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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>





<i><font color="Green" title="E6">A1</font></i>: <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  = 
<span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> 1
<b>by </b><i><a class="ref" href="euclid_5.html#D1" target="_self" title="EUCLID_5:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c1">x</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<i><font color="Green" title="E7">A2</font></i>: <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  = 
<span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> 2
<b>by </b><i><a class="ref" href="euclid_5.html#D2" target="_self" title="EUCLID_5:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c2">y</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  = 
<span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> 3
<b>by </b><i><a class="ref" href="euclid_5.html#D3" target="_self" title="EUCLID_5:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c3">z</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
;<br/>
<b>hence </b><a NAME="E4:4"/>
( <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K1" title="EUCLID_5:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K2" title="EUCLID_5:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> &amp; <span class="p1"><a href="euclid_5.html#K4" title="EUCLID_5:func.4">|[</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">z</font></span><a href="euclid_5.html#K4" title="EUCLID_5:func.4">]|</a></span> <a href="euclid_5.html#K3" title="EUCLID_5:func.3">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> )
 <b>by </b><i><a class="txt" href="euclid_5.html#E1:4"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="euclid_5.html#E2:4"><i><font color="Green" title="E7">A2</font></i></a></i>;<br/>


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