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

<b>let </b><font color="Maroon">a</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">c</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">a'</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b'</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">c'</font> be  <a href="xcmplx_0.html#V1">complex</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">x</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds   <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Olive">x</font>
 ;<br/>

<a NAME="E2:10"/><b>then </b>
 <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,0 <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,0
 
;<br/>
<a NAME="E3:10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">0 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,0
 
;<br/>
<a NAME="E4:10"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font>
 
;<br/>
<a NAME="E5:10"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E6:10"/>
 <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,1 <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,1
 
<b>by </b><i/>;<br/>
<a NAME="E7:10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,1
 
;<br/>
<a NAME="E8:10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font>
 
;<br/>
<a NAME="E9:10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E10:10"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font>
 
;<br/>
<a NAME="E11:10"/>
 <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E12:10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font>
 
;<br/>
<a NAME="E13:10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font>
 
;<br/>
<a NAME="E14:10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font>
 
;<br/>
<a NAME="E15:10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font>
 
;<br/>
<a NAME="E16:10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a'</font>
 
;<br/>
<a NAME="E17:10"/><b>then </b>
<font color="Maroon">c</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a'</font></span>)</span>
 
;<br/>
<a NAME="E18:10"/><b>then </b><i><font color="Green">E39</font></i>: 
0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a'</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E19:10"/><b>then </b>
<font color="Maroon">b'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font>
 
;<br/>
<a NAME="E20:10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<a NAME="E21:10"/><b>then </b>
2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b'</font> <a href="hidden.html#R1">=</a> 2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font>
 
;<br/>
<a NAME="E22:10"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">b'</font> <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font>
 
;<br/>
<a NAME="E23:10"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a'</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E24:10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b'</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font>
 
;<br/>
<a NAME="E25:10"/><b>then </b>
2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> 2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font>
 
;<br/>
<a NAME="E26:10"/><b>then </b>
<font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font>
 
;<br/>
<b>hence </b><a NAME="E27:10"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> )
 <b>by </b><i>, </i>;<br/>


</div>
