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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:39"/><i><font color="Green">E27</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:39"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:39"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E4:39"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E5:39"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="prepower.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="prepower.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E6:39"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0 implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0
 ;<br/>

<a NAME="E2:39_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E3:39_1"/><b>then </b>
 <a href="binari_4.html#K1" target="_self">MajP</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="binari_4.html#T22" target="_self">Th22</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:39_1"/><i><font color="Green">E32</font></i>: 
 <a href="binari_4.html#K1" target="_self">MajP</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = 2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E6:39_1"/>
2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="binari_4.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:39_1"/><b>then </b>
2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E8:39_1"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>then </b><i><font color="Green">E33</font></i>:  <a href="prepower.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="binari_4.html#E5:39_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="power.html#T32">POWER:32</a></i>
;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="nat_1.html#T63">NAT_1:63</a></i>
;<br/>
<i><font color="Green">E35</font></i>: <span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E9:39_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="int_3.html#T14">INT_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E10:39_1"><i><font color="Green">E34</font></i></a></i>
;<br/>
<i><font color="Green">E36</font></i>: <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="nat_1.html#T77">NAT_1:77</a></i>
;<br/>
<a NAME="E13:39_1"/>
2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="binari_4.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E14:39_1"/><b>then </b>
2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E15:39_1"/><b>then </b>
<span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E16:39_1"/><b>then </b>
 <a href="prepower.html#K1">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E37</font></i>: <span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="int_3.html#T14">INT_3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E12:39_1"><i><font color="Green">E36</font></i></a></i>
;<br/>
<a NAME="E18:39_1"/><i><font color="Green">E38</font></i>: 
 <a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="binari_4.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E19:39_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E20:39_1"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
;<br/>
<a NAME="E21:39_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="txt" href="binari_4.html#E19:39_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E22:39_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T148">XREAL_1:148</a></i>;<br/>
<a NAME="E23:39_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:39"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E24:39_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="binari_4.html#E18:39_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E25:39_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2
 <b>by </b><i><a class="txt" href="binari_4.html#E11:39_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="binari_4.html#E17:39_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="binari_4.html#E20:39_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="binari_4.html#E32"><i><font color="Green">Lemma21</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1"><b>suppose </b></a><a NAME="E1:39_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><i><font color="Green">E31</font></i>: <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2</span>)</span>,0,<a href="margrel1.html#K7">FALSE</a> ,<a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_4.html#E5:39"><i><font color="Green">E29</font></i></a>, <a class="ref" href="binari_3.html#D1">BINARI_3:def 1</a></i>
;<br/><span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2</span>)</span>,0,<a href="margrel1.html#K7">FALSE</a> ,<a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_4.html#E2:39"><i><font color="Green">E28</font></i></a>, <a class="ref" href="binari_3.html#D1">BINARI_3:def 1</a></i>
;<br/><b>hence </b><a NAME="E5:39_2_1"/>
<span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="binari_4.html#E3:39_2_1"><i><font color="Green">E31</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_2"><b>suppose </b></a><a NAME="E1:39_2_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0
 ;<br/><div class="add"><b>then </b><i><font color="Green">E32</font></i>: <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p0">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2</span>)</span>,0,<a href="margrel1.html#K7">FALSE</a> ,<a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_4.html#E5:39"><i><font color="Green">E29</font></i></a>, <a class="ref" href="binari_3.html#D1">BINARI_3:def 1</a></i>
;<br/><span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p2">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p5">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="binari_4.html#E1:39_2_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prepower.html#K1">abs</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p0">(<span class="default"><a href="binari_4.html#K1" target="_self">MajP</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 2</span>)</span>,0,<a href="margrel1.html#K7">FALSE</a> ,<a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="txt" href="binari_4.html#E2:39"><i><font color="Green">E28</font></i></a>, <a class="ref" href="binari_3.html#D1">BINARI_3:def 1</a></i>
;<br/><b>hence </b><a NAME="E4:39_2_2"/>
<span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="binari_4.html#E6:39"><i><font color="Green">E30</font></i></a>, <a class="txt" href="binari_4.html#E1:39_2_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="binari_4.html#E2:39_2_2"><i><font color="Green">E32</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
