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<span class="kw">let </span><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">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"> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z1</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c2">z2</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c1">z1</font></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span></span><br/>



<a NAME="E1:42"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z1</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c2">z2</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T86" title="QUATERNI:th.86">QUATERNI:86</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:42"/>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c1">z1</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><font color="Maroon" title="c2">z2</font></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="quatern2.html#K3" title="QUATERN2:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c1">z1</font></span>)</span></span><a href="quatern2.html#K3" title="QUATERN2:func.3">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="quaterni.html#T83" title="QUATERNI:th.83">QUATERNI:83</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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