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

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1;<br/>
<a NAME="E1:129_1_1"/><i><font color="Green">E72</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E2:129_1_1"/><i><font color="Green">E73</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="amistd_1.html#T55">AMISTD_1:55</a></i>;<br/>
<a NAME="E3:129_1_1"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="amistd_1.html#T51">AMISTD_1:51</a></i>;<br/>
<a NAME="E4:129_1_1"/><b>then </b><i><font color="Green">E75</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>;<br/>
<a NAME="E5:129_1_1"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="amistd_2.html#E1:129_1_1"><i><font color="Green">E72</font></i></a></i>;<br/>
<i><font color="Green">E77</font></i>:  <a href="ami_5.html#K5">pi</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:129_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:129_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="amistd_1.html#D22">AMISTD_1:def 22</a></i>
;<br/>
<a NAME="E7:129_1_1"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<a NAME="E8:129_1_1"/><b>then </b><i><font color="Green">E78</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<a NAME="E9:129_1_1"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<a NAME="E10:129_1_1"/><b>then </b>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<a NAME="E11:129_1_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E12:129_1_1"/><b>then </b><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<i><font color="Green">E81</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="txt" href="amistd_2.html#E12:129_1_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E11:129_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_1.html#T55">AMISTD_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T52" target="_self">Th52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="amistd_2.html#K12" target="_self">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E8:129_1_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="binarith.html#T56">BINARITH:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E5:129_1_1"><i><font color="Green">E76</font></i></a>, <a class="txt" href="amistd_2.html#E13:129_1_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E4:129_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="amistd_2.html#D16" target="_self">Def16</a></i>
<br/>.= 
 <a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E3:129_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="amistd_2.html#D15" target="_self">Def15</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="amistd_2.html#E6:129_1_1"><i><font color="Green">E77</font></i></a>, <a class="ref" href="amistd_2.html#T29" target="_self">Th29</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D22">AMISTD_1:def 22</a><br/>


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