<?xml version="1.0"?>
<div class="add">

<a NAME="E1:32_1_1"/>
 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">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="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">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"><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> )
 
<b>by </b><i><a class="ref" href="quaterni.html#D7" target="_self" title="QUATERNI:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E2:32_1_1"/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K7" title="QUATERNI:func.7">+</a> <font color="Maroon" title="c2">z'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="quaterni.html#K1" title="QUATERNI:func.1">QUATERNION</a> 
 ; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
