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<a NAME="E1:75_2_1"/>
 ex <font color="Olive" title="b1">y1</font>, <font color="Olive" title="b2">y2</font>, <font color="Olive" title="b3">y3</font>, <font color="Olive" title="b4">y4</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>  st <br/>( <font color="Maroon" title="c2">z9</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="Olive" title="b1">y1</font>,<font color="Olive" title="b2">y2</font>,<font color="Olive" title="b3">y3</font>,<font color="Olive" title="b4">y4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> &amp; <font color="Maroon" title="c1">x</font> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <font color="Maroon" title="c2">z9</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"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b2">y2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b3">y3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b4">y4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#D21" target="_self" title="QUATERNI:def.21">Def21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:75_2_1"/>
<font color="Maroon" title="c1">x</font> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <font color="Maroon" title="c2">z9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quaterni.html#K1" title="QUATERNI:func.1">QUATERNION</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="quaterni.html#D2" target="_self" title="QUATERNI:def.2">QUATERNI:def 2</a> <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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