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

<b>let </b><font color="Maroon">a</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>let </b><font color="Maroon">l</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">k1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">k2</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>







<b>set </b><font color="Maroon">i</font> = <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font>;<br/>
<b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p3">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Olive">s</font></span>)</span></span>)</span> where <font color="Olive">s</font> is   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : (  <a href="ami_1.html#K6">IC</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> &amp; <font color="Olive">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font> ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2;<br/>
<b>consider </b><font color="Maroon">w1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>
<a NAME="E2:30"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">l</font>
 
<b>by </b><i/>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:30_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<font color="Maroon">l</font>
 ;<br/><b>then consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <b> such that </b><br/><a NAME="E3:30_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <font color="Maroon">s</font></span>)</span>
 <b>and </b><br/><a NAME="E4:30_1"/><i><font color="Green">E38</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font>
 <b>and </b><br/><a NAME="E5:30_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font>
 ;<br/><b>consider </b><font color="Maroon">m1</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="E7:30_1"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">m1</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E8:30_1"/><i><font color="Green">E79</font></i>: 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s</font>,<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</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> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20">SCMPDS_2:def 20</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_1_1"/>
( <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0 or <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1"><b>suppose </b></a><a NAME="E1:30_1_1_1"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
<b>by </b><i>, <a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a>, <a class="txt" href="scmpds_9.html#E2:30"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_9.html#T2" target="_self">Th2</a>, <a class="ref" href="scmpds_9.html#T3" target="_self">Th3</a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/><b>hence </b><a NAME="E3:30_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18">Next</a> <font color="Maroon">l</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_2"><b>suppose </b></a><a NAME="E1:30_1_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a>, , </i>
<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a>, <a class="ref" href="scmpds_9.html#T3" target="_self">Th3</a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/><b>hence </b><a NAME="E3:30_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18">Next</a> <font color="Maroon">l</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:30"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K18">Next</a> <font color="Maroon">l</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/>

<b>consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>
<b>reconsider </b><font color="Maroon">il1</font> = <font color="Maroon">l</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">I</font> = <font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">l</font> <b>by </b><i><a class="ref" href="ami_1.html#D14">AMI_1:def 14</a></i>;<br/>
<b>set </b><font color="Maroon">u</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <font color="Maroon">l</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1"><b>suppose </b></a><a NAME="E1:30_2_1"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <font color="Maroon">l</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">u1</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon">u2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span>;<br/><a NAME="E2:30_2_1"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/><a NAME="E3:30_2_1"/>
<font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/><b>then </b><i><font color="Green">E85</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font>
<b>by </b><i><a class="ref" href="ami_6.html#T6">AMI_6:6</a></i>
;<br/><a NAME="E5:30_2_1"/><i><font color="Green">E86</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/><a NAME="E6:30_2_1"/><i><font color="Green">E92</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/><i><font color="Green">E93</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T2" target="_self">Th2</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T3" target="_self">Th3</a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">il1</font>
<b>by </b><i><a class="ref" href="ami_6.html#T6">AMI_6:6</a></i>
;<br/><a NAME="E8:30_2_1"/><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/><a NAME="E9:30_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2_1_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_2_1_3_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_3_1_1"><b>suppose </b></a><a NAME="E1:30_2_1_3_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_2_1_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_1_3_1_2"><b>suppose </b></a><a NAME="E1:30_2_1_3_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 ;<br/><div class="add"><a NAME="E2:30_2_1_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:30_2_1_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>then </b><font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a>, <a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E2:30"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a>, </i>
;<br/><b>hence </b><a NAME="E11:30_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<font color="Maroon">l</font>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E2:30"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_2"><b>suppose </b></a><a NAME="E1:30_2_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">k2</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">l</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 ;<br/><div class="add"><b>set </b><font color="Maroon">u1</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span>;<br/><b>set </b><font color="Maroon">u2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span>;<br/><a NAME="E2:30_2_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/><a NAME="E3:30_2_2"/>
<font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/><b>then </b><i><font color="Green">E109</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font>
<b>by </b><i><a class="ref" href="ami_6.html#T6">AMI_6:6</a></i>
;<br/><a NAME="E5:30_2_2"/><i><font color="Green">E110</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/><a NAME="E6:30_2_2"/><i><font color="Green">E111</font></i>: 
 <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/><i><font color="Green">E112</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T2" target="_self">Th2</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T3" target="_self">Th3</a>, </i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">il1</font>
<b>by </b><i><a class="ref" href="ami_6.html#T6">AMI_6:6</a></i>
;<br/><a NAME="E8:30_2_2"/><i><font color="Green">E113</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/><a NAME="E9:30_2_2"/><i><font color="Green">E114</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2_2_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_2_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_2_2_3_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> or <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_2_3_1_1"><b>suppose </b></a><a NAME="E1:30_2_2_3_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_2_2_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i>, <a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_2_2_3_1_2"><b>suppose </b></a><a NAME="E1:30_2_2_3_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font>
 ;<br/><div class="add"><a NAME="E2:30_2_2_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:30_2_2_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>consider </b><font color="Maroon">m1</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="E11:30_2_2"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">m1</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E12:30_2_2"/><i><font color="Green">E116</font></i>: 
 <a href="scmpds_2.html#K19">ICplusConst</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span>,<font color="Maroon">k2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">m1</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> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20">SCMPDS_2:def 20</a></i>;<br/><font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a>, <a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a>, , , , <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K1">.--&gt;</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E2:30"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a>, </i>
;<br/><b>hence </b><a NAME="E14:30_2_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">k1</font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">k2</font></span>)</span>,<font color="Maroon">l</font>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E2:30"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
