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

<b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V4">halting</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V7">steady-programmed</a> <a href="ami_1.html#V8">definite</a> <a href="ami_1.html#V10">realistic</a> <a href="amistd_1.html#V4">standard</a> <a href="amistd_2.html#V6" target="_self">without_implicit_jumps</a> <a href="amistd_2.html#V8" target="_self">regular</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="amistd_1.html#NM1">pre-Macro</a> of <font color="Maroon">S</font>, <font color="Maroon">G</font> be   <a href="amistd_1.html#NM1">pre-Macro</a> of <font color="Maroon">S</font>, <font color="Maroon">H</font> be   <a href="amistd_1.html#NM1">pre-Macro</a> of <font color="Maroon">S</font>;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:137_1"/>
( <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font> or <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font> or ( <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font> &amp; <font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_1"><b>suppose </b></a><a NAME="E1:137_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font> = 
<font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_2"><b>suppose </b></a><a NAME="E1:137_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font>
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font> = 
<font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:137_1_3"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E2:137_1_3"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font>
 ;<br/><div class="add"><b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 </span>}</span> ;<br/><i><font color="Green">E58</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></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">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

;<br/><i><font color="Green">E59</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</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">F</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <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">G</font></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">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1

;<br/><a NAME="E5:137_1_3"/><i><font color="Green">E62</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">S</font>,<font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 </span>}</span> 
 <b>by </b><i>, </i>;<br/><a NAME="E6:137_1_3"/><i><font color="Green">E63</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">S</font>,<font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 </span>}</span> 
 <b>by </b><i>, </i>;<br/><a NAME="E7:137_1_3"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 </span>}</span>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3"><b>proof </b></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="E1:137_1_3_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:137_1_3_3"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E4:137_1_3_3"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/>
<a NAME="E5:137_1_3_3"/><i><font color="Green">E66</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> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E6:137_1_3_3"/><i><font color="Green">E67</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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</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> <span class="p0">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</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">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:137_1_3_3"/><i><font color="Green">E79</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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</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">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i/>;<br/>
<i><font color="Green">E81</font></i>: <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i/>
<br/>.= 
<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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>
;<br/>
<a NAME="E9:137_1_3_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</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">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 
;<br/>
<b>then </b><i><font color="Green">E82</font></i>: <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
<b>by </b><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">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E11:137_1_3_3"/><i><font color="Green">E83</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">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p3">(<span class="default"><font color="Olive">m</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> where <font color="Olive">m</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Olive">m</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">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E12:137_1_3_3"/><i><font color="Green">E132</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E13:137_1_3_3"/><i><font color="Green">E133</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E14:137_1_3_3"/><i><font color="Green">E134</font></i>: 
for <font color="Olive">W</font> being  <a href="amistd_1.html#NM1">pre-Macro</a> of <font color="Maroon">S</font>  st <font color="Olive">W</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font> holds <br/>2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Olive">W</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">W</font> be   <a href="amistd_1.html#NM1">pre-Macro</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:137_1_3_3_3"/>
<font color="Maroon">W</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="amistd_2.html#K7" target="_self">Stop</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E2:137_1_3_3_3"/><b>then </b><i><font color="Green">E135</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">W</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E3:137_1_3_3_3"/><i><font color="Green">E136</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">W</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/>
<b>assume </b><a NAME="E4:137_1_3_3_3"/>
2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">W</font>
 ;<br/>

<a NAME="E5:137_1_3_3_3"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">W</font>
 
;<br/>
<a NAME="E6:137_1_3_3_3"/><b>then </b>
 <a href="card_1.html#K4">card</a> <font color="Maroon">W</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E7:137_1_3_3_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="cqc_the1.html#T2">CQC_THE1:2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E15:137_1_3_3"/><b>then </b>
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">F</font>
 
<b>by </b><i/>;<br/>
<a NAME="E16:137_1_3_3"/><b>then </b><i><font color="Green">E137</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E17:137_1_3_3"/><i><font color="Green">E154</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">G</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3_3_4"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:137_1_3_3_4"/>
( <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 or (  <a href="card_1.html#K4">card</a> <font color="Maroon">F</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 3 ) or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font> )
 </span><b>by </b><i>, , </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3_3_4_1"><b>suppose </b></a><a NAME="E1:137_1_3_3_4_1"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><div class="add"><a NAME="E2:137_1_3_3_4_1"/><i><font color="Green">E183</font></i>: 
 <a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a>  <a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T7" target="_self">Th7</a></i>;<br/><div><i><font color="Green">E184</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:137_1_3_3_4_1_1"/>
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:137_1_3_3_4_1_1"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:137_1_3_3_4_1_1"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a></i>;<br/><font color="Maroon">k</font> = 
<font color="Maroon">m</font> <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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>
<br/>.= 
<font color="Maroon">m</font> <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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
<b>by </b><i/>
;<br/><a NAME="E6:137_1_3_3_4_1_1"/><b>then </b>
<font color="Maroon">m</font> <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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, </i>;<br/><a NAME="E7:137_1_3_3_4_1_1"/><b>then </b>
<font color="Maroon">m</font> <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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E8:137_1_3_3_4_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E186</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:137_1_3_3_4_1_2"/>
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:137_1_3_3_4_1_2"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:137_1_3_3_4_1_2"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</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">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E15"><i><font color="Green">Lemma85</font></i></a></i>;<br/><a NAME="E5:137_1_3_3_4_1_2"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>;<br/><a NAME="E6:137_1_3_3_4_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E7:137_1_3_3_4_1_2"/>
contradiction
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/></div><b>end;</b></div><a NAME="E5:137_1_3_3_4_1"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="amistd_2.html#E3:137_1_3_3"><i><font color="Green">E64</font></i></a></i>;<br/><a NAME="E6:137_1_3_3_4_1"/><b>then </b><i><font color="Green">E188</font></i>: 
<font color="Maroon">x</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#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3_3_4_2"><b>suppose </b></a><a NAME="E1:137_1_3_3_4_2"/><i><font color="Green">E189</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><div class="add"><div><i><font color="Green">E191</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:137_1_3_3_4_2_1"/>
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:137_1_3_3_4_2_1"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:137_1_3_3_4_2_1"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</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">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E15"><i><font color="Green">Lemma85</font></i></a></i>;<br/><a NAME="E5:137_1_3_3_4_2_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, , <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>;<br/><a NAME="E6:137_1_3_3_4_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, </i>;<br/><a NAME="E7:137_1_3_3_4_2_1"/><b>then </b>
<font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 ;<br/><a NAME="E8:137_1_3_3_4_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T23">NAT_1:23</a></i>;<br/><a NAME="E9:137_1_3_3_4_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/><a NAME="E10:137_1_3_3_4_2_1"/><b>then </b>
 <a href="card_1.html#K4">card</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><b>hence </b><a NAME="E11:137_1_3_3_4_2_1"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><a NAME="E3:137_1_3_3_4_2"/><i><font color="Green">E193</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E4:137_1_3_3_4_2"/><i><font color="Green">E194</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <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">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E5:137_1_3_3_4_2"/><i><font color="Green">E195</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E6:137_1_3_3_4_2"/><i><font color="Green">E196</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E7:137_1_3_3_4_2"/>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0 <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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E8:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E197</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a>, </i>;<br/><a NAME="E9:137_1_3_3_4_2"/><i><font color="Green">E198</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, </i>;<br/><a NAME="E10:137_1_3_3_4_2"/><i><font color="Green">E199</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a></i>;<br/><a NAME="E11:137_1_3_3_4_2"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <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">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E12:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E200</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T12" target="_self">Th12</a>, , <a class="ref" href="amistd_2.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E13:137_1_3_3_4_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E14:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E207</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:137_1_3_3"><i><font color="Green">E67</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_2_2"><b>now </b></a><div class="add"><i><font color="Green">E208</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="realset1.html#K5">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
<span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span><a href="realset1.html#K5">}</a></span>
<b>by </b><i><a class="ref" href="amistd_1.html#T55">AMISTD_1:55</a></i>
;<br/><b>assume </b><a NAME="E2:137_1_3_3_4_2_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E3:137_1_3_3_4_2_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:137_1_3_3_4_2_2"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>;<br/><a NAME="E5:137_1_3_3_4_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/><a NAME="E6:137_1_3_3_4_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/><a NAME="E7:137_1_3_3_4_2_2"/><b>then </b>
 <a href="card_1.html#K4">card</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><b>hence </b><a NAME="E8:137_1_3_3_4_2_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><a NAME="E16:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E209</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E17:137_1_3_3_4_2"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">G</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:137_1_3_3_4_2_3"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">G</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/>
<b>hence </b><a NAME="E2:137_1_3_3_4_2_3"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">G</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">G</font> )
 <b>by </b><i>, , <a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a><br/>


</div><b>end;</b></div><a NAME="E18:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E210</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E19:137_1_3_3_4_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i/>;<br/><a NAME="E20:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E211</font></i>: 
not  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E21:137_1_3_3_4_2"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="amistd_2.html#D7" target="_self">Def7</a>, <a class="txt" href="amistd_2.html#E3:137_1_3_3"><i><font color="Green">E64</font></i></a></i>;<br/><a NAME="E22:137_1_3_3_4_2"/><b>then </b><i><font color="Green">E212</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <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#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a>, <a class="ref" href="card_1.html#T78">CARD_1:78</a></i>;<br/><i><font color="Green">E213</font></i>:  <a href="ami_5.html#K5">pi</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</span>)</span> = 
<font color="Maroon">G</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">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</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">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D9" target="_self">Def9</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</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">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D8" target="_self">Def8</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</span>)</span>
<b>by </b><i>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</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">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</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">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, , <a class="ref" href="amistd_2.html#D4" target="_self">Def4</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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, <a class="ref" href="amistd_2.html#D10" target="_self">Def10</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,0</span>)</span>
<b>by </b><i>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</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> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , <a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3_3_4_3"><b>suppose </b></a><b>that </b><a NAME="E1:137_1_3_3_4_3"/><i><font color="Green">E214</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">F</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E2:137_1_3_3_4_3"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 3
 ;<br/><div class="add"><div><i><font color="Green">E216</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:137_1_3_3_4_3_1"/>
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:137_1_3_3_4_3_1"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:137_1_3_3_4_3_1"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</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">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E15"><i><font color="Green">Lemma85</font></i></a></i>;<br/><a NAME="E5:137_1_3_3_4_3_1"/>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, , , <a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>;<br/><a NAME="E6:137_1_3_3_4_3_1"/><b>then </b>
<font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xcmplx_0.html#K4">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>hence </b><a NAME="E7:137_1_3_3_4_3_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><a NAME="E4:137_1_3_3_4_3"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="binarith.html#T52">BINARITH:52</a></i>;<br/><a NAME="E5:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E6:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E218</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E7:137_1_3_3_4_3"/><i><font color="Green">E219</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E8:137_1_3_3_4_3"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0
 <b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E9:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self">Th15</a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E10:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E220</font></i>: 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i/>;<br/><a NAME="E11:137_1_3_3_4_3"/><i><font color="Green">E221</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">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 3 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E12:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E222</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E13:137_1_3_3_4_3"/>
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E14:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E15:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i/>;<br/><a NAME="E16:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E17:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E3:137_1_3_3"><i><font color="Green">E64</font></i></a></i>;<br/><a NAME="E18:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E223</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><a NAME="E19:137_1_3_3_4_3"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E20:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E224</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E6:137_1_3_3"><i><font color="Green">E67</font></i></a></i>;<br/><a NAME="E21:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E225</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E22:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E226</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a>, <a class="ref" href="amistd_2.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E23:137_1_3_3_4_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></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">F</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E24:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E25:137_1_3_3_4_3"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E26:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E227</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:137_1_3_3_4_3_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:137_1_3_3_4_3_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/><b>then </b><font color="Maroon">x</font> = 
 <a href="amistd_1.html#K10">LastLoc</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span>
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_1.html#T55">AMISTD_1:55</a></i>
;<br/><b>then </b><font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1
<b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</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">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, , </i>
;<br/><b>hence </b><a NAME="E5:137_1_3_3_4_3_2"/>
contradiction
 <b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="amistd_2.html#T16" target="_self">Th16</a></i>;<br/></div><b>end;</b></div><a NAME="E28:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E228</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D7" target="_self">Def7</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E29:137_1_3_3_4_3"/><i><font color="Green">E229</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/><a NAME="E30:137_1_3_3_4_3"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="amistd_2.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E31:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E230</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E32:137_1_3_3_4_3"/><b>then </b><i><font color="Green">E231</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T12" target="_self">Th12</a>, <a class="ref" href="amistd_2.html#T14" target="_self">Th14</a></i>;<br/><div><i><font color="Green">E232</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_3_3_4_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:137_1_3_3_4_3_3"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:137_1_3_3_4_3_3"/><i><font color="Green">E233</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:137_1_3_3_4_3_3"/>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<font color="Maroon">m</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">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E5:137_1_3_3_4_3_3"/>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="amistd_1.html#T25">AMISTD_1:25</a></i>;<br/><b>then </b><i><font color="Green">E234</font></i>: <font color="Maroon">m</font> = 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span>

;<br/><a NAME="E7:137_1_3_3_4_3_3"/>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><b>hence </b><a NAME="E8:137_1_3_3_4_3_3"/>
contradiction
 <b>by </b><i><a class="ref" href="amistd_2.html#D11" target="_self">Def11</a>, </i>;<br/></div><b>end;</b></div><i><font color="Green">E235</font></i>:  <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T18" target="_self">Th18</a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">G</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">G</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#D8" target="_self">Def8</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">G</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <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">G</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="amistd_2.html#D10" target="_self">Def10</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">G</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, <a class="ref" href="amistd_2.html#D9" target="_self">Def9</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, <a class="ref" href="amistd_2.html#D9" target="_self">Def9</a>, , <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</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> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3_3_4_4"><b>suppose </b></a><a NAME="E1:137_1_3_3_4_4"/><i><font color="Green">E236</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2
 ;<br/><div class="add"><a NAME="E2:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E237</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, , <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E3:137_1_3_3_4_4"/>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, </i>;<br/><a NAME="E4:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E238</font></i>: 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E5:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E239</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <font color="Maroon">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E6:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E240</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E15"><i><font color="Green">Lemma85</font></i></a>, <a class="ref" href="amistd_2.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E7:137_1_3_3_4_4"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</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">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, , , </i>;<br/><a NAME="E8:137_1_3_3_4_4"/>
0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/><a NAME="E9:137_1_3_3_4_4"/><b>then </b>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">H</font>
 ;<br/><a NAME="E10:137_1_3_3_4_4"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E11:137_1_3_3_4_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></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">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i/>;<br/><a NAME="E12:137_1_3_3_4_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E13:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E242</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><a NAME="E14:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E243</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E15:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E244</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a>, </i>;<br/><a NAME="E16:137_1_3_3_4_4"/><i><font color="Green">E245</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><a NAME="E17:137_1_3_3_4_4"/><i><font color="Green">E246</font></i>: 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</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">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>;<br/><a NAME="E18:137_1_3_3_4_4"/><i><font color="Green">E247</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0 <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">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T49">AMISTD_1:49</a></i>;<br/><b>then </b><i><font color="Green">E248</font></i>:  <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</span>)</span> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#D5">AMI_5:def 5</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">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T17" target="_self">Th17</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>
;<br/> <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">G</font></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"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T9" target="_self">Th9</a></i>
<br/>.= 
 <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</a></i>
;<br/><a NAME="E21:137_1_3_3_4_4"/><b>then </b><i><font color="Green">E249</font></i>: 
 <a href="amistd_2.html#K8" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="ami_5.html#K5">pi</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <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">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_2.html#D7" target="_self">Def7</a>, </i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#T15" target="_self">Th15</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">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="amistd_2.html#T14" target="_self">Th14</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">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,0</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="amistd_2.html#T17" target="_self">Th17</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="amistd_2.html#D8" target="_self">Def8</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</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> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_3_3_4_5"><b>suppose </b></a><a NAME="E1:137_1_3_3_4_5"/><i><font color="Green">E250</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">F</font></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">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font>
 ;<br/><div class="add"><a NAME="E2:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E251</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, , <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E3:137_1_3_3_4_5"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <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="E4:137_1_3_3_4_5"/>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E11:137_1_3_3"><i><font color="Green">E83</font></i></a></i>;<br/><a NAME="E5:137_1_3_3_4_5"/><b>then </b>
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <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">F</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T23">XREAL_1:23</a></i>;<br/><a NAME="E6:137_1_3_3_4_5"/><b>then </b>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">H</font>
 <b>by </b><i>, , <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E7:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E253</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><a NAME="E8:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E254</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <font color="Maroon">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E9:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E255</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E15"><i><font color="Green">Lemma85</font></i></a>, <a class="ref" href="amistd_2.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E10:137_1_3_3_4_5"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E11:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E256</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E12:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E257</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E10:137_1_3_3"><i><font color="Green">E82</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E13:137_1_3_3_4_5"/><i><font color="Green">E258</font></i>: 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E14:137_1_3_3_4_5"/><i><font color="Green">E259</font></i>: 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</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">G</font></span>)</span></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">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E11:137_1_3_3"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E15:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E260</font></i>: 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></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">G</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E16:137_1_3_3_4_5"/>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><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">F</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, <a class="ref" href="amistd_2.html#D4" target="_self">Def4</a>, <a class="ref" href="amistd_2.html#T17" target="_self">Th17</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E17:137_1_3_3_4_5"/><b>then </b>
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E18:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E261</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><a NAME="E19:137_1_3_3_4_5"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E20:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E262</font></i>: 
<font color="Maroon">x</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#K10" target="_self">Shift</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_2.html#E14"><i><font color="Green">Lemma84</font></i></a>, </i>;<br/><a NAME="E21:137_1_3_3_4_5"/><i><font color="Green">E263</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E22:137_1_3_3_4_5"/><i><font color="Green">E264</font></i>: 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E23:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E265</font></i>: 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E24:137_1_3_3_4_5"/><i><font color="Green">E266</font></i>: 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i><a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="amistd_2.html#D9" target="_self">Def9</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E25:137_1_3_3_4_5"/><i><font color="Green">E267</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D10" target="_self">Def10</a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E26:137_1_3_3_4_5"/>
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <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">G</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E27:137_1_3_3_4_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">H</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E28:137_1_3_3_4_5"/><b>then </b>
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="amistd_1.html#T50">AMISTD_1:50</a></i>;<br/><a NAME="E29:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E268</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E30:137_1_3_3_4_5"/><b>then </b><i><font color="Green">E269</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="amistd_2.html#T18" target="_self">Th18</a></i>;<br/><i><font color="Green">E270</font></i>: <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D10" target="_self">Def10</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T16" target="_self">Th16</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> <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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a>, <a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, , </i>
;<br/><i><font color="Green">E271</font></i>:  <a href="ami_5.html#K5">pi</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">G</font></span>)</span> <a href="scmfsa_4.html#K1">+*</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K10" target="_self">Shift</a> <span class="p3">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <font color="Maroon">H</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</a>, <a class="ref" href="ami_5.html#D5">AMI_5:def 5</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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">G</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D11" target="_self">Def11</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">H</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">G</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T18" target="_self">Th18</a>, , <a class="ref" href="amistd_2.html#T19" target="_self">Th19</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">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p0">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">G</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<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">H</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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> <span class="p4">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <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">H</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">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T13" target="_self">Th13</a>, <a class="ref" href="amistd_2.html#T15" target="_self">Th15</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">H</font>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p0">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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> <span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T14" target="_self">Th14</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</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> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">S</font>,<span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#T11" target="_self">Th11</a>, <a class="ref" href="amistd_2.html#T20" target="_self">Th20</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K9" target="_self">IncAddr</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></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">F</font></span>)</span> <a href="binarith.html#K3">-'</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">S</font>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="amistd_2.html#D6" target="_self">Def6</a>, <a class="ref" href="amistd_2.html#D1" target="_self">Def1</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> <span class="p3">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">F</font></span>)</span> <a href="binarith.html#K3">-'</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">F</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="amistd_2.html#D8" target="_self">Def8</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="amistd_2.html#D7" target="_self">Def7</a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E8:137_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">G</font></span>)</span> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="amistd_2.html#K13" target="_self">';'</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="amistd_2.html#K13" target="_self">';'</a> <font color="Maroon">H</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
