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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font> implies <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font> )</span><br/>



<b>assume </b><a NAME="E1:5"/><i><font color="Green" title="E3">A1</font></i>: 
 <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_3.html#K1" title="EUCLID_3:func.1">cpx2euc</a> <font color="Maroon" title="c2">z2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font></span><br/>

<a NAME="E2:5"/>
<font color="Maroon" title="c2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="euclid_3.html#K2" title="EUCLID_3:func.2">euc2cpx</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>
 
<b>by </b><i><a class="ref" href="euclid_3.html#T1" target="_self" title="EUCLID_3:th.1">Th1</a></i>;<br/>
<b>hence </b><a NAME="E3:5"/>
<font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font>
 <b>by </b><i><a class="txt" href="#E1:5"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="euclid_3.html#T1" target="_self" title="EUCLID_3:th.1">Th1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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