><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E4:45"><i><font color="Green" title="E31">A3</font></i></a>, <a class="ref" href="quatern2.html#D1" target="_self" title="QUATERN2:def.1">Def1</a></i>
<br/>.= 
<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> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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="p2">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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="p2">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><span class="p4"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="#E5:45"><i><font color="Green" title="E32">A4</font></i></a></i>
;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </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> <font color="Maroon" title="c1">c</font></span>)</span> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span> = 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">x3</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p5">(<span class="default"><span class="p0"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">x4</font> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p4">(<span class="default"><span class="p5"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">c</font></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>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="#E6:45"><i><font color="Green" title="E33">A6</font></i></a>, <a class="ref" href="quaterni.html#D7" title="QUATERNI:def.7">QUATERNI:def 7</a></i>
<br/>.= 
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#D6" title="QUATERNI:def.6">QUATERNI:def 6</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E9:45"/>
<span class="p1">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c1">c</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="quatern2.html#K8" title="QUATERN2:func.8">"</a> </span>)</span>
 <b>by </b><i><a class="ref" href="quaterni.html#D8" title="QUATERNI:def.8">QUATERNI:def 8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
