<?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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green">E25</font></i>: 
( ( ( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>3</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 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0 ) ) &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="int_1.html#R1">are_congruent_mod</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:36"/>
<font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="binari_4.html#E1:36"><i><font color="Green">E25</font></i></a>, <a class="ref" href="int_3.html#T12">INT_3:12</a></i>;<br/>
<b>hence </b><a NAME="E3:36"/>
 <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> <a href="hidden.html#R1">=</a>  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="binari_4.html#E1:36"><i><font color="Green">E25</font></i></a>, <a class="txt" href="binari_4.html#E34"><i><font color="Green">Lemma23</font></i></a>, <a class="txt" href="binari_4.html#E35"><i><font color="Green">Lemma24</font></i></a></i>;<br/>


</div>
