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

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:1"/><i><font color="Green">E49</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font>
 ;<br/>

<b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> &amp;  <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 2 )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20">SCMPDS_2:def 20</a></i>;<br/>
<i><font color="Green">E51</font></i>: <font color="Maroon">k</font> = 
 <a href="ami_3.html#K16">il.</a> <font color="Maroon">m</font>
<b>by </b><i>, , <a class="ref" href="scmpds_3.html#D2">SCMPDS_3:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">m</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i><a class="ref" href="ami_3.html#D20">AMI_3:def 20</a></i>
;<br/>
<b>thus </b> <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s</font>,<span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font></span>)</span> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i>, , <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
 <a href="ami_3.html#K16">il.</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="ami_3.html#D20">AMI_3:def 20</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="scmpds_3.html#D2">SCMPDS_3:def 2</a></i>
;<br/>


</div>
