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<span class="kw">let </span><font color="Maroon" title="c1">g</font> be   <a href="quaterni.html#NM1" title="QUATERNI:NM.1">Quaternion</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">t</font>, <font color="Olive" title="b4">u</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 <font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K5" title="QUATERNI:func.5">[*</a><span class="default"><font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">t</font>,<font color="Olive" title="b4">u</font></span><a href="quaterni.html#K5" title="QUATERNI:func.5">*]</a></span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c4">t</font>, <font color="Maroon" title="c5">u</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E2:1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K5" title="QUATERNI:func.5">[*</a><span class="default"><font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">t</font>,<font color="Maroon" title="c5">u</font></span><a href="quaterni.html#K5" title="QUATERNI:func.5">*]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T7" onmouseover="rs('quaterni/T7')" onmouseout="rh()">QUATERNI:7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">r</font> = <font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c7">s</font> = <font color="Maroon" title="c3">s</font>, <font color="Maroon" title="c8">t</font> = <font color="Maroon" title="c4">t</font>, <font color="Maroon" title="c9">u</font> = <font color="Maroon" title="c5">u</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_0.html#D1" onmouseover="rs('xreal_0/D1')" onmouseout="rh()">XREAL_0:def 1</a></span>;<br/>
<a NAME="E4:1"/>
<font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K5" title="QUATERNI:func.5">[*</a><span class="default"><font color="Maroon" title="c6">r</font>,<font color="Maroon" title="c7">s</font>,<font color="Maroon" title="c8">t</font>,<font color="Maroon" title="c9">u</font></span><a href="quaterni.html#K5" title="QUATERNI:func.5">*]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:1"><span class="lab"><font color="Green" title="E2">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:1"/>
 ex <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</font>, <font color="Olive" title="b3">t</font>, <font color="Olive" title="b4">u</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 <font color="Maroon" title="c1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K5" title="QUATERNI:func.5">[*</a><span class="default"><font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b3">t</font>,<font color="Olive" title="b4">u</font></span><a href="quaterni.html#K5" title="QUATERNI:func.5">*]</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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