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<span class="kw">let </span><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</font>, <font color="Maroon" title="c3">x3</font>, <font color="Maroon" title="c4">x4</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a>  <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="Maroon" title="c1">x1</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x3</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">c</font> = <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>;<br/>
<a NAME="E1:28"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E2:28"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E3:28"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<a NAME="E4:28"/>
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x4</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:28"/>
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font>,<font color="Maroon" title="c3">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> <a href="quaterni.html#K31" title="QUATERNI:func.31">*'</a>  <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="Maroon" title="c1">x1</font>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">x2</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">x3</font></span>)</span>,<span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x4</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="txt" href="#E1:28"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="quaterni.html#T43" title="QUATERNI:th.43">QUATERNI:43</a></span>; <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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