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 ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">y1</font>, <font color="Olive" title="b6">y2</font>, <font color="Olive" title="b7">y3</font>, <font color="Olive" title="b8">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="c1">z</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">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> &amp; <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="b5">y1</font>,<font color="Olive" title="b6">y2</font>,<font color="Olive" title="b7">y3</font>,<font color="Olive" title="b8">y4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> &amp; <font color="Maroon" title="c1">z</font> <a href="quaterni.html#K7" title="QUATERNI:func.7">+</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="Olive" title="b1">x1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b5">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">x2</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b6">y2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">x3</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b7">y3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b4">x4</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b8">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#D7" target="_self" title="QUATERNI:def.7">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:33_1_1"/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K7" title="QUATERNI:func.7">+</a> <font color="Maroon" title="c2">z9</font> is  <a href="quaterni.html#V1" title="QUATERNI:attr.1">quaternion</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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