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

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





<b>assume </b><a NAME="E1:43"/><i><font color="Green">E29</font></i>: 
(  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>5</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="txt" href="binari_4.html#E1:43"><i><font color="Green">E29</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<i><font color="Green">E30</font></i>:  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
 <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <span class="p1">(<span class="default"><a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E5:43"/>
 <a href="binari_2.html#K4">Intval</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K10">+</a> <span class="p2">(<span class="default"><a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <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#E1:43"><i><font color="Green">E29</font></i></a>, <a class="txt" href="binari_4.html#E3:43"><i><font color="Green">E30</font></i></a>, <a class="ref" href="binari_4.html#T14" target="_self">Th14</a></i>;<br/>


</div>
