<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">a2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">a3</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c3</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">A1'</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">B1</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">B1'</font> be   <a href="real_1.html#NM1">Real</a>;<br/>









<b>assume </b><a NAME="E1:37"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">A1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1'</font> <a href="real_1.html#K3">+</a> <font color="Maroon">B1'</font> &amp; <font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B1'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">c2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 ;<br/>

<a NAME="E2:37"/><b>then </b>
( <font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A1'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a3</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font> &amp; <font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a3</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B1'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">a3</font> )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T4">XCMPLX_1:4</a></i>;<br/>
<a NAME="E3:37"/><b>then </b><i><font color="Green">E59</font></i>: 
( <font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A1'</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> &amp; <font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">a3</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">B1'</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> )
 
;<br/>
<a NAME="E4:37"/>
<span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A1'</font> <a href="real_1.html#K3">+</a> <font color="Maroon">B1'</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T8">XCMPLX_1:8</a></i>;<br/>
<a NAME="E5:37"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:37"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span></span>)</span>
 
;<br/>
<a NAME="E7:37"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span></span>)</span>
 
;<br/>
<a NAME="E8:37"/><b>then </b>
<font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E9:37"/><b>then </b>
<font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E10:37"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T4">XCMPLX_1:4</a></i>;<br/>
<a NAME="E11:37"/>
<span class="p1">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, </i>;<br/>
<a NAME="E12:37"/><b>then </b>
<font color="Maroon">A1</font> <a href="real_1.html#K4">*</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E13:37"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c3</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">a3</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">B1</font>
 ;<br/>


</div>
