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<b>let </b><font color="Maroon" title="c11">c1</font>, <font color="Maroon" title="c12">c2</font> be    <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>given </b><font color="Maroon" title="c13">x1</font>, <font color="Maroon" title="c14">x2</font>, <font color="Maroon" title="c15">x3</font>, <font color="Maroon" title="c16">x4</font>, <font color="Maroon" title="c17">y1</font>, <font color="Maroon" title="c18">y2</font>, <font color="Maroon" title="c19">y3</font>, <font color="Maroon" title="c20">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> <b> such that </b><a NAME="E1:27_1_2"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c1">x</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="Maroon" title="c13">x1</font>,<font color="Maroon" title="c14">x2</font>,<font color="Maroon" title="c15">x3</font>,<font color="Maroon" title="c16">x4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 <b>and </b><br/><a NAME="E2:27_1_2"/><i><font color="Green" title="E20">A4</font></i>: 
<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="Maroon" title="c17">y1</font>,<font color="Maroon" title="c18">y2</font>,<font color="Maroon" title="c19">y3</font>,<font color="Maroon" title="c20">y4</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 <b>and </b><br/><a NAME="E3:27_1_2"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c11">c1</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="Maroon" title="c13">x1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c17">y1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">x2</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c18">y2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c15">x3</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c19">y3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c16">x4</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c20">y4</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 ;<br/>

<b>given </b><font color="Maroon" title="c21">x1'</font>, <font color="Maroon" title="c22">x2'</font>, <font color="Maroon" title="c23">x3'</font>, <font color="Maroon" title="c24">x4'</font>, <font color="Maroon" title="c25">y1'</font>, <font color="Maroon" title="c26">y2'</font>, <font color="Maroon" title="c27">y3'</font>, <font color="Maroon" title="c28">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> <b> such that </b><a NAME="E4:27_1_2"/><i><font color="Green" title="E22">A6</font></i>: 
<font color="Maroon" title="c1">x</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="Maroon" title="c21">x1'</font>,<font color="Maroon" title="c22">x2'</font>,<font color="Maroon" title="c23">x3'</font>,<font color="Maroon" title="c24">x4'</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 <b>and </b><br/><a NAME="E5:27_1_2"/><i><font color="Green" title="E23">A7</font></i>: 
<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="Maroon" title="c25">y1'</font>,<font color="Maroon" title="c26">y2'</font>,<font color="Maroon" title="c27">y3'</font>,<font color="Maroon" title="c28">y4'</font></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 <b>and </b><br/><a NAME="E6:27_1_2"/><i><font color="Green" title="E24">A8</font></i>: 
<font color="Maroon" title="c12">c2</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="Maroon" title="c21">x1'</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c25">y1'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c22">x2'</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c26">y2'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c23">x3'</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c27">y3'</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c24">x4'</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c28">y4'</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 ;<br/>

<a NAME="E7:27_1_2"/>
( <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">x1'</font> &amp; <font color="Maroon" title="c14">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">x2'</font> &amp; <font color="Maroon" title="c15">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">x3'</font> &amp; <font color="Maroon" title="c16">x4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">x4'</font> &amp; <font color="Maroon" title="c17">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">y1'</font> &amp; <font color="Maroon" title="c18">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">y2'</font> &amp; <font color="Maroon" title="c19">y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">y3'</font> &amp; <font color="Maroon" title="c20">y4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">y4'</font> )
 
<b>by </b><i><a class="txt" href="quaterni.html#E1:27_1_2"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="quaterni.html#E2:27_1_2"><i><font color="Green" title="E20">A4</font></i></a>, <a class="txt" href="quaterni.html#E4:27_1_2"><i><font color="Green" title="E22">A6</font></i></a>, <a class="txt" href="quaterni.html#E5:27_1_2"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="quaterni.html#T12" target="_self" title="QUATERNI:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E8:27_1_2"/>
<font color="Maroon" title="c11">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">c2</font>
 <b>by </b><i><a class="txt" href="quaterni.html#E3:27_1_2"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="quaterni.html#E6:27_1_2"><i><font color="Green" title="E24">A8</font></i></a></i>;<br/>


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