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<span class="kw">let </span><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font> be   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><br/>



<a NAME="E1:13"/>
<span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p3">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T60" title="EUCLID:th.60">EUCLID:60</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:13"/>
 <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">z2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_3.html#T10" target="_self" title="EUCLID_3:th.10">Th10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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