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

<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">d</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">a'</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b'</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c'</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">d'</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>















<b>assume </b><a NAME="E1:23"/><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#K7" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,<font color="Olive">x</font>
 ;<br/>

<a NAME="E2:23"/><b>then </b>
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,0 <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,0
 
;<br/>
<a NAME="E3:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">0 <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">0 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,0
 
;<br/>
<a NAME="E4:23"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">0 <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">0 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</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">a'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">0 <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">0 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d'</font>
 
;<br/>
<a NAME="E5:23"/><i><font color="Green">E37</font></i>: 
0 <a href="prepower.html#K3">|^</a> 3 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/>
<a NAME="E6:23"/>
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,1 <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,1
 
<b>by </b><i/>;<br/>
<a NAME="E7:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">1 <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,1
 
;<br/>
<a NAME="E8:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="p3">(<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> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,1
 
<b>by </b><i><a class="ref" href="newton.html#T15">NEWTON:15</a></i>;<br/>
<b>then </b><i><font color="Green">E38</font></i>: <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#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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="p3">(<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> <span class="p2">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d'</font>
<b>by </b><i><a class="ref" href="newton.html#T15">NEWTON:15</a></i>
<br/>.= 
<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#K2">+</a> <font color="Maroon">c'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d'</font>

;<br/>
<b>set </b><font color="Maroon">r1</font> = <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>;<br/>
<b>set </b><font color="Maroon">r2</font> = <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>;<br/>
<a NAME="E10:23"/>
<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#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</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#K2">+</a> <font color="Maroon">c'</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E11:23"/><b>then </b><i><font color="Green">E39</font></i>: 
<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"><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>
 
;<br/>
<a NAME="E12:23"/>
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</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#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E13:23"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<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></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</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">d</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>
 
;<br/>
<a NAME="E14:23"/>
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="prepower.html#K3">|^</a> 3 = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default">1 <a href="prepower.html#K3">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="power.html#T2">POWER:2</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="real_1.html#K4">*</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
;<br/>
<a NAME="E16:23"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="prepower.html#K3">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T15">NEWTON:15</a></i>;<br/>
<a NAME="E17:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<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></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</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">d</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"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<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></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c'</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">d'</font>
 
<b>by </b><i/>;<br/>
<a NAME="E18:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</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">d</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"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c'</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">d'</font>
 
;<br/>
<a NAME="E19:23"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</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"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c'</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d'</font>
 
;<br/>
<b>set </b><font color="Maroon">r3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font>;<br/>
<b>set </b><font color="Maroon">r4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c'</font>;<br/>
<a NAME="E20:23"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c'</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E21:23"/><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#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b'</font>
 
<b>by </b><i/>;<br/>
<a NAME="E22:23"/><b>then </b><i><font color="Green">E51</font></i>: 
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="E23:23"/>
<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#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E24:23"/><b>then </b>
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font></span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font></span>)</span>
 
;<br/>
<a NAME="E25:23"/><b>then </b>
<font color="Maroon">a'</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font>
 
;<br/>
<a NAME="E26:23"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font>
 
;<br/>
<a NAME="E27:23"/>
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,2 <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,2
 
<b>by </b><i/>;<br/>
<a NAME="E28:23"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">2 <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>,<font color="Maroon">c'</font>,<font color="Maroon">d'</font>,2
 
;<br/>
<i><font color="Green">E54</font></i>: 2 <a href="prepower.html#K3">|^</a> 3 = 
2 <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="prepower.html#K3">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 2
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="prepower.html#K3">|^</a> 1</span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="real_1.html#K4">*</a> 2
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="prepower.html#K3">|^</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>

;<br/>
<i><font color="Green">E55</font></i>: 2 <a href="prepower.html#K3">|^</a> 1 = 
2 <a href="power.html#K4">to_power</a> 1
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
;<br/>
<b>set </b><font color="Maroon">r5</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 8</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">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon">r6</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> 8</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">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span>;<br/>
<a NAME="E31:23"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 8</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d</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">a'</font> <a href="xcmplx_0.html#K3">*</a> 8</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">d'</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E32:23"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> 8</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a'</font> <a href="xcmplx_0.html#K3">*</a> 8</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b'</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default">2 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, </i>;<br/>
<a NAME="E33:23"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 8 <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">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2
 
<b>by </b><i>, </i>;<br/>
<a NAME="E34:23"/><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#K6">-</a> <font color="Maroon">a'</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 8</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E35:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 6 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E36:23"/><b>then </b>
( <font color="Maroon">c'</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> 0 or 6 <a href="hidden.html#R1">=</a> 0 )
 
;<br/>
<b>hence </b><a NAME="E37:23"/>
( <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> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d'</font> )
 <b>by </b><i>, , , </i>;<br/>


</div>
