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<span class="kw">let </span><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font>, <font color="Maroon" title="c3">z3</font>, <font color="Maroon" title="c4">z4</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="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z3</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c4">z4</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z4</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c3">z3</font></span>)</span></span><br/>







<span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z4</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c3">z3</font></span>)</span> = 
<span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T24" title="QUATERN2:th.24">QUATERN2:24</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T23" title="QUATERN2:th.23">QUATERN2:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern2.html#T23" title="QUATERN2:th.23">QUATERN2:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</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">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</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="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern3.html#T55" target="_self" title="QUATERN3:th.55">Th55</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</font></span>)</span> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c3">z3</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="c1">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</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">z2</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c4">z4</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quatern3.html#T70" target="_self" title="QUATERN3:th.70">Th70</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:72"/>
<span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z3</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c4">z4</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z4</font> <a href="quaterni.html#K29" title="QUATERNI:func.29">-</a> <font color="Maroon" title="c3">z3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="quatern3.html#T57" target="_self" title="QUATERN3:th.57">Th57</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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