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<b>take </b>
<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="Maroon" title="c3">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="Maroon" title="c4">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="Maroon" title="c5">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="Maroon" title="c6">y4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  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">y</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; <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="Maroon" title="c3">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="Maroon" title="c4">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="Maroon" title="c5">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="Maroon" title="c6">y4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <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><br/>

<b>thus </b><a NAME="E1:73_1_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">y</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; <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="Maroon" title="c3">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="Maroon" title="c4">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="Maroon" title="c5">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="Maroon" title="c6">y4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <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> )
 <b>by </b><i><a class="txt" href="quaterni.html#E3:73"><i><font color="Green" title="E45">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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